complex near-surface...3-d seismic imaging of complex structures in near-surface deposits doctor of...

3-D SEISMIC IMAGING OF COMPLEX STRUCTURES IN NEAR-SURFACE DEPOSITS

Hamid Reza Siahkoohi

.A thesis submitted in conformity rvith the requirements for the degree of Doctor of Philosophy

Graduate Department of Pbysics University of Toronto

@ Copyright by Hamid R. Siahkoohi 1997

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3-D SEISMIC IMAGING OF COMPLEX STRUCTURES IN NEAR-SURFACE DEPOSITS

Doctor of Philosophy, 1997. Hamid R. Siahkoohi

Depart ment of P hysics. University of Toronto

Abstract

One of the most important methods of investigating the geological structure of sedimen-

tary rocks is controlled source reflection seisrnology. Reflection seismology h a . tradi-

tionally focussed largely on petroleum exploration problems. Le.. imaging formations in

consolidated sedimentary rocks at depths in the range O. 1 - 10 km. However. hydrogeo-

logical investigations and large engineering enterprises also may require detailed pict ures

of subsurface structure. but in relatively unconsolidated surficial sediments at typical

depths of 3 - 100 m. If subsurface structures are not too complex, relatively simple two

dimensional (2-D) seismic profiling methods can provide detailed cross-sections of the

lithological st ratigraphy and structure. But, as has b e n well demonstrated in petroleum

exploration. t hree dimensional (3-D) surveying met hods are required to obtain an accu-

rate picture of complex structures.

Nowadays. especially in areas of former glaciation. increasing efforts are being placed on

using 2- D seismology to obtain detailed images of near-surface geology in connection wi t h

groundwater. waste disposal. and engineering projects. But. akhough results are very

gratifying in sorne respects. the resolution of very local structures by 2-D seismic surveys

hm been insufficient to ident ify possible hydrogeological. and engineering problems.

It is natural to consider whether 3-D seismic survqing in shallow environment rnight yield

beneficial results similar to those it provides in petroleum seismology (always presuming

that survey cost can be restrained).

To address this question? 1 have investigated the imaging capability of 3-D multi-fold high-

resolution reflection seismology in near-surface complex deposits and designed a form of

three-dimensional seismology suitable for hydrogeological, geotechnical and other sirnilar

surficial exploration purposes. A test 3-D survey was carried out successfully and its

results surpassed expectations in several ways.

The survey was relatively easy to carry out using standard engineering scale seismic

equipment and a 3-4 person crew. It provided a cube of stacked data with fairly high

dominant frequency (- 300 Hz) covering a subsurface volume of 2 0 ~ 2 2 0 ~ 2 0 0 meters

with a trace bin of 3 x 3 meters. In addition to the reflect ivity image. the survey provided

a velocity mode1 to < 100 m depth that assisted greatly in geological identification of

the reflectors and rvas good enough to permit post stack depth migration. Details of the

stratigraphy are much more clearly revealed in the 3-D stacked sections than in nearby

2-D sections. Generally. tills are evpected to be massive units. However, the 3-D seismic

sections show st rong, highly continuous, reflectors wit hin the t il1 deposits which are of

much greater continuity and extent than has previously been realized. Foreset bedding

can be recognized in one of the sedimentary strata.

Results indicate that high resolution 3-D seismic surveying can contribute effectively to

the detailed hydrogeological and engineering assessrnent of sites with complex geology.

Acknowledgment s

Of the many people who contributed by their work and advice during the various stages of

this project. 1 would particularly like to thank rny supervisor Professor G.F. West for his

continuous guidance in al1 stages of this study. He was always available for discussion and

his suggestions provided the key to the solutions of many of the problems encountered.

Prolessors R.C. Bailey, R.N. Edwards. and J.X. Mitrovicaare appreciated for their helpful

comments and suggestions as rny research committee members.

1 am grateful to the Mernorial University of Xewfoundland for providing a 96 channel

Op-GeoSpace DAS-1 digital seismograph and to the Environmental Geoiogy group of

the U. of T. Scarborough campus for providing a shothole drilling machine.

I would like to thank B.B. Koseoglu and J.I. Boyce frorn Environmental Geology group of

the Scarborough campus and al1 my fellow graduate students at the geophysics Iaboratory

for their assistance during the field survey on the frozen tundra of East Toronto.

Russell Pysklywec for his grammatical help. hf laden Nedimovic for his non-dest riict ive(!)

system administration. Khader Khan and Raul Cunha for their drafting help deserve

t hanks.

Financial support was provided for four years in the form of a scholarship by the I M -

CHE (Iranian Ministry of Culture and Higher Education) then continued by an 'ISERC Research grant to professor West.

Finally. rny graduate study was made most enjoyable by the encouragement and support

of my wife and son who tried so very hard to be patient while rny work took 11p most

evenings, nig hts. weekends. and almost al1 t heir holidays.

To my Parents

Contents

Abstract

Acknowledgment s

List of Tables

List of Figures

1 Introduction and statement of problem 1

1.1 Seismic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . *)

1 . Reflection seismology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Reflection seismic imaging . . . . . . . . . . . . . . . . . . . . . . . . . . 5

- 1.4 The reflectivity image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.5 PracticaIseismicimaging.. . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.6 Engineering seisrnology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.7 Statement of the exploration problem . . . . . . . . . . . . . . . . . . . . 14

1.8 Structureofthethesis . . . . . . . . . . . . . . . . . . . . . . . - . . . . 18

2 High resolution 3-D seismic survey design and acquisition 20

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

. . . . . . . . . . . . . . . 2.2 Rescaling of a conventional 3-D seismic survey 'LI

*) . . . . . . . . . . . . . . . . . . . . . 2.2.1 Theory of geometry scaling -- 2.2.2 Desirable and practical scale factors . . . . . . . . . . . . . . . . . 24

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Site selection 26

. - 2.4 Basic concepts in 3-D acquisition geometry . . . . . . . . . . . . . . . . . > i

. . . . . . . . . . . . . . . . . . . . . 2.5 Testing different field configurations 29

. . . . . . . . . . . . . . . . . . . . . . 2.6 Comparing acquisition geometries 3-1

. . . . . . . . . . . . . . . . . . . . . . 2.7 Choosing basic design parameters 37

'2.8 Fieldprocedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9 Survey production 44

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10 Summary 44

3 3-D seismic data processing 48

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.1 Introduction 48

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Basic data preparation 48

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Pre-s tack processing 50

. . . . . . . . . . . . . . . . . . . . . . . . . . . .3.t3.1 Static correction 50

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.3.2 Noise removal 5.5

. . . . . . . . . . . . . . . . . 3.5.3 Surface consistent amplitude scaling 64

. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4 Velocity analysis 67

. . . . . . . . . . . . . . . . . . . . . . . . . . .3.3.5 i7eloci ty conversion 69

. . . . . . . . . . . . . . . . . . . . . . 3.3.6 Residual static correction 71

3.3.7 Test of muting procedure . . . . . . . . . . . . . . . . . . . . . . . 72

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Post-stack processing 72

C r . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 3-D Median filtering la

L C . . . . . . . . . . . . . . . . . . . . 3.4.2 3-D time and depth migration i ;J

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Summary 76

4 Geological interpretation/correlation 79

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 The study area 79

. . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Geological setting $1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-12 Work near P l 83

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Near-surface mode1 84

. . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 CMP stacked data volume SC

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 3Iigrated data volume 91

. . . . . . . . . . . . . . . . . -4.5 CorreIat ion of seismofacies wit h lit hofacies 92

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Geoiogical details 100

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Attenuation 103

. . . . . . . . . . . . . . . . 4 . 1 Near-surface attenuation mechanisms 103

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.S Summary 104

5 Conclusions

A Seismic wave attenuation

B Karhunen-Loeve transform 124

. . . . . . . . . . . . . . . . . . . . . . . . . . B.1 Mat hematical formulation 125

C Slant stack 128

. . . . . . . . . . . . . . . . . . . . . . . . . . C.1 iklathematical formulation 130

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.1.1 Line source 130

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.1.2 Point source 133

D Migration 135

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . D . 1 Phase-shift migration 135

. . . . . . . . . . . . . . D.l.l Phase-shift plus interpolation migration 157

List of Tables

2.1 Experimental values of Q p at near-surface sediments . . . . . . . . . . . . 21

2.2 Basic seismic survey attributes and their typical and desired values both

in petroleum and engineering scale seismology . . . . . . . . . . . . . . . 25

2.3 Acquisition parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

. . . . . . . . . . . 3 . 1 Data processing steps applied on 3-D seismic data set 5 1

1 Summary of the Quaternary stratigraphy in t h e GT.4 . . . . . . . . . . . S2

4.2 Sumrnary of seismofacies and corresponding stratigraphic units . . . . . . 95

List of Figures

1. I Seismic frequency spectrum . . . . . . . . . . . . . . . . . . . . . . . . .

1.2 Redundant variable offset seismic acquisition technique . . . . . . . . . .

1.3 A synthetic zero offset time section (CMP stack) and corresponding geol-

ogy section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.4 Common midpoint raypaths for a mode1 with two dipping interfaces . . .

1.5 Off-line reflections in 2-D seismic profiling . . . . . . . . . . . . . . . . .

1.6 Offset and azimuth distribution in a typical t rue 3-D seismic survey . . .

1.7 GT-A rnap indicates location of the site p l . . . . . . . . . . . . . . . . .

1.8 Un-migrated 2-D stacked section at site P 1 . . . . . . . . . . . . . . . . .

2.1 Basic terms in 3-D survey . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2 Different 3-D survey geornetry . . . . . . . . . . . . . . . . . . . . . . . .

2.3 Parallel and zigzag field configurations . . . . . . . . . . . . . . . . . . .

2.4 High resolution 3-D seismic survey layout using orthogonal line geometry

2.5 Parallel 3-D survey geornetry, overall fold and offset-azimut h distributions

2.6 Zigzag 3-D survey geomet ry, overall fold and offset-azimut h distributions

2.7 Orthogonal 3-D survey geometry, overall fold and offset-azimuth distribu-

tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.S High frequency signal attenuation within array components . . . . . . . .

2.9 An example of 3-D shot records with a good quality . . . . . . . . . . . .

.An example of 3-D shot records with a medium quality . . . . . . . . . .

An example of 3-D shot records with a bad quality . . . . . . . . . . . .

Amplitude spectra of the background noise and a seismic record . . .

An evample of direct and refraction arrivals in field records . . . . . . . .

. . . . . . . . . Estimated statics along the central shot and receiver lines

An stacked seismic section with and without static corrections . . . . . .

. . . . . . . . . . . . . . . . . . . . . . A typical 3-D seismic field record

Original air wave and reconstructed air waves using 1 < .L filter . . . . . .

. . . . . . . . . . . An example of 3-D shot record after air wave removal

Contarninated shot records by dispersed surface waves and coherent sur-

face waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.An esample of 3-D shot record wit h traces in poor reject ion zone . . . .

Schematic representation of poor rejection area in bot h shot and receiver

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . domains

. . . . . . . . . . . . . . . . . . . . . Surface waves after linear move out

. . . . . . . . . . . . . . . . . . . Spectral balancing using the R H 0 filter

An esarnple of 3-D shot record after elimination of the coherent noises .

Histogram of the iterative surface consistent scaling of 3-D field records .

An example of super ChIP gathers and selected stacking velocities . . . .

. . . . . . . h sample of stacking velocities aiong the diagonal directions

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T' - -Y2 plot

. . . . . . . . . . . . . . . . . . . . 3-D seismic data processing Row chart

3-D stacked sections before and after muting of the refraction arrivals . .

h cornparison between un.migrated, time-migratedo and depth-rnigrated

seismic sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xii

4.1 .A map indicates location of the site P l . . . . . . . . . . . . . . . . . . . 80

4.2 3-D survey area at site P l and surrounding boreholes . . . . . . . . . . . S3

4.3 A contour rnap indicating velocity of the iveathered and sub-weathered

Iayers from analysis of the first arriva1 picks . . . . . . . . . . . . . . . . S.5

4.4 .A contour map indicating topography of the site and thickness of the

weathered laver . . . . . . . . . . . . . . . . . . . . . . . . . - . . . . - . 86

4 3 .A view into the cubes of synthetic zero-offset da ta and interwl velocity

mode1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SS

4.6 .A correlation between a time stacked section along the in-Iine direction

and corresponding interval velocity model . . . . . . . . . . . . . . . . . Y9

4.7 .A correlation between a time stacked section along the x-line direction and

corresponding interval velocity mode1 . . . . . . . . . . . . . . . . . . . . 90

4.8 A view into the cube of the depth-rnigrated data . . . . . . . . . . . . . . 92

4.9 Conceptual model of subsurface geology at site P l . . . . . . . . . . . . . 93

4.10 Natural gamma logs from three surrounding boreholes . . . . . . . . . . . 94

4.11 h correlation between seismofacies and corresponding interval velocities . 97

4.12 Seismofacies and corresponding Quaternary lithofacies . . . . . . . . . . Y9

4.13 A detailed 3-D image of the interstadial deposits . . . . . . . . . . . . . . 101

4.14 .A wedge of contrasting material ivithin the Northern Till . . . . . . . . . 102

4.15 Two depth slices indicate the ivedge material within the Northern Till . . 102

4.16 Amplitude spectra of a trace subset a t two different traveltime windows . 105

4.17 Amplitude spectra of tivo trace subsets at two different shot-receiver offsets 106

5.1 klodified orthogonal 3-D survey geometry, overall fold and offset-azimuth

distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . 112

5.2 Shifted orthogonal 3-D survey geometry. overall fold and offset-azimuth

distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

. . . . . . . . . B.l Representation of data samples in a -n' dimensional space 129

. . . . . . . . . . . . . B . 2 Schernatic representation of the K-L transformation 126

xiv

Chapter 1

Introduction and statement of problem

The science of geophysics applies the principles of physics to the study of the earth.

Geophysical methods are of particular value as a tool to study the earth's interior and

explore its upper crust. Nowaday most of what we know about the earth below the limited

depths to which boreholes or mine shafts have penetrated has come from geophysical

observât ions. There is a broad division of geophysical investigation met hods into t hose

that make use of natural fields of the earth and those that require the input into the

ground of artificially generated energy.

Geophysical investigations involve t aking measurements at or near the eart h's surface.

These measurements are influenced by the interna1 distri but ion of physical propert ies.

Analysis of these measurements reveal how the physical properties of the earth's mate-

rials var. vertically and laterally. Experience has demonstrated that many subsurface

structures and minera1 deposits can be located, provided t hat detectable di fferences in

p hysical properties between t hem and surrounding materials exist.

The main physical properties exhibited by the more common rocks and formations are

density, magnetism. elast icity. and electrical conductivi ty. Investigating characterist ics

of any one of t hese physical properties is the subject of a major geophysical met hod. i.e..

the gravitational, magnetic. seismic, and electrical methods respectively. Geophysical

methods are often used in combination. Implernentation of more than one geophysical

method usually reveals a much more certain answer than is obtainable by any one method

alone.

Generally, environmental, geotechnical. and hydrogeological investigations require a de-

Chapter 1 : Introduction 3 -

tailed knowledge of discontinuities and sedimentation structures within near-surface un-

consolidated strata. often up to about 100 meters in t hickness. Hydrogeological met hods

and drilling are able to provide such information only at lirnited numbers of discrete

locations over the study area (see section 1.7). However, reflection seisrnology hw been

used to map main features of surficial strata for more than a decade. In this t hesis in order to further investigate the imaging potential of high-remlut ion reflection seismology.

the emphasis has been placed on seismic methods.

I O b ï nh souk range 1 Apdibic range 1 üiai somc

t-3

Earth oscillations

Earrhquakes and nuclear explosions

- - Ptmleum rcflcction Sonic logging

seismic

e-,

Engineering rcflection seismic

f-+

Cnistai reflection seismic

Figure 1.1: Schematic diagram of the seisrnic frequency spectrum and its applications.

1.1 Seismic methods

Seismoiogy is a remote-sensing technique which aims to record detailed pic~ure of subsur-

face geology by t h e study of mechanical wave motions following earthquakes or artificially-

made disturbances. Seismic methods have their uses in several areas of the earth sciences.

bot h fundamental and applied. Figure 1.1 indicates the full range of the seismic spect rum

as aell as the bandwidth used for applicatioris at many scales, irom global to local over

a few tens of meters.

At the infra-sonic end are the ver- low frequency seismic events associated with free

Chapter 1 : Introduction 3

oscillations of the earth. They are caused by a very large earthquake which make the

whole earth ring like a bel1 a t very low frequencies. The oscillations are very complex

and have periods ranging from 300 to 3000 seconds. They are used to study the whole

earth on a global scale.

Seismic waves with frequencies ranging from 0.5 to 2 Hz generated by deep controlled

nuclear sources provide another area of seismic application. L i h earthquakes. ouclear

explosions are a very high-energy controlled seismic source that have allowed seismologists

to study deep geological structures. The advantage of nuclear explosions over earthquakes

in such studies is that the precise location. depth and t ime of the seismic event is known

in advance and need not be deduced from observations.

In addition to the information about global earth structure provided by earthquake da ta

and nuclear explosions, over the last 15 years the important advances have been made

in studies of the earth's crust and upper mantle and of the boundary between them, the

MohoroviCiE Discontinuity (Moho). These experiments (e.g.. LITHO PROBE in Canada)

have been carried out by setting up controlled surveys, and using bot h seismic refraction

and reflection rnethods. The operational frequency range for crustal refraction surveys

(due to the length of profile. -1000 km) is about 1-10 Hz. However, crustal reflection

studies can be accomplished using standard oil exploration techniques operating in the

10-40 Hz range.

Oil exploration is the major application area of the seismic reflection method, and it

stands a t the nest frequency bandwidth. It is principally concerned with geological and

lit hological variation in the uppermost 5 km of the crust, and it uses frequencies ranging

from 10 to 100 Hz.

Since 1980. high-resolution reflection seismology has been used increasingly to map shal-

low structures (< 150 meters depth) in near-surface geological and engineering studies.

For such surveys. both seismic source and acquisition technique are designed to operate

in a higher frequencies ranging from 100 to 500 Hz (Knapp and Steeples. 1986a).

In the marine environment a further range of seismic reflection profiling tools are em-

ployed to investigate the soi1 conditions close to the seabed; sparker profiling, boomer

and pinger echo sounders, different systems operating in different frequency ranges up to

a few kHz (McQuilIin and Ardus. 1977). Finally, the ultra-sonic seismic energies are used

both in laboratory testing of rock samples and for sonic-logging in borehole geophysics.

Chapter Ir Introduction

1.2 Reflect ion seismology

The seismic reflection met hod is a powerful geophysical exploration technique t hot has

been in ividespread use in the petroleum industry for more than 50 years. Its predomi-

nance over other geophysicai methods is due to a variety of factors. the most important

of which are its high accuracy. high resolution, and great penetration in suitable sedimen-

tary environments. The method has recently been used in shallow depths for engineering,

ground water. and environmental st udies.

Depending upon the depth of investigation, seismic reflection methods fa11 into three

main categories:

Crustal - provides image of crystalline rocks at dept hs in the range 10-50 km.

Petroleurn - provides image of formations in consolidated sedimentary rocks at depths in

the range 0.1-10 km.

EngineeRng - provides image of unconsolidated surficial sediments at typical depths of

3-150 m.

This method provides a mode1 of subsiirface formations by measuring the times required

for a seismic wave generated on or near the earth's surface to return to the surface

after reflection from interfaces between formations having different physical properties.

specifically acoustic impedance ( product of density and veloci tu). The seismic waves are

usually generated by an esplosion. mechanical impact, or vibration. Under favorable

conditions a given geologic horizon a few thousands of meters deep can be mapped by

reflected seismic waves.

The reflection arrivals are recorded by detecting instruments which respond to ground

mot ion (geophones). In reflection profiling surveys (2- D surveying) geophones are laid

along the seismic profile at many distances from the point of generation (shot point),

most of which are less than the depth of the reflectors.

In many of t h e sedirnentary basins explored by petroleum exploration seismology. the

eart h is. to a first approximation, a horizontally stratified medium. The stratification

h a resulted from the slow deposition of sediments, sands, and so on. Due to compaction,

erosion, change of sea level, and many other factors, the geologic and hence elastic char-

acter of the layers varies with depth and age. They can Vary in thickness from less than

a centimeter to many hundreds of meters.

Chapter 1: Introduction 5

Because of tectonic and other dynamic forces at work in the earth. a first-order view of the

subsurface geology as a layered cake must often be modified to take account of bent and

fract ured st rata. Furt her. even on the relat ively localized scale of exploration seismology.

there may be significant lateral variations in material properties. For example. if one

Looks at the sediments carried downstream in a river channel. it is clear that lighter

particles will be carried further. while bigger ones will be deposited first; flows near the

center of the channel will be faster than the Aow on the sides. This gives rise to significant

variation in the porosity. density? and seismic velocity of a given sedimentary formation

dependent on just how the sediments were deposited.

As a result. seismic waves propagating in the earth will be refracted. reflected and

diffracted. In order to be able to image the earth, to see through the complicated dis-

tort ing lens t hat i ts heterogeneous subsurface presents. seismologists need to undo al1 of

these wave propagation effects. In fact. it is the goal of seismic imaging to transform

a suite of seismograms recorded ~t the surface of the earth into a depth section (Le., a

spatial image) of some physical property of the earth. usually seismic P wave velocity or

veloci ty gradient ( -. reflect ivity ).

1.3 Reflect ion seismic imaging

In parallel with other types of wave imaging such as optics? radar! sonar. etc.. seismic

reflection methods utilize the fact that as seismic waves are transmitted through the

earth. some of the wave energy propagating to depth in the earth is partially (or even

totally) reflected by any comparatively abrupt spatial variation in the density and elastic

moduli of the rocks. However. the procedures used to extract an image of structure a t

dept h from sets of seismic recordings differ fundamentally from t hose used in ot her wave

imaging methods. The main reasons are the following:

1. The structures to be imaged are distributed densely throughout a three dimensional

volume, not just on a single surface such as the earth's topographic surface or the ocean

floor.

2. The eart h ( particularly its surface formations) attenuates short wavelengt h seismic

waves to such an extent that i t is generally impractical t o utilize ivaves that are shorter

than a few hundredths to a few thousandths of the total length of the wave path. Since

low frequencies must be used. the sources and receivers have to operate in a non resonant

manner. so the maves used have a relatively wide fractional bandwidth. usually a t least

Chapter 1: Introduction

:3 octaves.

Thus. in contrast to other wave imaging methods like optics, radar, and even modern

sonar, seismic reflection signals provide accurate timing information but very poor di-

rectionai information. The data from a single recording of reflected seismic waves made

with a single impulsive source and receiver can directlp provide relatively precise dis-

tance information about any reflectors. but it cannot provide anything but the crudest

estimates of hom the reflectors are oriented or in which directions they are located.

3 . There are several types of seismic waves. e.g., P (compressional) and S (shear) waves.

and a variety of surface and interface waves that al1 travel at different speeds. In general.

it is impossible to generate and detect only a single type. Also. it is very difficult or

impossible to form images from different types of waves simultaneously. Thus, it is

necessary to build into the methodology a stage where ivaves of the desired type (usually

P waves) are extracted from al1 others.

4. Most image-forming methods require that at least a spatially areraged estimate of wave

velocity in the propagating medium be known in advance. In most non-seismic imaging

methods. this is the case. The velocitp of wave propagation is relatively predictable

(usually constant, e.g., the velocity of electromagnetic waves in air or sound in water)

and known to fairly high accuracy before the field experiment. But the velocity of a

seismic wave field is variable with position in the earth (and is sometimes even a weak

function of local propagation direction), and it is often uncertain a priori by as much as

a factor of two. Thus. seismic imaging must usualiy be conducted in a series of iterations

wherein the average velocity model of the earth is estimated. an image is constructed.

and then the degree of iocusing achieved in each part of the image is investigated t o

refine the velocity model.

5. The precise timing, amplitude and spectral response of seismic sources and detectors

is seriously affected by the geometrical irregularity and highly heterogeneous nature of

the Earth's surficial materials. This is l i h having an irregular sheet of glass in the light

path of a telescope. It must be possible to provide ways of correcting these problems

using aspects of the recorded data.

In order to take account of al1 the above points. seismic imaging methods require re-

dundant variable offset recording of shots (pressure or force impulses, or t heir equivalent

using "Vibroseis" technology ). That is, the seismic wave field must be recorded at several

nonzero offsets as the source-receiver array (Figure 1.9a) is moved along the profile over

Chapter 1: Introduction c.

1

the ground surface (known as the CMP method). Each individual trace is assigned to the

midpoint between the source and receiver locations associated with the trace. Traces with

same midpoint location are grouped together. making up a CMP gather. The geometry

of a CMP gather is depicted in Figure 1.2b.

S R R R R R R

1 Variable Offset --+ S3 S2 S1 CMp R1 R2 R3

\ ? .=v

image point

(b)

Figure 1 .%: Acquisition of seismograms wit h variable offset. ( a ) Data acquisition at multiple offsets. ( b ) Collection of wave reflections for imaging a reflection point.

1.4 The reflectivity image

The goal of a wave imaging method is to construct a picture of local wave reflectivity in

the ground that is accurate in the spatial Location and sign of the reflectivity. However,

it needs to be only qualitatively correct in its amplitude. Indeed, reflectivity itself is a

somewhat il1 defined quantity. In one dimensional seismic wave theory. it is easy to show

for relatively weak contrast t hat the fractional reflected amplitude is proportional to the

gradient in the wave propagation direction of the ratio of the local and the spatially

Ctiapter 1: Introduction 8

averaged acoustic impedances (impedance Z = p v ) . Thus reflectivity can be defined as

a relative acoustic impedance gradient (Vin( 2)) . However. in two or t hree dimensional

wave propagation. the intensity of wave scattering at any point is related both to the

vector gradients of the physical properties of the medium and the geometry of the incident

wave. In t his context, gradients need to be calculated over a distance range comparable

with a quarter wavelength of the seismic signal.

In general, the sign of the local reflectivity in a medium is relatively insensitive to angle.

for reflection anywhere near the normal incidence. Thus we can consider the ultimate

objective of a reflection seismic imaging method to be a set of cross-sectional images

of local vertical (or whatever is the dominant propagation direction in the experiment )

reflectivity in the ground, or an analogous three dimensional volume in the case of three

dimensional survey techniques. The resolution limit of the reflect ivi ty image corresponds

to about a quarter wavelength of the highest frequency wave components used in the

imaging. Xlso, because imaging does not attempt to measure amplitude precisely, and

because low frequency reflection information is missing from the data, the zero level of

the reflectivity scale will be imprecise. Thus. it will be impractical to discern an. regions

where the reflectivity has a single sign over an extensive region (i-e.. such as might

correspond to a region of smooth persistent velocity gradient in the ground) because the

local reflectivity value in such a zone is necessarily weak.

1.5 Practical seismic imaging

The image of the earth structure referred to in the preceding section corresponds in nor-

mal seismic imaging terminology to a "depth migrated (usually prestack depth-migrated)

image' section or volume. It is not usually possible to create this immediately from the

raw seismic data because of the problems described above. One generally begins first

witli preparatory steps designed to purify or rectify the data; corrections are made for

surficial conditions; unwanted wavetypes are attenuated by various filtering processes.

Then imaging of structure is carried out in a series of iterative steps. In each step, a

model of the earth's (spatially smoothed) velocity structure is estimated, with this model

gradually becoming more complete and detailed. As the average velocity model is re-

fined, the method for imaging the reflectivity (local variation in velocity and density ) caii

be refined also. The process usually begins with a provisional assumption that average

velocities are constant or a smooth function of depth only, and that reflectors are smooth

surfaces of low dip. This permits the robust and simple method of image formation


Figure 1.3: A single reflection event on a synt hetic zero offset stack) ( a ) and its corresponding depth migrated section (b ) .

time section (CMP

known as comrnon inid-point ( C M P ) stacking to be employed (Mayne. 1962).

In the CMP stacking method. recorded traces for each source-receiver pair in the ChIP gather (Figure L2b) are summed together (-stackedv)' but only after time correcting

al1 the recordings with non-zero offset for their longer ray-paths (known as removal of

normal moveout or an YMO correction). The combined traces are then considered to be

a signal enhanced version of the zero offset trace. and when stacked traces for midpoints

along a profile are assembled the resul t ing profile distance-reflec t ion t ime section is known

as a synthetic zero offset seismogram section or, more colloquiaily. a CMP stacked time

section for the surveyed area (see Figure 1.3).

The CMP stack assumes that data sharing the same acquisition midpoint locations on

the surface of the earth also share reflection points (image points) for al1 reffectors and.

as shown in Figure l.Zb, the reflection point or image point lies directly under the mid-

point. Although this rnay be an adequate approximation for near-horizontal stratification

(Le. zero order approximation), there are some fundamental problems in considering the

CMP stacked tirne section to be good approximation to a zero-offset time section when

appreciable dip is present. As shown in Figure 1.3b, the zero offset image points ( D l and

D3) of a dipping reflector are updip of the CMP locat.ion, and they rnove further updip


as dip increases. A s indicated in Figure 1.4, the amount of movement is dependent upon

reflector depth, reflector dip, and source-to-receiver offset.

Seismic processing can take account of the migrations of reffection points from under

the CMP's. -4s a first order approximation. ChIP stacking adds t hese reflection events

together as if the- al1 reflected from the same subsurface point. Although post-stack

migration will determine the shift between the zero offset reflection point and the CMP.

and reposition the reflection in the migrated image. the actual image points of the indi-

vidual trace reflection data ma? not coincide, resulting in a somewhat smeared result. A

proper stacking process should include both the zero dip normal moveout (NMO) time

correction and the offset dependent time and space correction of the input seismograms

to the image point.

Figure 1.4: Common midpoint raypaths for a model with two dipping interfaces. The subsurface reflection points (image points) are not coincident and are located updip of the ChlP location.

II the smearing is too severe. it will be necessary to perform t h e migration process before

combining data with different offsets (prestack migration). This is perfectly possible. but

only after initial steps have established a t least a first order velocity model. As mentioned

earlier, for the initial steps it is generally necessary to assume that all data that share a

midpoint position aiso share image points. As an alternative procedure? one can perform

partial migration before stack (known as dip moveout (DMO) correction) plus stacking

Chapter 1 : Introduction

to create true synthetic zero offset section, then followed by a zero-offset migration after

stack.

If structures are complex enough that migration will be required to position reflection

points properl- it rnay well also be the case that relatively simple two dimensional (2-D)

profiling cannot provide detailed cross-sections of the lithological stratigraphy and striic-

ture. Generally, in 2-D seismic surveys it is fundamental assumption that the reflected

ray paths lie in the vertical plane containing the seismic survey profile. This will only

be the case if t he structure is two-dimensional (is laterally uniform along some strike

direction) and the survey profile is straight and at known angle to strike. .As a result.

2-D seismic methods are well accepted tools only for the mapping of structures which

are not too complex.

Figure 1.5: Schematic representation of the reflection energies t ha t corne from outside the plane of recording (sideswipe). Dotted line on the reflector indicates location of the reflection points assumed by 2-D seisrnic method.

In cases where the geological structures Vary in three dimension. the seismic energies are

reflected in three dimension (i.e., outside the plane of the seismic profile. see Figure 1.5).

Chapter Ir Introduction I:!

Despite the remarkable imaging capability of available algorit hms. t hey are lundamentally

unable to reposition the off-line events of a 2-D seismic section to their proper location.

It has been weil demonstrated in petroleum exploration t hat three dimensional (3-D)

surveying methods often are required to obtain an accurate picture of cornples structures.

The first report on petroleum scale 3-D acquisition was published by Walton ( 1972). since

then. many thousands of square kilometers have been surveyed using 3-D techniques

( Weimer and Davis. 1996). The surveys have confirmed the hypothesis (French. 1974)

that 3-D data usually give superior results to even the most supremely sophisticated 2-D

processing.

Figure 1.6: Schematic representation of the offset and azimuth distribution in a typical true 3-D seismic survey.

A true 3-D survey should provide a suite of shot-receiver points for every possible image

point (reflection point) in the region t o be explored. Each suite should contain a broad

range of shot-receiver offsets and variety of shot-receiver azimuths as is shown in Figure

1.6.

Generally, 3- D seismic data processing is divided into t hree distinct steps:

The first step deals with the da ta in a surface coordinate system referenced to the ac-

quisition geometry. CMP gathers are analyzed to obtain an initial velocity mode1 which

Chapter 1: Introduction 1 3

then permits X M 0 corrections to be made and the traces stacked into a synthetic zero

offset reflection time data cube. Sections through CMP stacked (unmigrated) time cube

are the basic quality control tools at this step. At this stage. the goal is to suppress

noise and resolve stat ics ( t rave1 tirne anornaly caused by near-surface heterogeneity ) for

optimum near surface time correct ions. and progress is monitored by the quality of the

CMP stack.

The second group of processing steps deal wit h subsurface geomet ry in t ime. Hotvevitr, If

dips are large (> 30 degrees) especially in the near surface part of the data where offsets

might be comparable to reflector depth. it may be necessary t o redo the initial stack.

For instance, proceeding t hrough 3-D DMO-NMO velocity analysis to a 3-D DMO-NMO

stack and full 3-D time migration (likely using a steep dip algorithm). However. the 3-D time migrated data is not necessariiy a final product. Processing results from the second

group can provide an improved 3-D velocity-dept h model to permit t hird and final group.

The t hi rd group of processing steps represents interpretive processing. Three-dimensional

image ray technology (Hubral. 1977) can be used to convert time maps or time migrated

data to depth. .Alternatively. if structures are not very steeply dipping or cornplex. 3-D depth migration can be performed on the 3-D DMO-NMO stack. At this stage one should

plan to perform dept h migration a number of times as the accuracy of the velocity model

is improved. as errors in the velocity mode1 can strongly influence the results.

1.6 Engineering seismology

My research is involved with delineation of possible moderately cornplex structures in

shallow unconsolidated sediments (at depths of up to 150 m). the remainder of this

t hesis rnost ly emphasize engineering scale seismology.

Shallow-penet ration. high-resolution reflect ion seismic profiling began wit h oii-related

prospecting (Pakiser and Warrick, 1956: Warrick and Winslow. 1960; Meidev? 1969; and

Schepers? 1975). However. until the last decade it could not be successfully applied for

near surface engineering investigations, because equipment and acquisition techniques

needed to be modified to operate in a higher frequencies ranging from LOO to -500 Hz. Furthermore. a simple down scaling of data acquisition geometry tends to result in about

the same cost per survey station, not similar cost per kilometer of survey. and engineering

applications could not accept this.


Hoivever, since about 1980, development of low-cost digi tal engineering seismographs.

computing systems and algorithms has led to the introduction of high-resolution seismic

reflection techniques to near-surface studies. Two different approaches have been taken

in the development of 2-D shallow seismic reflection methods:

One approach is to use the simplest possible technology, so the work is economical. This

is known as the " optimum offset " method; and it was initially the dominant technique

for shallow investigations. Each trace of the final section is obtained by recording the

output of a single geophone separated from the source by a given offset. The section

is produced trace-by-trace by moving the position of the source and of the recording

peophone progressively down the line in equal increments (Hunter et al.. 1989: Pullan

and Hunter, 1990). It is a satisfactory method in area where signal to noise ratio (SIN) is high and data are required for onlp a very limited depth range.

The other approach has been to adapt the 2-D acquisition and processing techniques used

in the petroleum industry, i-e. the conventional common depth point (CDP) technique, to

high resolution shallow applications (Steeples and Miller. 1990). This method is normally

carried out along a survey line by progressively moving the shot point and its associated

spread of receivers along t h e line to build up lateral coverage of the underlying geological

section. The 2-D CDP profiling method is currently the dominant surveying technique

for shallow investigations.

1.7 Statement of the exploration problem

Much of the population of Canada live within the area previously covered by ice sheets

during Pleistocene glaciation (1640-10 ka ago). These areas are often covered by till

deposits. which in some regions reacli tliicknesses of up to 100 m. For example the

Creater Toronto Area (GTA) is a large urban center on Pleistocene glaciated terrain.

Physiographically. most of the region is a gently rolling till plain which is dissected by

post glacial stream vaileys flowing to Lake Ontario (Figure 1.7). In some places. morainal

deposits and drurnlins lie on the tills. Interglacial lacustrine sediments and early till

remnants underlie the younger tills associated wit h the CVisconsin degiaciation. The

whole Pleistocene sequence, which usually is less than 100 m thick, rests disconformably

on a glacially eroded sequence of nearly Bat -1ying Paleozoic sediments t hat i tself overlies

a Precambrian igneous-metamorphic basement at a depth of at least several hundred

meters.


LAKE o m 1 0

O S - bn

Figure 1.7: A map of Toronto area. It indicates the location of site p l (test 3-D survey area) and post glaciai Stream valleys flowing to Lake Ontario.

Although densely reforested after the glacial retreat. much of the GTA area has been

cleared active farm land for some 150 years. However. intense urban and suburban

expansion is now changing the environment rapidly. Water supply, sewage and solid

waste disposa1 have become major issues. Although Lake Ontario offers a copious supply

of fresh water for the fully developed areas, water weils are widely used in the lesser

developed regions because good aquifers are often present in the glacial beds. Water

pollution is a serious concern.

According to physical property measurements at the meter and submeter scale. most

of the glacial tills are impermeable enough to protect aquifers in underlying sands from

contamination by surface activit ies such as municipal waste landfills. However, ot her

field evidence points to some interconnection between surface and deeper waters (Gerber

and Howard. 1996). Thus, in the vicinity of any prospective landfill or other potential

source of contaminated water, there is a need to detect any possible pathways through

the till aquitards. for example. such features as permeable crossbeds. glacially induced

fadts. etc.

Hydrological techniques to determine in situ variations in fluid conductivity typically

involve drilling, pump tests or tracer tests over distances of meters to tens of meters.

In typical environmental sites. variations of these properties on the scale of centimeters

Chapter 1 : Introduction 16

vertically (or across bedding) and meters horizontally (or along hedding) are important.

Hgdrological methods cannot directly detect such fine scale distributions of in situ sub-

surface fluid conductivity except at limited numbers of discrete locations near wells.

Generally, geological and hydrogeological investigations require an extensive knowledge

of subsurface structures and stratigraphy. Such investigations are usualiy carried out over

a large area and relat ively t hick overburdens. often u p to about 100 meters in t hicknesses.

Clearly? conduct ing a subsurface investigation by the drilling of rnany boreholes over such

a large area ivill be an extremely expensive and t ime consurning approach. and it may

itself disrupt tphe hydrological environment unless the holes are carefully cemented.

For more t han a decade. surface and borehole geop hysical techniques ( specially reflect ion

seismic profiling) have been used as modest-budget tools for the rnappinp of subsurface

strata. Currently. state of the art tmo-dimensionai multifold high-resolution reflection

seismology employs (as a dominant method) a simplified version of the 2-D methods used

in petroleurn seismology. In recent years. t his met hod has proven itself to be practicai for

tracing the main features of near surface strata in rnany geological environments (e-g..

Steeples and hfiller. 1990). I t has been used with considerable success (see Figure 1 . Y ) in

the GT.A region for several years to map the general aspects of the glacial stratigraphy

(Pullan et al.. 1991: Boyce et al.. 1995).

However. the resolution of very local structures by the 2-D seismic suri-eys has been

insufficient to identify geologic characteristics that might control possible local hydroge-

ological/engineering problems. In order to image geological structures and stratigraphie

targets that do not fit the standard 2-D assurnption (see section 1.5). seismic data must

be acquired with a sufficient densitv and uniformity of coverage over a n area on the

eart h's surface.

Since 3-D seismic surveying methods developed in petroleum exploration generally pro-

vide a mucli liigher horizontal resolution than comparable 2-D surveys (Weimer and

Davis. 1996). it is natural to consider ivhether 3-D surveying might yield similarl~. bene-

ficial results in the shallow environment.

.A search of the published literat ure at the start of t his project ( 1994) has revealed no ex-

amples yet of small scale 3-D surveys. However. equipment manufacturers advertisements

frequently mention capability for small scale 3-D surveys. So clearly there is consider-

able interest in the possibility of full 3-D seismic surve!+ing techniques for near-surface

investigations.


The most obvious reason for not applying 3-D surveys for near-surface investigations

is a lack of confidence that the methods will image unconsolidated surficial sediments

sufficiently well to justify the additional cost and effort. However. since early 90's. ad-

vances in engineering seismic data acquisition systems (e.g.? >Y6 recording channels) and

desk-top computing power for data processing appear to provide the technical means for

conducting such seismic surveys in a reasonably economical manner.

To address the question of whether 3-D seismic surveying can be fruitfully ernployed

for mapping details of the stratigraphy at such shallow depths. in my Ph-D. program

1 have investigated the imaging capability of 3 - D multifold high-resolution reflection

seismology in near-surface complex deposits and I have developed and tested a iorm of

t hree-dimensional seismology suit able for environment al. geotechnical. hydrogeological,

and other similar surficial exploration purposes.

Designing such a survey required consideration of two basic constraints. One mas the

necessi ty of preserving of higher frequency components: the ot her was t hat any seismic

survey for environmental and engineering applications h a . to be carried out in a more

restricted economic regime in order to compete with aiternative methods such as drilling.

The test sur- kvas successfully carried out using standard engineering scale seismic

equipment and a minimal crew (3-4 persons). The results indicate that 3-D high-

resolution seismic surveying can contribute substantially to the detailed hydrogeologi-

callengineering assessment of a t i 11-covered si te.

1.8 Structure of the thesis

The remainder of this thesis is organized as iollow:

Chapter 2 discusses various design constraints and their impacts on acquisition parame-

ters toget her wi th the theoretical requirements for survey geomet ry scaling. Three 3- D seismic survey geometries designed for engineering scale seismic surveys are introduced

and their attributes are compared. The chapter is finishes with a detailed explanation of

the way the 3-D seismic survey was conducted.

Chapter 3 provides a detail description of the 3-D seismic data processing sequences.

Despite the fairly high dominant frequency in the records and because no shotlreceiver

arrays were employed. the records contained strong, dispersed and scattered surface waves

which heavily obscure the reflection signal in parts of the record. The chapter provides

Chap ter 1 : Introduction 19

details of the somewhat unusual procedures that were employed to remove these source-

generated coherent noises effectively.

Chapter 4 reviews t.he geological framework of the study area as well as previous work

done in the area (e.g. borehole logs. 2-D seismic profiles. etc.). It presents the various

3-D reflectivity data CU bes and the :3- D subsurface velocity mode1 obtained from 3 - D data analysis. and establishes the correlation between the seismofacies and the geological

units. A close study of the depth-migrated zero offset stacked sections indicates that

the interpretational results are real, and more spatially detailed than could be provided

by 2-D surveying. Detailed seismic images of some of the local features extracted from

stacked data volume are presented. The chapter finishes by comparing the attenuation

of seismic energy in shallow and deep formations by analyzing of the 3-D seismic data

set.

Finally. conclusions are given in chapter 5 . as are suggestions for related future research.

Chapter 2

High resolution 3-D seismic survey design and acquisition

2.1 Introduction

.As mentioned in the previous chapter. due to the lack of eramples of previous engineer-

ing scale 3-D seismic surveps in literature. it rvas necessary to select a suitable survey

geometry on the basis of published ( 1994) pet roleum scale 3 - D seismic survey practice.

For more than a decade 3-D seismic surveying techniques had been successfully used in

petroleum industry to image complex structures in consolidated formations. hlost of the

publications in this regard have been dedicated to:

1. Case-histories that present the imaging potential of the techniques (e.g, Brown. 1988:

and more recent one Weirner and Davis, 1996),

2. Presentation of wrious field layout patterns (e.g.. CValton. 1972: Crews et al.. 1989 -

1991; hlusser et al*, 1989; and Ritchie, 1991).

However. the attributes of different survey geometries (e.g.. overall CMP fold pattern,

offset-azimuth distributions a t CMP's. etc.) and the knoic-ledge of how to get the best

exploration value from a certain 3-D survey geometry have been preserved as a property

of the oiI companies.

As a result, to design my test small scale 3-D survey I needed to carry out some of the

survey design analysis (e.g.. field configuration, offset-azimuth distribution. fold patterns,

etc.) from the basic steps.

Recently. some of the related publications have provided general guidelines for shooting 3 -

Chapter 2: 3-D seismic survey II

D survey (Galbraith, 1994 and 1995: Wisecup, 1994; Bouska. 1995: Ian and Voskuyl. 1995; 1995; and Stone. 1994). In addit ion. current lp available ( 1997) commercial :3-

D seismic software packages in the market are capable of graphically presenting of the

geometry attributes both at the design stage and in the field during data acquisition

( real- t ime) .

In this chapter, rescaling of a conventional petroleum style 3-D seismic survey geometry

is discussed, t hen some of the typical survey at t ri butes are compared to corresponding

theoretical (expected) values. Diffcrent limitations in designing a small scale 3-D acqui-

sition geometry and their impacts on final results and survey cost are presented. Three

different shooting schemes suitable for engineering scale 3-D seismic surveying are intro-

duced. Their attributes are compared in order to choose the optimum field configuration.

The chapter finishes with a detail explanation of the field procedures utilized to perform

a trial. small scale (220 x 220 meters) 3-D high-resolution seismic survey.

2.2 Rescaling of a conventional 3-D seismic survey

Modification of a conventional petroleum scale 3-D seismic survey geometry into a size

and form appropriate for engineering/environmental projects is more tlian just resizing of

thc survey dimensions. The spatial scale of a conventional 3-D seismic survey is directly

related to the usable frequency range and together they control the resolving power of

the technique.

Cost effectiveness was the important non geophysical limiting parameter had to be con-

sidered. In t h e course of time. developments in methodology and teclinology could relieve

this parameter but it is always the major determinating factor for survey designers.

The main way to reduce cost is to make it possible to conduct the survey without using a

full petroleum scale seismic crew, i.e. to avoid the mobilization cost. Thus. the following

constraints should be observed.

1. Must use easily available equiprnent. i.e. engineering seismograph < 120 channel.

2. Must use simple cables, not telemetry.

3. Must use a simple source.

1. Rollalong boxes (switches which connect the desired set of geophones on a cable into

the desired set of seismograph inputs) would be helpful but should not be essential.

Chapter 2: 3-0 seismic survey

Acquisition cost and field efforts can also be minimized by optimizing of both the ~ h o t

points interval and the receiver points interval.

2.2.1 Theory of geometry scaling

Let us consider seismic surveying of two regions which are geometrically exactly similar

to one another. but have ver. different scales which ive describe as bipetroleum" and

-.engineering9 scale investigations. Despi te the different size of survey dimensions. the

wave equation has to hold true for both the engineering and petroleum scale seismic

surveys

C'sing subscripts o and e for petroleum and engineering scale seismic surveys respectively.

the following relations must hold if the aavefields in the two cases are to be similar:

ivhere 1 is distance. t is time. and f is frequency. Using the subscripts and Helmholtz

equation in frequency domain. Equation 2.1 changes to

also

where LI is the Fourier transform of u. From Equation 2.2 it is concluded that

where the dirnensionless ratio of is independent of survey size and must have the same

value in both petroleum and engineering seismic surveys i f the resulting images are to

Chapter 2: S D seismic survey 2.3

be equivalent. Üsing Equation 7.3. one cari obtain the frequency ratio of tivo different

seisrnic survey geomet ries as

Equivalent ly, wavelengt h must be scaled as survey geomet ry

Seismic wave velocities in near-surface unconsolidated sediments tend to be Iower than

the velocities in consolidated rocks (i-e. u, < u,). typically about half. As a result. a

reduction of a seismic survey dimension will necessitate the application of higher fre-

quencies. However, the frequency scaling factor will tend to be about half of the spatial

scaling factor.

.\t tenuat ion is anot her concern. Generally, the practical measure of at t,enuat ion proper-

tics is the dimensionless quality factor Q (Knopoff 1964). Experimental data shows that

Q generaily is nearly independent of frequency over a broad frequency range. especially

for dry rocks ( Born 194 1; .McDonal et al. 1958; At tewell and Ramana 1966; Kjartansson.

1979; Nur and Winkler 1980; and Tittmann et al. 1981). Q is defined as 2s times the

ratio of stored elastic energy E in a certain volume to the energy A E dissipated in one

cycle of a harrnonic excitation in the same volume (Sheriff 1984).

The spatial attenuation of a plain harrnonic wave is then e-"' where

and û is the spatial absorption coefficient and X is the wavelength (see .4ppendix A ) .

Since experimental evidence suggests that Q tends to be frequency independent. the

absorption coefficient a is approaimately proportional to frequency and " a A " is roughly

constant for a particular rock type. By substitution of X from Equation 2.6, Equation

2.5 becomes

C'hapter 2: 3-0 seismic survey

Both quality factor and velocity show similar behavior with respect to factors sirch as

porosity. confining pressure. and consolidation. Thus. Q's of unconsolidated sediments

at shallow depths are expected to be lower than those of deeper consolidatecl rocks.

Therefore. in near-surface studies. absorption may limit depth of penetration to fewer

wavelengths or make high frequency response more difficult to obtain on long paths than

in a geometrically equivalent oil scale problem. Table (2.1 ) indicate the results of in situ

measurements of Q p at near surface materials.

Table 2.1 : Velocity and quality factor of unconsolidated sedimerits from McCann et al. ( 1989) (using compressional waves with frequency range of 0.5-2.5 k H z ) .

Sediment t y p e Weathered clay

2.2.2 Desirable and practical scale factors

Sand layer Clay. Silt

Table 2.2 shows the typical range of values for several survey attributes which are gen-

erally used in petroleum and as appropriate for engineering scale seismic surveys. .A

desirable size scale factor of 1/30 is obtained from the ratio of the masimuni depths of

interest. In order to achieve the desired survey size with no loss of proportional reso-

lut ion, wave propagation theory requires an increase in the usable frequency bandwidt h

(see Equation 2.4).

Qp :37&8

As indicated in Table 2.2. the usable frequencies in petroleum seismology typically range

from 20 to SO Hz. Based on the desirable spatial scale factor of 1/30 and typical velocity

ratio of about 112. the desirable range of frequencies for engineering seismic is found to

be from 300 Hz to 1.2 kHz. However, although such a frequency range is theoretically

quite acceptable absorption constraints indicate that it may not be practical.

1 4

For instance, considering a typical case in petroleum survey with a dominant frequency

of 50 Hz, quality factor of 150, and velocity of 4500 m/s, the loss in amplitude over

the full propagation path of 5.000 m (2 x depth of interest) is found to be about 16

V, (m/sJ 1'107

depth (m) 10

'218'7 '2076

30 5 O

Chapter 2: 3- D seismic survey '25

db. Hoivever. corresponding value for an engineering scale seismic survey when using the

desired scaling factors given in Table 2.2 turns out to be about 32 db. which is about six

t imes larger.

Table 2.2: Some of the basic attributes of a seismic survey and their typicd (g iven) and desired (calculated) ranges both in petroleum and engineering scde seismology.

Survey Attributes

:\faxim urn Depth of interest (ml

-4 verage celocity (km/s) Quality fnctor

Petrole um

Usable frequency bandwidth (Hz)

1 seisrnic sprrad (rn) 1 3000 - 5000 ( 100 - 200 1 - 1/30 1 - 1/15

-4ttenuation to masimum depth 01 interest ( d b ) length of the active

Desired wavelengt hs in engineering seisrnic surveys can be determineci ranging from 1 ..5

to ï m by using the desired frequencies and typical velocity and Q values for shallow

sediments (see Table 2 . 2 ) . The wavelengths are equivalent to vertical resolution of about

0.3 to 1.5 m.

Engineering

T y p ical calu es

Typ ical

20 - 80

Current seismic instruments are well able to generate and/or detect seismic signals with

frequency contents wi t hin the range int roduced t heoret ically. Nevert heless. for following

reasons, the expected range of frequencies are not necessarily required:

- 1/30 - 112 - i / 2

:3000 - 5000 :3.0 - 4.5 70 - '200

16

1. Frequencies above 1 kHz a r e attenuated very quickly in unconsolidated materiais and

especially in aerated surface soil. Practically, they are not usable for irnaging from the

land surface.

Desired scaling factor

- 1/15 - 112 -Y l/L

100 - 1.50 1.7 - 2-2 20 - 70

Desired

300 - 1200

2. There is no need for such a high vertical resolution. 1t would only be useful i f a

concomitant increase in horizontal resolution was also provided and this would be very

Pra ct ical scaling factor

32

- 15 - S

- -

Chap t er 2 3-0 seismic surve-v 26

costly for land surveys. A reasonable vertical resolut ion in engineering seisrnology is

about 1 to 2 meters which corresponds to wavelengths of 4 to 8 meter.

A test 2-D seismic data (see next section) showed that a frequency range of 200 - 500

Hz was practical. This suggests that it is feasible to scale frequencies about S times

(rather than 15) without encountering a serious attenuation problem. .As iridicated in

the final column of Table 2.2. the spatial scale factor will accordinglg change to 1/15.

Returning to the above mentioned calculations. the loss in amplitude using the practical

dominant frequency of i300 Hz for engineering seismic survey is then found to be about

13 db. similar to the petroleum scale case. In such a survey the resolution wili be about

one half of the scaled down resolution.

2.3 Site selection

The objective of mu trial survey was to find out i f 3-D survey techniques could delineate

fine structural details of stratified glacial formations with a reasonable field effort and

cost. According to geology visible in ravine walls. possible abrupt structures a t the

survey area could consist of, a variety of sedirnentation structures in a roughly horizontal

s tratigraphy. glacio- tectonic fau1t.s. and other deformations induced Li- the overriding ice.

Since about 5 km of 2-D seismic profile had already been obtained by the University of

Toronto group east of Toronto in Durham Region in an area known as site P l which

was being considered for a possible large municipal landfill. the test 3-D survey site was

located in a farni field there. The site P l covers about 3 km' and had already been

investigated by drilling and other studies (sec section 4.1 for more details).

The collected 2-D data for the area helped to determine the general aspects of subsurface

geology but, initially, the ability of the test site to transmit high frequency seismic energies

kvas of prime concern. ünlike 2-D profiles which could be carried along compacted road

beds (an environment known to be favorable for seismic surveying with a hammer source),

3-D surveying techniques in this area require the seismic layout to be extended into farm

fields. Since soft aerated soil is iisually highly absorptive of high frequency seismic energy,

especially from an impact source, it was necessary to look for a suitable alternative to

replace the sledge hammer used in 2-D surveys.

A test 2-D profile was conducted over the farm field to evaluate performance of a shot-

gun source (generally known as a "Buffalo gun", see Pullan and MacAulay, 1987) and

determine an appropriate manner of geophone-ground coupling on the plowed farm soil.

Chap t er 2: 3-0 seismic survey 27

T h e results indicated that shooting in a 1 m water-filled hole and burying of the firmly

planted geophone a t depth up to 0.5 meter would give a good response. Seismic energies

with usable lrequency of 200 to 500 Hz and a dominant frequencx about 300 Hz were

obtained. These are sufficient to obtain the required imaging resolution.

Due to the size of a n available site. practical survey time (early December) and available

budget the test survey was restricted to a about 220 x 220 meters area. The seismic

equipment available to perform this survey was a 96-channel digital seismograph. four

Wtakeout receiver cables, and a large number of 50 Hz geophones.

2.4 Basic concepts in 3-D acquisition geometry

To discuss possible acquisition geometries it is necessary to define some of the terms

shown in Figure 2.1.

Rece ive r l ine

Although telemetric seismic recorders permit arbitrary placement of receivers. most 3-D surveys still place receivers on sets of parallel lines. Since an- engineering scale survey

must be conducted only with cable-connected geophones. the only practical receiver

configuration is multiple parallel lines if this is logistically possible. The distance between

two adjacent receiver lines is usually called the receicei line interval.

Shot line

A line along which shots are taken at reguiar interval. Unlike 2-D' the shot lines in 3-D

survey do not coincide with the receiver lines. The orientation of the shot lines with

respect to receiver lines depends on the selected survey geometry (see Figure 2.2). The

distance between one shot line and the next is usually called the shot line intetual.

Common Mid-Point (CMP) bin

Each recorded shot point-receiver point pair has a midpoint. If the shots and receivers

lie a t nodes of a rectangular grid. the midpoints will lie on a grid with half the ce11 size

of the shot receiver grid. If the survey grid is irregular. a grid of midpoint bins can be

established and any midpoint falling in the bin will then be treated as if it was at the bin

Chapter 2 3-D seismic survey 2s

center. The bin has to be small enough to produce a sufficient nurnber of stacked traces

over the smallest features that are planned to be imaged.

A Common Depth-Point (CDP) bin (as an alternative terminology) has exactly the same

practical definition as a CMP bin, except that it is projected downwards as the assumed

lateral position of al1 reflect ion points w hen the s t rata are horizontal.

* , Super CMP bin . * A A A A A A A A A A A A A A A A A A A A A A

* * * *

* CMP bins * * *

Receiver Line A A A Shot Line * * *

Figure 2.1: A representation of the basic elements in 3-D seismic survey. This figure indicates part of an orthogonal 3-D seismic survey geometry, where shot lines run normal ta receiver lines. Some of the basic elements inciuding shotlreceiver line, CMP bins. and Super CMP bin are shown. The super CMP bin (arbitrarily) contains 15 adjacent CMP bins.

Super CMP bin

In velocity analysis and other similar operations, a very large suite of offsets and azimuths

may be required to get good results. This may be achieved by sacrificing spatial resolution

and gathering a group of neighboring CMP bins into a big CMP bin. Super bins are

especially required when azimuth depended velocity analysis is to be performed.

Chap ter 2: 3-0 seismic survey

Recording patch

A fixed area that contains al1 the active recording channels of one or a group of shots.

After al1 the shots within a given recording patch have been fired. the patch is -rolled

along" the in-line or the cross-line direction with a certain amount of overlap until al1

the survey area has been covered. If a telemetry recording system is in use. the patch

may move with each shot. With simpler equipment. the patch may record a substantial

number of shots before it is moved.

2.5 Test ing different field configurations

Seismic data collected during a 3-D survey is typically subjected to a series of processing

steps. The success or failure of survey in general and each processing step in particular.

depends on how the seismic data are collected. 3-D acquisition geometry therefore can

have tremendous impact on botli the cost of a survey and the quality of final seismic

image. Careful pre-acquisition planning is required in order to design a 3-D survey

geometry that will provide imageable data and meet the survey's other objectives.

For 2-D seisrnic methods. acquisition geornetry decisions are reasonably straightiorward.

The nurnber of seismic channels recorded. the receiver point interval. the source point

interval, and the line configuration are manipulated to provide the desired combination of

multiplicity (or fold). spatial sampling, and source-receiver offset range while conserving

the available field effort. In 3-D acquisition, wliile the goals are same, the decisions are

considerably more cornplex.

For 3-D survey. spatial sarnpling takes place in two dimensions (in-line and cross-line)

forming a grid of cells. Multiplicity is examined for each of t hese cells over the survey

area rather than along a single line. The simple source-receiver offset range irom 2-D

seismic becomes a complicated distribution of both source-receiver offsets and azimuths.

In the last decade many different geometries have been devised for the acquisition of

petroleum scale 3-D seisrnic data. Depending on the arrangement of shots and receivers.

3-D geomet ries can be classified as. line geomet ry. patch geomet ry. and miscrllaneous

geomet ry.

Line geornetries as shown in Figure 2.2 are distinguished by dense sampling of shots

and receivers along acquisition Iines, which are not necessarily closely spaced. There are

t hree main types of line geornetry. Parallel geometries, Ag.zag geomet ries. and orthogonal

Chapter 2: 3-D seismic survey

geomet ries.

In the parallel geometry. shot and receiver lines are parallel. This geometry is basically

an extension of 2-D geometry where shot and receiver lines coincide. It is mainly used

for marine da ta acquisition.

The zigzag geometry is a field configuration with the shots being fired along zigzag lines

between the receiver lines. This is known as a very efficient geometry for data acquisition

in deserts or similar areas where shot points can be put anywhere.

In the orthogonal geometry shot and receiver lines are orthogonal. This is a typical land

geornetry allowing 3-D coverage with a minimum of effort required in the field. Galbraith

( 1994) describes different patterns in t his category.

(a) Parallel

(c) Orthogonal

(b) Zigzag

(d) Patch

Figure 2.2: Some of the conventional 3-D seismic survey geometries.

Patch geometries as shown in Figure 2.2 are characterized by a dense areal arrangement

of receiver stations and sparse sampling of shots, or the other way around. A short

description and attributes of the patch geornetry for land 3-D seismic data acquisition

can be found in Crews et al. (1989 and 1991). Given the amount of field effort needed

to deploy receivers in t his configuration, it does not seem practical as a suitable shooting

scheme for engineering scale seismic surveys.

Apart from the two main types of 3-D data acquisition geornetry, there have been 3-D

Chapter %. 3-0 seismic survey 31

land surveys that cannot be classified in any of the discussed geometries. For instance.

raadom geometry described in Bertelli et al. ( l992), and seisloop geometry described in

Ritchie ( 1991 ) fa11 into the miscellaneous category

Since the line geometries seem to be more convenient configurations for near-surface

seismic surveying, t hree different acquisi tioa geornetries based on parallel. zigzag, and

ort hogona1 configurations were designed and t heir at t ributes were compared (see next

section),

Al1 three geometries were designed to perform a test 3-D survey over the selected site

(i.e., a 210 x 220 meters area) and using the available seismic equipment (i-e.. a 96 channel

engineering seismograph and four receiver cables each with 24 takeouts).

The paralle1 configuration consisted of 9 parallel shot Lines a t 24 meters spacing and 10

parallel receiver lines with 24 meters spacing. The shot lines were located between two

adjacent receiver lines (see Figure 2.3 (top)). Shot spacing on the shot lines was 6 meters:

geophone trace spacing on the recording line was 3 meters, rvit h only single shots and

geophones a t each point. Each recording patch consisted of 3 parallel shot lines with 12

shot points a t each line and -4 parallel receiver lines with 24 receiver stations at each line.

The zigzag configuration consisted of 9 zigzag shot lines a t 24 meters spacing and 10

parailel receiver lines with 2-4 meters spacing. Again the shot lines were located between

two adjacent receiver lines (see Figure 2.3 (bottom)). Shot spacing on the sliot lines

\vas 6 meters both in the in-line and x-line directions; geophone trace spacing on the

recording line wvas 3 meters. rvit h only single shots and geophones at each point. Each

recording patch consisted of 3 zigzag shot iines with 12 shot points at each line and 4

parallel receiver lines with 24 receiver stations at each line.

The orthogonal configuration (see Figure 2.4) consisted of 7 parallel shot lines at 36 meters

spacing orthogonal to 10 parallel receiver lines with 24 meters spacing. Shot spacing on

the shot lines was 6 meters; geophone trace spacing on the recording line was 3 meters.

with only single shots and geophones a t each point. Each recording patch as indicated

in Figure 2.4a consisted of 2 parallel shot lines each with 12 shot points orthogonal to 4

parallel receiver lines each wit h 24 receiver stations.

These survey geometries differed only in orientation of their shot lines and/or arrange-

ment of t heir shot points. The rest of design parameters e-g., size of the recording patch,

size of the overlap between adjacent patches. and so on were kept the same. Figure

2.4b indicates the assumed size of the active patch and the overlaps between adjacent


24 IN-LINE

48

24 IN-LINE

48

* SHOT S ï N A REC. S'IN

Figure 2.3: Different small scale 3-D seismic survey configurations. ( top) Parallel acquisition geomet ry. (bot tom) Zigzag acquisition geometry. The shaded rectangle indicates a recording patch. It contains three shot lines with 12 shot points and four receiver lines wit h 24 receiver stations.


Figure 2.4: 3-D seismic survey using orthogonal line geometry. (a) T h e shaded rectangle indicates the active recording patch. It contains two shot lines and four receiver lines. ( b ) Active recording patches after being roiied one unit d o n g the in-line direction and one unit in the s-line direction.

Chap t er 2: .3- D seismic survey 34

recording pat ches for al1 t hree field configurations. The amount of res hoot ing required

will not be too serious if 3 96 active channels are available at each recording patch.

2.6 Comparing acquisition geometries

Different acquisition geomet ries usually Vary in t heir ability to provide an imageable

seismic data set and in cost. The best possible geometry is achieved when the parameters

cont rolling cost (such as field hardware ut ilizat ion) and geophysical cons t raints have

been simultaneously optimized and still achieve the necessary resolut ion of the geologic

objective. Criteria for evaluation of three different designed geometries were survey cost.

field efforts. offset-azimuth distribution at each ChIP bin. and overall fold uniforrnity.

The parallel geometry as shown in Figure ?.sa did not provide a uniforrn enough overall

fold distribution. The fold was one at the sides but it reached. by seemingly random

increments. as high as i S at inner parts of the survey area. It only filled every forth CMP bin line and left a large number of the CMP bin lines (or subsurface area) uncovered. .As

shown in Figure 2-31, the corresponding offset-azimut h distribution was good. but t here

was too much redundancy a t each particular offset or azimuth. The sniallest minimum

offset in this survey geometry was 19 meters, larger t han the minimum offset in the other

two survey geometries.

The zigzag geometry also as shown in Figure 2.6a did not provide a uniform overall fold

distribution. The fold was ranged from one at the sides through 21 nt inner parts of

the survey area. However, as indicated in Figure 2.6b. the corresponding offset-azimuth

distribution was better than for the other two survey geometries.

-4s shown in Figure ?.Ta. the orthogonal geornetry provided a uniform overall fold of 12

over the inner parts of the survey area. but it ranged from 9 down to 1 within 20 meters

of the edges. CMP gathers for bins near the crossing points of the shot and receiver

lines (see Figure 9.7b) contain a broad rznge of shot-receiver offsets as well as good

distribution of azimuths. The total number of shots required by the orthogonal survey

geometry in this cornparison was 50% less than the total shots required by the other two

survey geometries. this means an appreciable less field efforts, processing time. and cost.

In parallel and zigzag acquisition geornetries, most of the shot points are distributed over

the inner part of the active patch. The surface waves generated by t hese shots usually

mask usable reflection arrivals of the field records and require more processing efforts to

Chapter 2: 3 - 0 seismic survey

OVERALL CDP BIN FOLD Fold

IN-LINE BIN NUMBER

OFFSET-AZIMUTH DISTRIBUTION

26 27 28 29 30 31 32 33

IN-LINE BIN NUMBER

Figure '2.5: Pardlel 3-D survey geometry. (a) Fold distribution over survey area. ( b ) Offset-azimut h distribution over a rectangle area (see part (a ) for exact location). The rectangle area is same as in Figures 2.6a and 2.7a. Note that shorter lines may be hidden by longer ones in the same direction.


OVERALL CDP BIN FOLD

1 1 0 20 30 40 5'0 60 ?O

IN-LINE BIN NUMBER


Fold

24

20

15

10

5

O

25 26 27 28 29 30 31 32 33 34 35 36

IN-LINE BIN NUMBER

Figure 2.6: Zigzag 3-D survey geornetry. (a ) Fold distribution over survey area. ( b ) Offset-azimuth distribution over a rectangle area (see part (a) for exact location). The rectangle area is same as in Figures 2.5a and 2.ïa. Note that shorter lines may be hidden by longer ones in the same direction.

Chapter 9: 3-D seismic survey 3 '1

be eliminated. However, with the orthogonal survey geometry. this is the case only for

shot points located on the inner shot line (i-e. less than 50% of the shots within an active

recording patch).

.As seen in Figure ?.Tb, in some of the C M P bins (e.g., 27-30) the traces have only tivo

or three different azimuths. This is due to the asymmetric distribution of the shot lines

over the recording patch; in other words. by not including shot points along the third

shot line in the patch. Shot-receiver offsets in these CMP bins are mostly in the near to

middle range (20-60 m). In hindsight, this probably was a false economy in the survey

procedures. Offset and azimuth distribution can be further irnproved by including the

shot points along the third shot line of the active patch and shifting every other shot line

along the cross-line direction. This problem is discussed with more detail in chapter five.

and improved orthogonal survey geometries are also presented.

Note that in order to improve the visibility, in Figures (Z.5b. 2.6b. and 2.7b) the size of

each line is equal to the cube root of the shot-receiver offset norrnalized by the cube root

of maximum shot-receiver offset wit hin the CMP gat her.

2.7 Choosing basic design parameters

Some of the design const raints encountered during pre-acquisi t ion planning are discussed

in this section. They are several considerations that had to be taken into account in

order to confirm some of the important theoretical requirements (e.g.. shotlreceiver array

requirement. adequate spatial and temporal wavefield sampling. etc.).

Recording the reflected wavefield

It is generally difficult to generate broadband high frequency seismic signals without also

generating large low frequency component (<IO0 Hz). It is therefore desirable to employ

detectors (geophones) that were designed t o detect high frequencies without distortion

in the output signal. These geophones usually have a high ( 2 4 0 Hz) natural frequency.

Lower frequency geophones often exhi bit parasi tic resonances wi thin the band p a s of

high resolution seismic data. This phenornenon causes non-linear response related to low

frequency mot ion parallel or perpendicular t o the axis of intended motion. Resonances

tend to occur at frequencies more than an order of magnitude above the natural frequency

of the geophone (Steeples and Miller, 1990). Therefore, the rule of thumb is to choose a



IN-LINE BIN NUMBER


IN-LINE BIN NUMBER

Foid

12

9

8

6

4

3

2

1

*++ X X X # # X WkX

Figure 2.7: Orthogonal 3-D survey geometry. (a) Overall fold distribution over the CMP bins. Most of the CMP bins have a uniform overall fold of 12. ( b ) Offset-azimuth distribution over an area bounded by two adjacent shot lines and two adjacent receiver lines. (see part ( a ) for exact location). Note that shorter Iines may be hidden by longer ones in the same direction.


receiver wit h a natural frequency t ha t is at least 10 percent of the highest frequency likely

to be recorded. The utilized geophones were 50 Hz. and were estremely light weight ( - k 1

g) in order to follow the motion of light porous soil wit hout perceptible delay.

As long as the geophones are able to record ground motion without distort ion, frequency

filtering within the seismic recorder can be used to control data bandwidth. In order

to select an appropriate seismograph, a set of minimum requirements rvere considered

including the high system dynamic range (2 100 db). analog low cut filtering capability

prior to A / D conversion. and small sampling interval (50.25 ms).

To obtain a good P wave image of the ground. it is essential to attenuate surface \va[-es

and ambient ground noise. Olten, it is best to use shot and receiver arrays to do this.

However. for the reason shown below this is not the case in high resolution seisrnic surveys:

We expect to record useful reflections from shallow strata at large angles of incidence

on the free surface. Therefore, an array of sufficient size to attenuate surface waves

sufficiently will also attenuate useful reflection signals (see Iinapp and Steeples. 1986b).

In addition. the surface material in which the geophones are planted is often character-

ized by a low velocity. with considerable lateral variation. Even slight variations in the

t hickness or velocity of t his layers can cause differential t inie delays between geophones

within the array? which are sufficient to attenuate high frequency reflection signais.

Summing a number of seismograms corresponding to elements in a shot and/or geophone

array where, there are small random arriva1 time differences among them is equivalent to

applying a high cut frequency filter. This is illustrated in Figure 2.8. In the summation.

low frequency components interfere constructive.ely. ivhereas high frequency components

tend to interfere destructively.

Therefore, to prevent any attenuation of the high frequency components, only a single

shot and geophone were employed a t each point.

Near surface corrections

In the survey area the farm field was covered with perhaps a half meter of aerated soil

with a very low, air-like velocity. Underlying the topsoil is a layer of more compacted

and humid (e.g., weathered till), commonly known as the wcathered zone. Shots and

receivers are often buried to get them at least partly beneath the aerated layer. but any

velocity or thickness variation within the unpenetrated top soil or in weathered zone can


IO 100 1000

FREQUENCY (Hz)

Figure 2.d: High frequency signal at tenuation due to difference in the arrival times of array coniponents ( in ms). The numbers on the curves are standard deviations of the arrival time differences among the array components.

result in variable delays on reflection arrivals. These are known as **static time shifts'.

Static shifts usually degrade seismic reflect ion data which. in turn. impacts the quali ty.

and resolution of the final imaged seismic sections unless appropriate decisions are made

during the survey planning so the shifts can be determined and corrected in processing.

Refracted seismic energy has the potential to identify velocity and thickness variation

within the weathered layers. Thus. the first imaging requirement was to assure that

enough near and far source-receiver offsets occur in each recording patch to provide the

required direct arrivals and refraction events to establish an accurate weat hered layer

mode1 for the survey area. .As shown in Table 2.3. in each recording patch the ofset

to the nearest receiver from the source ranged from :3 to 10 meters. In other words.

the smallest minimum offset within the recording patch was 3 meters and the largest

minimum offset was 10 meters. With the weathered layer expected to be no more than a

few meters thick, this ensured that both direct wave in the weathered layer and shallow

refraction arrivals from beneat h the weat hered layer could be recorded more than once

Chapter 2 3- LI seismic survey 41

along the x-line. This is important in order to provide x-line and in-line coupling during

static correction. Competing against this need for near offset data. was the deleterious

effects of source generated noise. i.e.. groundroll and air-coupled waves. They are usually

so large in amplitude to mask a11 the events on the near offset traces. Thus reflect ion

data are often clearer on large offset recordings.

The smallest maximum offset within the recording patch ivas 5.5 meters. while the largest

maximum offset was 10'2 meters. The largest maximum offset approximately kvas set

equal to depth of the bedrock at survey area. As large as possible a maximum offset \vas

wanted to aid velocity analysis. However, there was little point in it being so large that

most of the desired reflection events would lie outside the mute zone applied during the

processing.

Spa t i a l a n d t e m p o r a l sampl ing

Aliasing is an inherent property of al1 systems that sample; whether the sampling is

done in time, in space, or any other domain. According to the sampling theorem. no

information is lost by regular sampling provided that the sampling frequency is greater

than twice the highest "frequency" component in the function being sampled. This is

equivalent to saying that there must be more than two samples per cycle for the liighest

frequency. In practice. this is an under sampling, as high cut filtering to prevent aliasing

requires a substantial interval between the highest passed frequency and the frequencies

at which total attenuation has been achieved. Four samples per cycle of the highest

passed frequency is a typical minimum practical sampling rate.

Sampling in t ime is controlled directly by the recording capability of the seismograph.

The utilized seismograph was set to record seismic wave field with a sampling frequency

of S kHz which was four octaves higher than the desired maximum frequency of 500 Hz.

Spatiai aliasing usually occurs when geophones are spaced improperly to detect the seis-

mic energy. In 2-D seismic methods, the spatial sarnpling frequency is controlled simply

by the interval between adjacent geophones. However in a 3-D seismic survey. since the

spatial sampling is carried out in two different dimensions (in-line and cross-line), its spa-

tial frequency limit is controlled by the separation of both adjacent shots and adjacent

geophones (or simply by the size of CMP bin). The spatial sampling may be different

for in-line and cross-line directions.

With an average velocity of 2000 m/s obtained from the test 2-D seismic profiles over the

Chapter 2: 3-0 seismic survejf 42

survey area, a dominant frequency of 300 Hz. and an exaggerated maximum dip angle of

:3O degrees. the possible shortest apparent horizontal wavelengt h was almost 13 meters.

For such shortest apparent wavelength. the selected bin dimensions ( 1.5 x 3 meter) were

capable to provide 4 subsurface samples along the cross-line direction and S subsurface

samples along the in-line direction. The selected bin size was small enough to avoid

spatial aliasing.

2.8 Field procedures

A summary of the 3-D seismic survey acquisition parameters is shown in Table 2.3. Field

operation including gridding, leveling, drilling, and seismic data collection was started in

early December 1994 just at the onset of winter, when agricultural activity would not be

disturbed and when water tables are highest and frost was hardening up the topsoil.

Prior to data collection. both shot and receiver grid points had to be marked over the

survey area. and their elevations relative to a known reference point had to be measiired.

Also. al1 the shot points had to be drilled a rd sealed. It was found usefui to have

different type of markers (e-g., large stakes with different colors) in order to identify the

shot/receiver line orientation or border of the survey area, and so on. Holes two inches in

diameter and one meter deep were drilled at each of the -5.50 shot points using a drilling

machine was mounted on a truck towed by a jeep. Al1 were sealed after drilling using

wooden stakes. Since the site had a nearly Rat topography. leveling was carried out

optically on a grid of 21x36 meter points. The maximum relief uTns about :J meters over

the survey area.

Data were recorded using an Oyo-Geospace DAS- 1 digi ta1 engineering seismograph wit h

24 bit ..\ID converter; used with 50 Hz geophones. a 140 Hz low cut filter. and a sampling

interval of 0.135 ms. The source was a Buffalo gun firing a 12 gauge blank shotgun shell

in a one meter deep, water filled. shot hole.

As shown in Figure 2.4a each recording patch was a 72x72 meter area. Each receiver

line within the patch consisted of 24 recording points and each shot lines had 12 shot

points per line. At each receiver point a single geophone was buried about 30 cm below

the surface. A single 12 gauge blank shotgun shell was fired at each water-filled shot hole

using a Buffalo gun.

To cover the entire survey area, the active recording patch as shown in Figure 2.4b had


Table 2.3: 3- D seismic survey acquisition parameters.

Record length 250 ms Sampling interval 0.125 ms Low cut frequency 140 Hz Shot point interval 6 m Number of shots per line 138 Number of shot lines -.

I

Shot line interval 36 m Receiver point interval 3 m Number of receivers per line 1'2 Number of receiver lines 10 Receiver line interval 24 rn

Recording patch size 73 x 72 m Number of shots per recording patch 24 Number of receivers per recording patch 96 Number of shot lines per recording patch -1

Number of receiver lines per recording patch 4 Smallest minimum offset 3 m

II Largest minimum offset Smallest maximum offset Largest maximum offset 102 m Nominal bin size 1.5 s 3 m Nominal fold 6 Total recording patches 10 Total shot records 5-50 Xpprosimate survey size s l* l~ -- s 220 rn

to be rolled both along the in-iine and the cross-line directions. Since moving of two

receiver cables along the cross-line direction required less efforts and time than rolling of

four receiver cables along the in-line direction, the survey was carried out by successively

shooting and rolling of the recording patch along the cross-line direct ion wit h two receiver

lines overlapped (48 meters) until it reached the survey boundary. Then al1 four receiver

cables within the recording patch were roiled along the in-line direction with one shot

line overIap (i36 meters).


2.9 Survey production

With a crew of only 3-4 persons, field operations were completed in 12 days. Short

daylight hours and inexperience with the equipment limited product ivity It could be

done in less time by an experienced crew and using four rollalong boxes. Nevertheless.

almost two recording patches were collected every day.

Each field record consisted of 96 traces (example field records are shown in Figures 2.9

through 2.1 1). Each seismic trace was recorded by a single geophone with a 0 . l Z ms

sampling interval and total record lengt h of 250 ms. The total nurnber of records a t each

recording patch was 24. Twenty recording patches were surveod in order to cover the

entire survey area. The whole data set consisted of 5.50 shot records or 52SOO traces in

total.

In general the seismic data had a good quality. Some of the records contained strong

dispersed and scattered surface waves that obscure the reflection signal in many parts of

the records (see Figure 2.11). Nevertheless, very clear reflections are present outside the

surface wave arrivals.

2.10 Summary

In this chapter theoretical discussion on survey geometry scaling indicated that for equiv-

alen t resolution. wavelengt h must be scaled as survey geometry. Therefore. irequency

needs to be raised by ( 5 - k). From 2-D test profiles abb Buffalo gun8* source gave records

with a frequency bandwidth up to 500 Hz. It w a s therefore a suitable seismic source fur a

survey with a 3 m lateral sampling interval (bin size). Three different acquisition geome-

tries including parallel, zigzag, and orthogonal were investigated and t heir attri butes were

compared. The orthogonal 3-D shooting scheme was found most feasible of the t hree;

and it was utilized to perform the test 3-D seismic survey. Among different geophysical

and non-geophysical constraints. preservation of the high frequency wave cornponents

was the major issue. It influenced nearly al1 survey design steps. The parameters used

in the actual survey were presented along with some typical field records.

Chapter 2 3-0 seismic survey

Figure 2.9: . l n example of 3-D shot records wit h a good quaiity (S/N ratio). Records with such quaiity were coilected over the part of site where according to near-surface mode1 (see section 4.2) the weathered l a p r was thin. For presentation purposes, a ( 100,150,3.50,650 ) band-pass filter. time- and offset-weighted amplitude scaling were applied.


Figure 2.10: An erample of 3-D shot records with a medium quaiity . Almost half of the field records had such quality. For presentation purposes. a ( 100, I5O,Ml,6.50) band-pas filter. time- and offset-weighted amplitude scaling were applied.

Chapter 2: SD seismic survey

Figure 2.11: An example of a 3-D shot record with strongly dispersed and scattered surface waves. Records with strong dispersed and scat tered surface waves came from the part of site where according to near-surface mode1 (see section 4.2) the weat hered fayer is thick. For presentation purposes, a (100,150,550.650) band-pass filter. tirne- and offset- weighted amplitude scaling were applied.

Chapter 3

3-D seismic data processing

Introduction

This chapter explains in detail most of the processing steps applied on 3-D seismic data.

The basic principles of 2-D seismic processing are applicable to 3-D processing? except

in a few very important regards, mainly dealing with migration.

Seismic data processing strategies and results are strongly affected by the field acquisi-

tion parameters. although the ability of the seismic analyst can be as important as the

acquisit,ion parameters in determining the quality of final product from data processing.

Seismic data are usually collected in less than ideal conditions. So. eventually. one has to

deal rvith whatever data have been obtained. One can only hope to enhance the signals

in processing to the full extent allowed by the quality of field data.

In this study, al1 the processing except statics was carried out using the Landmark

INSIGHT-5 2-D and :3-D softwares on a Sun workstation.

3.2 Basic data preparation

In general, seismic records from my 3-D survey contained usable frequency up to 600 Hz with a dominant frequency of about 300 Hz. As shown in Figure 3.1, frequency contents

of the ambient noises rvere largely below the cut-off frequency of the analog low-pas filter

applied during data acquisition (140 Hz with 12 db per octave). The following are some

preliminary steps that had to be taken prior to the main prestack processing.

Chapter 3: 3-D data processing

Editing of shot triggers, bad traces, and headers

In some of the shot records. bad traces due. for instance. to poor geophone connection

required editing. Some records were " mis-triggered" . Le.. the tirne ongin was incorrect

due to poor operation of the shot time break detector. Al1 mis-triggered shot records

were adjusted by comparing t heir onsets with that of other records at the same shot hoies

in the course of the survey. Any remaining error was t hen removed by the procedure for

the stat ics correct ion.

- shot record

ambient noise

O 0.25 0.5 0.75 1 1.25 1.5

FREQUENCY (KHz)

Figure :3.1: X cornparison between amplitude spectrum of the ambient noise and a sample of the 3-D seismic shot records. (Composite spectrum of al1 traces in suitable time windows 25-100 ms.)

To incorporate the survey layout and field information such as elevation, coordinates of

each station and so on, into the trace lieaders, detailed header information was Ioaded

into the seismic data set. During this process. the nominal CMP bin size was increased

from 3 x 1.5 meters to 3 x3 meters, thereby halving the trace count in the stacked data

set and doubling the average fold.

Resampling and bandpass filtering

The original field records were over sampled in tirne. In order to speed u p the processing,

Chapter 3: 3-0 data processing 5 O

t hey were resampled into 0.25 ms. The resulting Nyquist frequency was st il1 high enough

(2000 Hz) that field data were not aliased.

Spectral balancing is often applied at an early stage of processing in order to compen-

sate for the earth's lorpass filtering effects. Since 3-D data set had acceptable range of

usable high frequency seismic signals (mostly due to the carefully shooting and receiver

planting), only a bandpass filter was applied, mainly to suppress the low frequency com-

ponents. Cut-off frequencies of the filter were set a t 100- 150-700- 1000 Hz.

Time, distance scaling

Amplitude balancing of the trace was the next step tliat had to be done prior to pre-stack

processing. Because of geometrical spreading. signal amplitude over a shot record varies

enormously. This was done by applying both offset-weighted and time weighted gain on

each individual trace within the data set. The gained trace was of the form:

TRACE,&. t ) = TR.4CEin(+. t ) x ( t )LpO"er x ( r ) rpower

where tpozoer and xpou~er are desired wveights. which can be positive or negative numbers.

After a nurnber of tests. the esponent in Equation 3.1 for travel-time ( I p o t a c i ) was set

to 1.4 and for offset (xpower) was set to 0.3. These gains are removable and can be

eliminated at any step of the processing in order to recover the true amplitudes.

3.3 Pre-stack processing

Table 3.1 indicates siimrnary of the processing steps applied on 3-D data set. This section

will cover only pre-stack processing routines. Post-stack processing steps are esplained

in section :3.4.

S t at ic correct ion

Refraction- based static algorithms are commonly used to determine the t rave1 time

anomalies introduced by rapid variations in thicknesses and/or velocities of near-surface

layers. A number of methods have been proposed to analyze the first arriva1 times and

calculate static corrections (e.g., Russell, 1989 and blarsden. 1993). In this study, static

Ch ap t er 3: *3- D data processing -5 1

corrections were estimated from complete first arrival data picks (Figure 3.2) with the

Hampson- Russell G L N D software package. The method uses 3- D generalized linear in-

version (Hampson and Russell. 1984) to develop a 3-D curved interface layered mode1 of

the subsurface.

First arrival data picks are first analyzed visually to build an initial guess for the near-

surface model. This tells the program how many layers are expected and their approx-

imate velocities and thicknesses. Sets of time-distance graphs of first arriva1 picks were

built by rolling square patch of 56x36 meters over the entire survey area. and the initial

model was determined by fitting a best line interactively to each segment of the graph

of actual first arrivai picks. It was concluded that a -two-layer' model (a thin layer

underlain by a sub-space) was a suitable starting model.

Table 3.1 : Data processing steps applied on 3-D seisrnic data set.

BASIC PREPARATION

EditingJresampling Data gaining and filtering

PRE-STACK PROCESSING

Short-wavelengt h refract ion stat ic correction -Air-wave a t tenuat ion Surface-wave attenuation Spectral balancing Surface-consistent amplitude scaling Velocity analysis and NMO correction Long-wavelengt h refract ion static correct ion Residual static correction S tacking

POST-STACK PROCESSING

Co herency maximizat ion 3-D time and depth migration

Thickness of the weathered layer was determined to range from 2.3 meter at the thinnest

part through 6.S meter a t the thickest part (see more details in chapter 1). In addition.

Chap t er 3: 3- D data processing .j'3

velocity for the weathered Iayer ranged from 800 m/s through 1000 m/s: for the un-

weathered sub-space. velocity ranged from 2400 m/s through 2700 m/s.

The program then performs a series of iterations in which the model first arrivals are

calculated by ray-tracing and compared with the observed first arrivals. then changes are

made in the mode1 and a new set of first arrivals calculated. This procedure is repeated

until some acceptable agreement is reached between observed and model first arrivals. It

ivas found to predict the observed first arrivals to within a '20 misfit of 0..5 ms. Less than

10% of modeled pick times had such a misfit.

Figure :3.;>: Direct and refraction arrivals in one of the field records. - l n abrupt change in arriva1 times (e.g.. at trace 39) is due to a sudden jump i n shot-receiver offset.

The smooth model is used to calculate spatially smoothed estimator of shot and receiver

statics. Then a local shot and/or receiver static is found for each station. so that shot

depth and mistiming and local geophone siting condition can be estimated. The total

shot and receiver refraction statics ranged from -6.3 to 2.1 ms and from -5.7 to -1.6

rns respectively. Figure 3.3 indicates estimated static values along the central shot and

receiver lines (i.e. shot line 4 and receiver line 6). The range of static values supports the

idea that implementing of shot/receiver array would attenuate the high frequency wave

components due to the timing errors (see Figure 2.8).

An example of a brute stacked section (along the in-Iine direction) before and after refrac-

tion static corrections is indicated in Figure 3.4. In both sections the ( 100,1w50,550.6ejO)

band-pass filter. time- and offset-weighted scaling have been applied and trace oriented

energy equalization in a 100 rns time window and a 50% stretch mute were applied for

Chapter 3: 3-0 data processing

ALONG SHOT LiNE 4

L " ~ ~ I ~ = - ~ I ~ ~ ~ ~ ~ - ~ ~ ~ ~ . . . I m . . . I . . . . I . v ~ - - . short wave :

- -

::j - elevation '

-

* - 4 . C

C *

. *

ALONG RECEIVER LENE 6

elevation 1

IN-LINE (rn)

Figure 3.3: An esample of the estimated long- and short-wave refraction and elevation statics dong the central shot and receiver lines. The misfit between actual and estimated pick tirnes dong each line also indicated.


Figure 3.4: Brute stacked section along in-line direction (CDP line 66) . (Top) before refraction static corrections, ( Bottom) after refraction static corrections. For presentation purposes, trace oriented energy equalization in a 100 ms time window, and 50% stretch mute were applied on both data.

Chapter 3: 3-0 data processing .5.j

presentation purposes. As seen in the figure. the refraction statics correction has en-

hanced lateral continuity of events and. as well. has compensated for push-down effect

of the weathered layer at 0.02 sec between traces 25 and 55.

3.3.2 Noise removal

Improving data quality requires enhancement of signal to noise ( S / N ) ratio of the seismic

records. The term signal is usually used to describe any event on the seismic record from

which one obtains information. Everything else on the record is considered as noise.

Seismic noise may be eit her coherent or incoherent.

Incoherent noises due to such causes as wind shaking, etc. are not predictable and are

considered random noises. In contrast, source generated coherent noises such as surface

maves. back scattered waves, and air waves on a given trace are predictable from a

knowledge of nearby traces.

In some cases part of the seismic noises can be attenuated in the field bp using source/receiver

arrays and analog low-cut filters. However, to preserve the high frequency energy con-

tents of the field records, rny 3-D seismic survey (see section 2.6) had to b e carried out

without source/receiver arrays . Consequently. source generated noises remained Iargely

untouched on the field records.

Figure 3.5 illustrates an example of the 3-D seismic shot records. Beside random noise,

the illustrated shot record contains tivo different types of source generated coherent noises

including surface waves and air waves. For presentation purposes, a band-pass fiiter wit h

cut-off frequencies of ( 100- l.iO-.i50-650) was applied to eliminate the very low frequency

component seismic noises from the record. Nevertheless, as seen on the record. a ma-

jor part of the seismic coherent noise has a spectrum that overlaps the seismic signal

spectrum. Filtering techniques other than frequency filtering methods are required to

attenuate the noise without damaging the seismic signals.

In conventional 2-D seismic data processing usually CMP gathers contain enough range

of shot-receiver offsets that any standard stacking procedure can attenuate the surface

waves and the air waves. However, due to the simplicity of my 3-D survey geometry.

3-D CMP gathers had less a regular range of offsets than typical 2-D data. and stacking

procedures were not suitable to eliminate the source generated noises. As a result, 3-D data set required development of some techniques capable of attenuating the noises in

shot and/or receiver domain rather than conventional CMP domain.

Chapter 3: 3-D data processing 5 6

Several methods were tested; the most effective were a K-L (Karhunen-Loeve) decompo-

sition technique (Levy et al.. 1983: Ulrych e t al.. 1953: Jones and Levy, 1987) to eliminate

air waves and a 3-D local slant stacking (3D-LSS) technique to attenuate surface waves.

Each filter technique emphasizes a certain characteristic of the seismic record in order

to discriminate a coherent event from non-coherent one or [rom other existing coherent

events. The fi-L decomposition technique is based on time, but not amplitude similarity

of events in a trace-to-trace sense. The 3D-LSS technique takes the advantage of dif-

îerences between the apparent velocity of events within the seismic record but is more

dependent on amplitude similarity. See Appendix B and C for theoretical outline of t hese

techniques.

Figure 3.5: An example of the 3-D seisrnic shot record after (100-150-550-630) band- pass filtering. The record contains 96 traces recorded by -4 receiver cables each with 23 geophones.

Air wave attenuation

Air waves are a portion of the seismic source generated energy which propagate in air a t

Chapter 3: 3-0 data processing -F

3 1

the velocity of sound. In 3-D seismic survey due to the lack of enough water inside some of

the s hot holes, part of the explosive energy was released into the air (sound) and detected

as air waves (Figure 3.5). Almost one tenth of the field records were contaminated by

the air waves. Beside relat ively high amplitude, t his source generated coherent noises

had a rvide range of spectral overlap with seismic signals. Consequently. conventional

band-pass filtering could not suppress them.

The I i -L decomposition technique treats each trace as a data vector. and computes a set of

uncorrelated (orthogonal) principal component traces from an eigenvalue decomposition

of the matrix of zero lag cross-covariances of the given multi-trace input data set. The

principal component traces are arranged in order of decreasing energy content. i.e. the

signal with the largest variance (energy) will appear as first. principal component and

so on. Subsequently, the out put records are reconstructed utilizing only the information

contained in a specified selection of the principal component traces, those associated with

large eigenvalues. This amounts to reconstruction of the coherent energy present in the

input data set.

Figure 3.6: A cornparison between (top) the original flattened air wave and (bottom) the reconstructed version using a K-L filter.

The K-L decomposition technique was applied on 96 trace shot records flattened on the

air waves (330 mis). then the first five of the 96 principal components were used to

estimate the airwave component of the records. A windowed version of the air ivaves

rvas then subtracted from the original input record. Figure 3.6 gives an example of the

original and reconstructed air waves. Figure 3.7 depicts the same shot record as in Figure

3..5 after suppression of the air waves.


Surface wave attenuation

Surface waves were another set of the source generated coherent noises that appeared

in almost al1 of the shot records. Mostly they are Rayleigh waves. which are vertically

polarized waves that propagate along a free surface of a solid. Because of the nature

of the particle motion (ellipt ical retrograde), Rayleigh waves at the surface of the eart h

are often called ground roll. Although these waves are mainly confined to the surface

layer. and have dirninishing amplitude with depth. they sarnple a depth range of a few

wavelengt hs (several meters). Due to systematic velocity variation wit h dept h. t hey

usually have a dispersive velocity. Due to lateral heterogeneity in the near-surface they

often suffer some degree of reflection or scattering.

Figure 3.7: The same field record as in Figure 3.5 alter elimination of the air waves with the K-L filter.

As shown in Figure 3.8 the surface waves are of low velocity and tend to have lower

frequency than the P wave reflections and refractions. But, their amplitude in the P wave spectral window is high enough to ma& completely the other events. In some

Chapter 3: 3 - 0 data processing

Figure 3.8: A cornparison between 3-D field records (top) contaminated by dispersed and scat tered surface waves, and (bot tom) contaminated wi t h coherent surface waves. Both records have been filtered using a ( 100-150-550-650) band pass filter.

Chapter 3 : 3-0 data processing 60

parts of the survey area because of the near surface inhomogeneity. seismic shot records

contained strong dispersed and scattered surface waves. An example of such dispersed

surface wave is shown in Figure 3.8.

In addition to the strong dispersion, 3-D seismic surveying with simple field configuration

introduced another difficulty for the elimination of coherent noises. As an example. the

first 120 ms of a field record is shown in Figure 3.9. In this record some of the receiver

stations at each recording cable (i.e. each trace subset of 24 traces in the record) have

received seismic energies (e-g. surface waves) almost at the sarne time (indicated by two

arrows facing opposite direction).

Figure 3.9: -4n esample of 3-D field records. Each 24 traces are derived from separate recording cables. T h e width of two oppositely faced arrows indicates a poor rejection area for any rejection method based on apparent velocity of surface wave. .4s seen in the figure, the number of traces in poor rejection area incrases wit h shot-cable lateral offset.

As seen in the record, the shot is located between traces 12 and 13 very close (3 meter) to

the first recording cable. There is an acceptable uniform increase in arriva1 times at the

receiver stations along the first cable. However, as the recording cable moves away [rom

the shot point (Le. each successive trace subset of 24 traces in the record) the number

of traces that participate in the Bat events are increased. The trace increment is not

same for al1 seismic events (compare the number of such traces in refracted events and

the surface waves), it depends on the apparent velocity of the seismic events.

Chapter 3: 3-0 data processing 61

Apparent velocity-based filtering techniques obviously have difficulty eliminating such

(flat) coherent noises. This portion of the recording patch is called a poor rejection area.

-4s depicted schematically in Figure 3.10, the size of the poor rejection area depends

o n the lateral distance between shot and recording cable as well as apparent velocity of

seismic energy. The larger the shot-cable offset the wider the poor rejection zone.

a) shot domain

in-line

b) receiver domain A rec. stn f shot srn

Figure 3.10: Schematic representation of poor rejection area in bot h shot and receiver domains. The size of the base of triangles indicate the width of poor rejection area for each shot/receiver. The size of poor rejection area directly depends on shot-cable offset and inversely depends on apparent velocity.

The K-L method was tested for removal of surface waves, but was rnuch less satisfactory

than for air waves because of the dispersed, back- and side-scattered components. Thus. as seen in Figure 3.11 it could not be satisfactorily "flattened' a t any single velocity. A

Chapt er 3: 3-0 data processing 6'2

3-D local slant stacking technique (3D-LSS) was therefore used. The shot gather was

first approximately NMO corrected to make reflection events nearly Bat. Then a local

slant stack was used to remove al1 events wit h very different slopes.

Figure 3.1 1 : Surface waves as in Figure 3.8 after application of a linear t irne move- ou t a t 950 m/s velocity. ( t o p ) strong dispersed and scattered surface waves. ( b o t t o m ) coherent surface waves.

Prior to slant stack transform, the 3-D seisrnic data set was re-organized in such to

take account of the fact that it could contain several different trace records for a single

shot Jreceiver station point. This was done by vertical stacking of the al1 traces associated

wi t h the given shot-receiver pair. The duplicate, triplicate, and quadruplicate records

arose because of the overlap of adjacent seismic patches. As a result. the 3-D data set

and subsequently required processing efforts were reduced almost by factor of two. The

reduced data set contained 266 shot records.

In 2-D seismic profiling, the source-receiver offset is usually incremented uniformly from

trace to trace, but for 3-D surveys the source-receiver separation is not incremented

iiniformly. The next step prior to slant stacking was to split each shot record into a

number of sub-records in order to supply the slant stack routine with inputs that contain

a uniform spatial sampling. For a given shot gather each sub-record contained traces

Chapter 3: 3-D data processing 63

which were recorded only by one of the receiver cables (or receiver lines) within the

active seismic patch.

The RD-LSS procedure was therefore applied on 3-D data set twice. once along the in-line

direction and then along the cross-line direction. The second pass along the cross-line

direction (or in common receiver domain) was done in order to attenuate the remainder

of the coherent noises from traces located within the poor rejection area.

The local slant stacking technique applied a forward slant stack (or r - p) transformation

to a srnall subset of the input seisrnic gather; followed by an inverse transformation,

to construct the rniddle trace of the selected trace subset. Since the reconstruction

was designed to include only a desired range of apparent velocities. only this range was

included in the forward transformation. The trace subset window was slid forward trace

by trace until the entire gather had been processed.

In the first pas. normal move out (NMO) corrected cornmon shot gathers were trans-

lormed from conventional time-offset ( t ?x) domain into the intercept-ray parameter ( r - p )

domain. The transformation was carried out on a subset with five traces using nine ray

parameters ranged from -0.5 rns/trace to +0.5 msltrace. This was followed by an inverse

slant stack transformation to reconstruct the middle trace of the input subset. The trace

subset window then slid forward and filtering procedure was repeated until ail input data

set (at the first p a s ) were filtered. Afterwards. the YhlO corrections were removed from

the data set.

In the second pass, the output of the first pass was sorted into the common receiver

gathers and the same filtering procedures as in the first pass were repeated on a subset

with three traces. As part of the Local slant stack, a spectral adjustment ivas made

to compensate for the radon t ransform's t heoretical w-' spectral at tenuat ion and also

to improve the high/low frequency balance of the record see Figure 3.12). This was

done by using a -rho7 filter (Claerbout, 1985) which takes the values in a selected range

of amplitude spectra and multiplies them by the corresponding frequency taken to a

specified power (the utilized power value was 1.5). Due to the acceptable performance of

rho filter in adjusting the frequency spectrum, there was no need to apply deconvolution

on the 3-D data set. An erample of the surface wave removed 3-D seismic record is shown

in Figure 3.13.


O 200 400 600

FREQUENCY (Hz)

Figure 3-12: Spect rai balancing using the R H 0 filter. High Irequency componeiits at the visible range were gained between 3-9 db.

3.3.3 Surface consistent amplitude scaling

-4ttenuation of the coherent noises provided an opportunity to perforrn surface consistent

amplitilde scaling in order to cornpensate for the lack of amplitude consistency frorn one

record to another within the 3-D seismic data set.

Amplitude and spectral inconsistency arnong the shot records is one of the well known

acquisition problem for engineering seismic surveys. During data acquisition. attention

was paid to keep t h e shot holes filled with water in order to preserve the sliot effectiveness

a t al1 holes. However, some of the field records had considerably higher or lower energy

level t han ot hers.

A surface consistent amplitude scaling was applied to the 3-D seismic da ta set by an iter-

ative procedure based on those parts of the record that contained most of the reflection

arrivais (time interval 40 to 120 ms). The Root-Mean-Square (RMS) amplitude of each

Chap ter 3: 3-D data processing

Figure 3.13: The same field records as in Figure 3.8 after attenuation of the surface waves using the 3-D local slant stack filter. Spectral balancing and surface consistent amplitude scaling were d s o applied to this data after filtering.


SCALE FACTOR

SCALE FACTOR

0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15

SCALE FACTOR

Figure 3.14: Histogram of the iterative surface consistent scaling of 3-D field records to adjust their amplitude in-consistency.


record was estimated and then it ivas rescaled. Then data regathered in the complemen-

t ary (s hot Ireceiver ) domain and the procedure repeated. Figure 3.14 indicates t hat t lie

range of average RMS amplitudes in 3-D field records ranged from 60-400 (see scaling

factors at 1st iteration) as well as the effectiveness of the scaling procedure to adjust

thern (see scaling factors a t 3rd iteration).

3.3.4 Velocity analysis

Velocity analysis is an estimation of the RMS averaged vertical velocity I/jPars(to) from

datum to reflector a t various CMP locations in the survey area. If certain approximations

relat ing to reflector dip and maximum shot-receiver offset are fulfilled. t his quant itji can

be measured directly from the t ime-moveout of reflect ions as a function of shot-receiver

offset. If the approximations are not fulfilled, the determination can still be made. but

the result is known as stacking velocity "Ky.

VeIocity analysis is usually performed on selected CMP gathers or on groups of gathers.

Since individual CMP gathers in my survey did not always contain a suitable range of

trace offsets. adjacent CMPs were grouped into super ChIP gathers containing a patch

of nine adjacent individual ChfP bins. In order to have a fairly broad offset range within

the super CblP gat hers t hey were selected at the crossing points of shot-receiver Lines.

In total. velocity analysis was carried out on 72 super CMP bins spread over the entire

survey area on a 24x36 grid. The results were combined to estimate 3-D relocity mode1

over the ent ire survey area.

The velocity analysis utilized a conventional coherency rneasurement along various travel

time hyperbola on super CMP gathers. Desired stacking velocities corresponded to those

hyperbola producing maximum coherency in the primary reflect ion events. The output

from this type of velocity analysis. as shown in Figure 3.15, is a plot of color contoured

numbers as a function of velocity versus zero-offset two-way t ime (veloci ty spectrum).

These numbers represent the measured signal coherency along the hyperbolic trajectories

governed by veloci ty, offset, and traveltime.

A good velocity resolution was obtained during velocity analysis. Stacking velocity of a

given reflector at different super CMP1s was determined with an error of .- 10% down to

60 ms and - 20% down to about 100 ms, with error increasing rapidly a t greater times

(depths). However. the stacking velocity differences between different reflectors observed

on the same super CMP gather could be determined to several times better accuracy

Chap t er 3: 3-0 data processing

Figure 3.15: An example of super CMP gathers. (left panel) Theoretical hyperbola fitted on reflection events. (right panel) Velocity spectrum, a coIor plot of event coherency versus s tacking veloci ty and two- way zero offset t rave1 time.

than the above limits imply. The analysis clearly indicated that velocity a t the study

area does not increase monotically with depth. The zero time velocity was set at the

value equal to the obtained stacking velocity for the first reflector. However, correlation

wit h the velocity value determined by the refraction analysis was very good.

Stacking velocity in an area with steeply dipping reflectors and/or appreciable lateral

inhornogeneity should expected to deviate systemnticaliy frcrn VRMS(to) and be a function

of source-receiver azimiith (Levin 1971). Thus, it can be desirable to perform azimuth

dependent velocity analysis. However, t his was not done because:

1. Analysis of the nearby borehole logs, 2-D seismic profiles, and the 3-D brute stacks did

not provide any evidences for existence of steeply deeping reflectors a t the study area.

2. Performing of an azimuth dependent velocity analysis requires al1 CMP data to be

sorted into subgroups of different azimuth ranges. Because of the simple acquisition

Chapter 3: 3-D data processing 69

geometry used in my survey, subgroups w-ould not have acceptable ranges of source-

receiver offset with a uniform increment to do reliable velocity analysis.

Due to the lack of steeply dipping reflectors in my survey, the stacking velocity model

was considered to be a good approximation of the RMS velocities of the 3-D data set.

For migration and interpretation purposes an interval velocity mode1 was established

based on the stacking velocities. The final stacking velocity model of the 3-D data set

was estimated after a series of iterative refinements. After each iteration. the interval

velocity model ivas also improved. The stacking velocities indicated in Figure 3-16 are

selected along the diagonal directions of the CblP stacked data cube. Despite the az-

imuth independent velocity analysis. results after depth migration (see next chapter)

gave confidence in the established 3-D velocity models.

3.3.5 Velocity conversion

.At this point it is desirable to define different type of velocities that can be estracted

irom the knowledge of the stacking velocity and their interrelations. Apart from 3 h l O

correction in data processing. for migration and interpretation purposes one requires

velocities t hat are of physical significance, namely the RMS average veloci ty ( I / ' ~ . I ~ ~ ) .

average velocity (Ci), and the interval velocity (b:). The RhIS velocity is simply and

directly related to the interval and average velocities.

1. The RMS velocity is given by

where \;'in, is the instantaneous velocity. defined as the velocity in an infinitesimally small

interyal, and T is the total travel time. The RMS velocity aIso called time-weighted RklS

average velocity

2. The average velocity along the source-receiver trajec tory is given

the principle of least time path requires that Ta > TRMS, that is V. 5 V R , L ~ ~ . Where Ta and TRAIS are two-way travel times corresponding to and VRnrs respectively. In strata

of typical variabiiity the difference between two velocities is typically up to -- 5 - 7%.

Chapter 3: 3 - 0 data processing

Figure 3.16: Two cross sections from the volume of stacking velocities dong the (a) nort h-south

3. The interval

times) is given

diagonal, and (b) east-west diagonal.

velocity as a velocity over an interval between two depths (or twu-way

where V ( t ) can be either the average velocity when represents the average velocity

of the interval or can be the RMS velocity when Knt indicates the RMS velocity of the

interval.

In terms of the TZ - ,Y2 plot shown in Figure 3.17, K2 is the inverse dope of the straight


Figure 3.17: T' - S2 plot showing schematicdly the relation between t h e straight Iine (dash line) best fitting the reflection locus. the tangent to the reflection locus at -Y = O (dotted line). and the straight line (solid line) corresponding to t h e refraction- free trajectory.

line best fit ting the reflection travel time locus: b&s is the inverse dope of the tangent

to the reflection locus at .Y2 = O (i-e.. normal incidence trajectory): and c,' is the inverse

slope of the straight line corresponding to the refraction-free trajectory. The straight line

obtains from plotting T.' (two-way travel time corresponding to the average velocity )

versus .Y2. The relationship between the slopes of the three straight lines requires that.

& 5 hnrs 5 K.

3.3.6 Residual static correction

The refraction statics correction (short-wavelength components) was applied a t t he early

stage of the processing in order to compensate for the effects of near-surface irregularities

on reflection times. .A significant part of the reflection time distortions was removed at

this step. The long-wavelength components of the estimated statics were not applied

until the da ta were NMO corrected.

Cfiap ter 3: 3-0 data processing 1'2

However. in some of the NMO corrected CMP gathers, reflection arrivals still were oot

as well aligned as expected. To improve the estirnate of static corrections. a surface

consistent residual statics estimation based on Ronen and Claerbout's (1982) stack-power

optimization algori thm was calculated and applied just prior to final stack. Calculations

were performed iteraiively using a correlation window of 40 to 120 ms (correspondent to

the interval of best recorded reflections) and a maximum allowable shift of 1.0 ms.

Xfter the residual statics correction. the velocity analysis was revised in order to refine

the final stacking velocities. The final stacked data volume consisted of 7-4 sections each

with 73 traces. Figure 3.18 gives the Row chart of 3-D seismic data processing sequences.

3.3.7 Test of muting procedure

Reflections from shallow depths ( 5 25 ms) are much more clearly visible and continuous

in the 3-D stacked sections than in nearby 2-D sections. In order to determine whether

t hese are t rue reflections or mis-ident ified refractions from shallow refractors. two sections

were created: one using a preferred "stretch" mute that removes any far offset. early time

data t hat has been time stretched more than 3-596 by the XMO correction; the ot her where

the first two cycles following the first arriva1 have been "surgically" muted but the stretch

mute has been set back to a 50% level. A surgical mute zeroes the amplitude of data

samples ivi thin a selected region on the seismic record. An example of sections from the

sets is presented in Figure 3-19.

A close esamination of the upper parts of the sections (above 30 ms) shows that the

surgical mute removed al1 data above about 13 ms and greatly reduced event amplitudes

between 13 and - 30 ms. However. both sections display the same correlatable horizons.

Thus. the preferred 95% stretch mute does not seem to be admitting any spiirious re-

fraction or multiple reflection-refraction events to the section. at least below 13 ms. It

aiso indicates the effectiveness of the employed filtering technique (3-D local slant stack)

in preserving near-surface near-offset reflection energy in the shot records during surface

wave removal.

3.4 Post-stack processing

As described below, post-stack processing included a step of coherency maximization,

and time and depth 3-D migration by the phase shift method.


r-& , : UNEAR TIME MOVE

l 1

RECONS'IRUCTTON OF I : AIR WAVES BY K-L j .

1

TevIE AND OFFSET / WEIGH'IEDGALN

1 AIR WAVE 1. .

1 INTo 4 SWB RECORDS 1

SUBSET OF 5 'IRACES ' i SURFACE CONSISENT 1 AMRIIUDE SCAUNG 1

I i RESIDUAL STATICS 1 I i : REBUILDING OF ?HE

MIDDLE ïRACE

' SUDING THE SüBSET : , 1 ?RACE KIRWARD / STACKING 1

1 COMMON SHOT : !+.

Figure 3.18: A flow chart indicating processing sequences applied on the 3-D seisrnic data set.


I 1 I I 1 1 I I I l I I I I 1 I I i

Figure 3.19: A corn parison between the same unmigrated zero-offset stacked sections (a ) before. and ( b ) after muting of the refraction data. Near-surface refiection events are seen in both of the sections.

Chapter 3: -3-0 data processing

3.4.1 2-D Median filtering

In some of the CMP gathers, bin gathers contained only 2 or 3 distinct shot-receiver

offsets. rather than a uniform distribution of offsets. As a result the CMP stacking

routine could not at tenuate effectively any remaining coherent noises. Thus. the st.acked

data set contained a few traces of relatively low S / N ratio. To obtain a more uniform

result but with as Little as possible loss of spatial resolution. a 2-D niedian filter was

applied on a square patch of nine adjacent CDP bins to rebuild the middle stacked trace.

In many areas. this produced little modification. However, it further improved trace to

trace coherency, and especially removed the occasional bursts of surface wave noise that

could not be suppressed by the slant stack because of unfortunate shot-receiver geometry

or occasionally poor shot conditions.

3.4.2 3-D timeand depth migration

I t is useful to consider seismic data as recordings of a wavefield in a data space of time.

CMP position and offset. The recording geometry provides the wave field at nonzero

offset. In a typical processing, the offset aris is collapsed by stacking the data onto the

midpoint-time plane a t zero offset.

Basically. zero-ofset stacked sections are a graphic displays of the recorded reflection

energy. No matter where in space the reflection actually occurs. each event on a stacked

section is plotted directly beneath the source-receiver midpoint. They are onlj. a rough

approach to geological sections and are difficult to interpret in complex area. Migration is

the process of constructing the reflector surfaces from the recorded seismic data. It nioves

dipping reflectors from t heir plot ting position in the time (or apparent dept h) section into

their true subsurface positions and collapses diffractions. Detailed subsurface features are

thereby delineated. Naturally, migration does not displace horizontal reflection events.

Regardless of the migration algorithm used, the interpretability of a migrated section

will depend on the quality of the input stacked section (how closely it approximates a

zero-offset section), the signal to noise (SIN) ratio, and the velocities used in migration.

hIigration requires a spatially smoothed estimate of the true medium velocity. If one uses

a velocity modei that is significantly different from the actual medium velocity, then the

migrated section can be misleading.

I performed 3-D migration on my stacked data volume both in time and depth using


algorithms based on the 3-D phase-shift migration technique of Gazdag ( 19%). According

to Gazdag, this method is capable of migrating reflectors with dips up to 75 degrees. (See

Appendix D for t heoretical out lines.)

Al1 migrations can be considered to be downward continuation of an upward propagated

wavefield (reverse propagation). Gazdag's method is based on the idea that downward

continuation amounts to a phase shift in the frequency-wavenumber domain. The imaging

principle is invoked by summing over the frequency components of the extrapolated

wave field a t each depth step. The basic phase-shift method can only handle vertically

varying velocities.However, Gazdag and Squazzero (1984) extended the method to handle

moderate lateral veloci ty variations.

The initial input parameters to perform migration were :

veloci ty 85% of the stacking velocities maximum aperture 30 degrees Frequency cont.ent 140 to 450 Hz input data length 0.0 to 0.200 s maximum rnigrated depth 250 m

The whole migration process took place in 222 depth steps each with 66 frequency slices.

First. a laterally-averaged velocity function was used to perform the phase-shift migration

in a frequency-by-frequency manner. Then, to achieve a 3-D depth migration. a first-order

phase correction was applied at each frequency to account for lateral velocity variations.

Figures S.2Oa-c present an example of the stacked seismic section (only 60 ms of record)

along the in-line direction before and after timeldepth 3-D migration. As seen in part

( a ) of the figure, dipping events located between traces 1-41 and time window of 65-85

ms. were shifted up-dip after migration. As a result, the foreset bedding become in t his

stratigraphic interval more clearly recognizable on the migrated sections (par t b and c).

The next chapter reviews the geological framework of the study area and provides ex-

amples of seismic sections. constant depth slices from volume of the stacked data and

correlate t heir events rvit h subsurface geologic uni ts.

Summary

In summary. my raw 3-D seismic data set had a fairly good signal to noise ratio. The

dominant frequency was about 300 Hz and the bandwidth of usable reflection signals

Chapter 3: 3-D data processing -- I I

ranged from 170 to 450 Hz. To compensate for the effects of near surface inhomogeneity

on refiection times, refraction arriva1 pick times were used t o estirnate a mode1 for near

surface weat hered and sub-weat hered Iayers.

1 1 1 2 1 31 4 l 51 6 1 72

Figure 3.20: -4 comparison between (60 ms of) one of the stacked sections along the in-line direction ( a ) before migration. ( b ) after time migration. and ( c ) after depth migration. In this comparison stacked data between 10 to 100 ms of the record are used.

Extensive tests of filtering techniques were done to find a suitable techniques to attenuate

source-generated coherent noises. The K-L decornposition technique and 3-D local slant

stacking technique were found fairly effective met hods in t his regard. Veioci t y analyses

were carried out on super CMP gathers. The resulted stacking velocities provided a good

velocity-depth mode1 for the survey area and a cube of stacked data. with good resolution

Chapter 3: 3-0 data processing 7s

(both in time and space) was obtained from stacking of t h e CMP gathers. The velocity

model was used to perform a successful 3-D phase-shift dept h migration on stacked data

set.

Chapter 4

Geological interpretat ion/correlat ion

This chapter begins by reviewing the geology of the study area as well as the previous

work carried out over the area (e-g. borehole logs. etc.). Then resuits of borehole logs and

outcrop information are used to correlate the seismofacies wit h geological units. Samples

of seismic sections' constant depth slices. etc. extracted frorn the volume of 3-D depth

migrated stacked data. are also given in this chapter. Finally. an attempt is made to

determine where attenuation is strongest in the test region.

4.1 The study area

The Greater Toronto Area (GTA) is a large urban center located in an area previously

covered by North American ice sheets during Pleistocene glaciations ( 1640-10 ka ago).

Glaciers are moving solids (ice) t hat can erode and transport huge quantities of materials,

especially unconsolidat ed sediments and soil. Al1 sediments deposi ted as a conseqiience

of glacial activity are referred to as glacial d$.

Geologists generally recognize two distinct types of glacial drift. till and stratified d 4 t .

Till is a clastic sediment containing grains of very different size that is deposited directly

by glacial ice. It is not sorted or stratified; that is, its particles are not separated by size

or density, and it generally does not exhibit layering, a t least on a fine scale. Tills are

formed by relatively warm glaciers where. perhaps with the aid of meltwater lubrication

and partial Rotation, the ice cao move over the ground surface. Since cold glaciers have

t heir base frozen on to the permafrosted ground surface, tills are not formed there.

Chapter 4: in t erpre t ation/correlat ion

UIM ZONE 17

O OWCRoF' LOCAllON

A KRnccÿSéiSMiC~RlE

- - - - SaSMlC UNE

1 ~ S a S M t C s U R K V

Figure 4.1: A map indicates the location of site Pl. proposed and esisting landfill sites. and previous investigations in the study area.

Stratified drift is sorted by size and density and, as its name implies. is iayered. In

fact, most is sediment transported by streams that receive their water and sediment load

directly from melting glacial ice. Glacial ice rnay be present, if it is floating above the

ground surface.

Geographically, GTA is located on a lightly dissected Pleistocene glacial till plain resting

on impermeable Paleozoic shale. The 3-D test survey was carried out at site P l (Figure

4.1); one of several sites considered (in 1989) as a possible large municipal landfill site

(M.M. Dillon Ltd., 1990). The site covers about 3 km2 near the Whitevale community in

Durham Region, east of Toronto. Existing land use in the study area is predominantly

agricultural.

Chapter 4: interpretation/co~elation S1

There is little topographic relief over most of the survey area. and soils are often developed

directly on the uppermost glacial till. Thus, most information about t he Pleistocene

st ratigrap hy h a corne from drilling. However, the glacial format ions are occasionallp

well exposed in outcrops along steep banks of the Rouge River and West Duffins Creek

(Figure 4.1) allowing some detailed cornparisons and correlation of seismofacies wit h

lithofacies to be made.

4.1.1 Geological s e t t ing

A summary of the Quaternary stratigraphy for the GTA presented in Table 4.1. It has

been derived from a number of sources such as Karrow (1967). Sharpe (1980), 1I.M. Dillon Ltd. (1990), and Boyce et al. (1995). Some of the listed units have not been

ident ified in the survey area.

At site P l only the Wisconsin glaciation is recorded. Because Toronto is near the edge

of the ice caps and glaciation and deglaciation are not uniform processes. ice came and

went several times in this period. In general, growth of the ice cap occurred mucli

more gradually t han its disappearance, so the oscillations at P l during onset are spread

over a much greater time period (Early and Middle Wisconsin) than the deglaciation

oscillations (Late Wisconsin). At site Pl Pleistocene deposits are about 90 meters tliicli

and are divided in to two main depositional sequences. The upper package (- 50 m

thick) is composed of Late Wisconsin Tills including Halton Till and Xorthern Tili. The underlying package ( - 40 m thick) consists of Middle Wisconsin Thorncliffe Formation.

Sunnybrook Till, and Early Wisconsin Scarborough Formation (Iiarrow 1967: Sharpe

1980; Boyce et al. 1995).

Tlie Late Wisconsin tills record two main phases of ice advance across t h e area. The

younger till (Halton Till, up to 17 m thick) wris deposited by a short-lived north-flowing

resurgence of ice from the Lake Ontario basin about 13.000 years before present (B.P.). However, the older till (Northern Till up to 50 m thick) was deposited by southerly-

flowing ice during most of Late Wisconsin time about 15,000-13,500 years B.P. The two

tills are separated by thin (2 to 10 m) silts, sands, and graveis which record a short-lived

interstadial period (possibly the klackinaw Interstadial; Iiarrow and Occheiet ti 1989:

Boyce et al. 1995).

The Thorncliffe Formation comprises deltaic sands and lacustrine silt and clay deposited

in proglacial lakes that appeared during the middle part of the Wisconsin glaciation.

Chap t er 4: in t erpre t a t ion/correla tion 82

Table 4.1: h summary of the Quaternary (Pleistocene) geologic sequences in the Greater Toronto Area. Uni ts marked - * 'were not encountered in the survey area.

Late Iroquois deposits ( IR)

Halton Till (HT)

Oak Ridges Moraine (ORM)

Interst adial sedi ment s

(1s

Yort hern Till ( NT)

Thorncliffe Formation (TF)

inter bedded by :

Seminary Till and

Meadowcliffe Till

Sunnybrook Till (ST)

Scarborough Formation ( S n

Don Formation

York Till

Whit by Formation [SHI

Lithology

Beach and near shore deposi ts ( e - g . sand. gravel.

silt. and clay)

Silty/sandy till interbedded with underlying interstadial

sand. gravel

Prominent ridge of sand and gravel outwash

Sandy fluvial gravel with lacustrine silt and clay

Stony. sandy-silt till

Deltaic sand

Clayey silt

Clayey silt

Clay till with laminated silty clay

Deltaic sand and glacio- Iacustrine sand and clav

Fluvial succession of clay. silt. and sand

S hale-rich, clayey sand till

Black shale

.lot pmsenl at the study

wea

Chapter 4: interpretation/correlation $3

ünderlaying the Thorncliffe Formation is the Sunnybrook Till. It is a distinctive dark

grey. fine-grained. clayey-silt t ill. This unit records the earliest Wisconsin Ice advance

into the area. The Scarborough Formation consists of deltaic sediments deposited about

90.000 years ago in a glacial lake (Lake Scarborough). It represents the earliest \Visconsin

age deposits in the Toronto area (Sharpe 1980).

In the study area, bedrock comprises grey shale ( Whit by Formation) deposited during the

Upper Ordovician period approximately 460-410 M years ago. Depth to the bedrock is

in the order of 85 to 90 meters. Bedrock \vas encountered ocly in two of the 36 boreholes

drilled on site.

4.1.2 Work near Pl

Since 1989, extensive hydrogeological investigations have been carried out at si te P 1.

They included hydrological field and laborator- tests (Gerber and Howard. 1996). drilling,

core sampling, well logging (M.M. Dillon Ltd.. l99O), down-hole seismic logging (by

Geoiogical Survey of Canada), and seismic surveys (Boyce et al. 1995).

Figure 4.2: 3-D survey area at site P l and surrounding deepest boreholes.

.A total of 36 boreholes were drilled to depths between 11 to 109 meters below the ground

surface (cumulative dept h 3 1.57 m). Figure 4.2 indicates location of the three drill holes

Chapt er 4: in t erpret ation/correlat ion S4

nearest (and deepest ) to the 3-D seismic survey area. Natural gamma logs and electri-

cal conductivity Logs were collected in deep wells. They are useful in identiiying and

correiating different units or sequences within (and between) the boreholes.

As shown in Figure 4.1 several 2-D seismic profiles were collected near different parts of

site Pl . Major stratigraphic features are easily identified on the stacked sections of the

2-D seismic profiles. .An example section was given in chapter 1 (see Figure 1 .S ).

According to Gerber and Howard (1996): isotopic evidence ( * H . 180. and H) from North-

ern Till's pore waters indicates the presence of modern (post 1952) waters a t depths of up

to 50 meters (Le., a vertical groundwater flow velocity of approximately one meterfyear).

This suggests perhaps some facies of the till are more permeable than t h e majority of

the tills or there are some other poorly understood hydraulic pathways through the till.

4.2 Near-surface model

The configuration of the 3-D seismic survey provided enough near and far source-receiver

offsets in each recording patch to establish a n accurate near-surface (weathered) layer

model for the survey area by the analysis of direct and refraction first arrival events (see

section 3.3.1). The result is a velocity model for the uppermost .- 10 m of the survey

area. The model consists of a constant velocity weathered layer underlain by a constant

velocity sub-space but both velocities are permitted to Vary laterally over t h e survey area.

It was found t o provide a good match between actual first arrival picks. .As rnentioned

earlier in chapter :3. 20 misfit between real refraction pick times and the modeled times

w w 0.5 rns of two way travel time. corresponding to - 0.25 m of thickness. for a 1000

m/s iayer velocity. Less than 10% of modeled pick times had such a misfit.

The near-surface velocities are indicated in Figure 4.3. Both layers have higher velocities

towards the south and southwest corner of the site. Figure 4.4 (bot tom) shows the

estimated thickness of the weathered layer over the survey area ranges i rom 2.3 to 6.8

m. They may be as much as 20% different from the stated value, if the layer velocity

estimate is similarly off.

Thickness of the modeled near-surface layer correlates t e l l wit h topography of the survey

site. In fact the base of the weathered layer is nearly horizontal. The shallow structure

correlates well with the quality (SIN ratio) of the field records. Records were better at

the south and south-west corner of the site. T h e cause could be the thin soi1 in this area.

100 IN-LINE ( m )

Figure 4.3: Veloci t y of the weat hered layer ( top) and sub-weat hered layer (bot tom) at site P Z from analysis of the first arriva1 picks. The contour interval is 20 m/s.

Chap t er 4: in t erpre t a t ion/correia t ion

100 IN-LINE (m)

100 IN-LINE (m)

Figure 4.4: Topography of the site ( top) and thickness of the modeled w Iayer from analyses of the refraction pick times (bottom). T h e contour interv m.

~eat hei .al is O.

Chapter 4: interpretation/correlation

4.3 CMP stacked data volume

The final products of pre-stack processing sequences are a set of synthetic

(CMP stacked) seismograms and the interval velocity model.

zero-offse t

Figure 4.5 presents an example 3-D view of the pair. The synt hetic zero-offset stacked

data volume is a 74 x 73 x 1001 matrix of seismic reflection amplitudes covering a sur\-ey

area of 220 x 220 m with a trace bin of 3 x 3 m to a two way travel time of 2.50 ms.

The seismograms in the data volume have a vertical half wavelength resolution of about

1.2 rns corresponding to about 1.5 m of depth, and a horizontal resolution of about 10

m at the base of tills (- 50 ms two-way time) decreasing to about 20 m on the bedrock

surface. The velocity model data matris has the same dimensions as the seismogram

matrix. but it has much lower intrinsic resolution in time and space.

One view of the cube of interval velocity mode1 is sliown in Figure 4.5b. For cornparison.

it is selected from the same view point as the cube of time stacked data. The color range

for the cube of interval velocities was set to get more detailed interval velocities within

the till deposits. This prevented the events below the bedrock surface (especially the one

at two-way-time about 110 ms) from being seen. It can be seen in the interval velocity

sections along the in-line and s-line directions whicb are presented in Figures 1.6 and 4.7.

A s illiistrated in the figure. 3-D data volumes are capable of being displayed dong any

arbitrary space direction. or time plane. Perspective pictures of isosurfaces c m also be

constructed from it.

Sarnples of the time stacked sections along in-line (line 67) and s-line (line 13) directions

together with their interval velocity models are shown in Figures 4.6 and 4.7 respectively.

Since the interval velocity model is derived from measurements made on selected reflec-

tions in the prestack data volume, it is not surprising that it shows a good correlation

wi t h corresponding synt hetic zero-offset stacked time sections. Hoivever. i t is estremely

helpful to identify rvhich reflectors correspond to the bounclaries betiveen different geo-

logical units on the synthetic zero-offset sections. The low velocity zones in the interval

velocity sections at about 15-20 ms and 50-55 ms obviously correlate with the Halton-

Xorthern Till interstadial deposits and the sedimentary base of the Northern Till (see

section 4.5). The latter possibly could be a thin er~sion laver on top of the Thorncliffe

Formation or perhaps a sandy bed deposited just beneath the Northern Till by running

melt waters.

Figurie 4.5: A view into the cube of synthetic zen>-offset seismograms (a) and the cube of intmal w1ocities (b).

The time slice at - 85 ms shows ~flections h m near the bedruck surface.

Chap t er 4: int erpretat ion/correlation

Chap t er 4: Nit erpre t a t ion/correlat ion

Ch ap t er 4: in t erpret at ion/correlation 91

A fairly high (- '1800 m/s) interval velocity block is seen at two-way-time about 30-40

ms. This corresponds to a quiet zone within the Northern Till (see section 4.5) on the

stacked sections and contrasts with a zone of low interval velocity and continuous high

amplitude reflectors near the base of the till. This block can be correlated with a zone

(up to 20 m) of more compact and c l - - r i ch till in the lower part of the Northern Till

observed in gamma logs and during drilling ( M M . Dillon Ltd.. 1990; Boyce et al.. 1995).

4.4 Migrated data volume

There is a fundamental weak link between an- seismic depth section and geology. It is

velocity. Even though reflection time data may be very precise, a dept h section never is

entirely reliable because of the uncertainty in velocity estimation.

As mentioned earlier. in most of the non-seismic imaging methods which work in an air

or water medium (e-g.. radar. sonar. etc.). the velocity of wave propagation is relatively

predictable and known to fairly high accuracy before the field experiment. But. the

velocity of a seismic wave field is variable with position in the earth and is sometimes

even a weak function of local propagation direction.

The configuration of the test survey provided stacking velocity to be determiried with

high accuracy (10 - 20%) down to about 100 ms declining to relatively poor accuracy

below -- 100 ms. However, the Paleozoic section beneat h - 90 nis was known to be quite

uniform, bot h laterally and vertically.

Thus. interval velocity model was considered reliable enough to perform post-stack depth

migration. One view of the cube of depth migrated stacked data is shown in Figure 4.S.

Note that this cube has been rotated 180 degrees with respect to the cube of time stacked

data shown in Figure 4.5a. ..\lthough not very clear in this display, the reflecting horizons

in the Paleozoic section are noticeably smoother than those in the Quaternary section.

This is to be expected from the known geology, and indicates that the velocity model

contains no lateral errors that ivould lead to spurious "pull ups" and "push downs' of

reflect ors.

Chap t er 4: in t erpre t a t ion/correlat ion

4.5 Correlat ion of seismofacies wit h lithofacies

The wealth of data in the survey area produced by the search for a new landfill site

(see Figure 4.1) has provided an opportunity to the glacial geologists to establish a good

geological model of the Pleistocene deposits below the site Pl. Boyce et al. (1995) have presented the most recent geological model (Figure 4.9) showing stratigraphy and

intemal architecture of Late Wisconsin tills and older sediments below the site P 1. Their

model is based on 2-D seismic-reflection, borehole, and outcrop data.

Figure 4.8: A view into the cube of the depth-migrateci data. The depth slice at 95 m shows reflections from near the bedrock surface. A sample of the depth-rnigrated section dong the in-Lne direction together with its geological interpretation is shown in Figure 4.12.

Lithological logs for the nearby boreholes in the site P 1 were obtained using drillers field

reports based on cuttings. Therefore, the best way of correlating the 3-D seismic sections

Chap t er 4: in t erpret at ion/correla t ion

Figure -1.9: Conceptual mode1 showing stratigraphy and interna1 architecture of Late Wisconsin tills and older sediments below site P 1 based on seisrnic-reflection, borehole. and outcrop data. 1, drumlinized surface of Halton Till; 2, sorted (interstadial?) sediments separating Northern and Halton tills; 3, gently dipping erosion surfaces and associated sorted sediments wit hin the upper Northern tili subunit; 4. glaciotectonized sediments comprising a distinct lower Northern till subunit. (From Boyce et al.. 199.5)

wi th geological units was to use the available geophysical logs (gamma and conduct ivi ty )

from nearby boreholes.

In principle. a natural gamma log indicates the amount of gamma rays emit.ted by some

elements as they decay to a more stable state. T h e most conirnon contributors are

uranium. thorium, and potassium. Among these elements, potassium is found at 2 4 %

concentrations in clay rich deposits (Schon, 1996). In practice. natural gamma logs of

sedirnents are used as a qualitative measurement of the amount of clay rninerals in the

strata surrounding the borehole.

Three boreholes bracket the survey area, respectively, 100, 350, 700 m from it in the NW, NE, and SE direction. Quaternary stratigraphic 1init.s f ~ r the srirvey site were identified

using natural gamma logs from the nearby boreholes (see Figure 4.2 for location). The

result is presented in Figure 4.10. A consistent gamma stratigraphy can be identified

within the Northern Till below site P l (Boyce et al., 1995). Some logs however. do show

local variability resulting from lithological changes in the till (e.g., borehole 27).

The low gamma rate (30 countfsec, 'cpsn) in borehole 27 a t depth ranges of 10-16 rn and

the high and fluctuating counts a t depth 55-70 m can be attributed to the interstadial

deposits (sandy fluvial gravels) and Thorncliffe Formation (successions of deltaic sand

and clayey silt) respectively. In boreholes 27 and 17, the Northern Till exhibits relatively

uniform gamma counts (-50 cps) between 16-50 m. In borehole 26 and in other boreholes,

however, the Northern Till shows more variable gamma counts. A zone of increased

gamma in the lower part of the till (about 30 - 45 m depth) can be traced below a large

area of the Pl site. The bedrock a t borehole 17 and 26 with high gamma rate is seen at

depth near 83 m.

Figure 4.10: A simplified subsurface stratigraphy of the survey area. This obtained by simply correlation of the units on three natural gammz !CES 8û3i surrounding boreholes. Where HT=Hal ton Till, IS=Lnterstadial cornplex, NT=Nort hern Till, LC=Lacustrine Sediments, SH=Shale Bedrock.

Table 4.2 is a summary of seismofacies and other properties of the identified units in

seismic data volume. Interpretation of the seismic data began with a blocking or classi-

fication of the seismic responses into seismofacies units. These are defined by their

Table 4.2: Summary of seismofacies and comsponding stratigraphie units

Seismofacies - - - - - - . -. - - - - - - . - - A -. - - - . - - -

Superficial matenal, too shallow to be resolved on stack section

>2 closely spaced continuous reflect ors

2 closely spaced continuous and undulating reflectors, conformable with overlying unit, slightly disconfonnable with undedying reflectors

Few reflectors, with poor continuity, dmost transparent

'Ibo closely spaced, high amplitude reflectors at the base

Semi-continuous flat reflectors, base at disconfomity with underlying unit

High amplitude continuous reflectors, apparently indicating foreset bedding

2 closely spaced flat reflectors

Interval Velocity ( W s )

0.8-1.0 h m static analysis

2.4-2.7 from static analysis, 2.0-2.2 h m stacking vel.

low about 1.7

high about 2.5-2.8

about 2.3-2.5

about 1.7-2.0

about 2.0-2.2

Corresponding S tratigraphic Unit

Top soi1 + superficial glacial materials

Interstadial Complex

Upper Norihem T'iil

Thomcliffe Fm. +

(Sunnybrook Fm. 3)

Scarborough Fm.

Weathered Bedrock

Ch ap t er 4: in t erpret at ion/correldtion 96

seismic characterist ics i-e.. the st rengt h. continuity, and geometry of the reflect ions t hey

generated along with their estimated velocity. For instance, Figure 1.11) shows a corre-

lat ion between seismofacies units and corresponding interval velocit ies along the in-line

44. In general. there is a good correspondence with the stratigraphic facies identified bu

Boyce et al.. (1995).

The uppermost defined seismic facies unit (unit 2) occurs in the depth range 6 to 13

m. Overlaying this unit are superficial materials ivhich are too shallow to be resolved on

seismic sections. In the reflection data this unit consists of 2 (or occasionally 3) closely-

spaced generally cont inuous reflectors wit h undulatory geomet ry. From stat ic analysis

the lateral wlocity of this unit ranges [rom 2400 to 2700 m/s. However. because of the

low velocity superficial cover. the stacking velocity from the surface to base of this unit

ranged from 2000 to 2 0 0 m/s. This unit correlates stratigraphically with the Halton

Till.

Unit 3 occurs in the depth range about 13 to 20 m. It is bounded by two continuous

reflectors indicating the top and the bottom surfaces of the unit. The reflectors are

conformable with overlaying unit but slightly disconformable with underlying reflectors.

Interval velocity drops in this unit to about 1700 m/s. It correlates stratigraphically the

Interstadial complex of sands and gravels that separates the Halton and Northern tills.

Unit 4 is characterized bj* iew reflectors. less continuity. and a high interval velocity and

is closely associated with unit 5 beneath it. Unit -4 (depth 20 to -10-45 m ) is almost

acoustically transparent with interval velocity ranging from 2500 to 2300 m/s. Hoivever,

unit 5 (depth about 40-45 ( top) to 50-55 (bottom)) has slightly lower interval velocity

ranging from 2300 to 2500 m/s and more reflectors in it. Two closely-spaced continuous

reflectors can be identified at the base of the lower part of this unit. Units 4 and 5

respectively correlate the Upper and the Lower Northern Till below the site.

From 30-55 m down to 65-75 m semi-continuous Rat reflectors that exhibit occasional

slight disconformity with the overlaying unit mark a unit 6. The base of this unit appears

to sit disconformably on the underlying reflectors (apparent foreset bedding). Interval

velocity ranges from 1700 m/s to about 2000 m/s, sharply lower than in unit 5 .

Below this depth interval veloci ty becomes increasingly hard to estimate accurately. Thus

it is difficult to be sure whether the rise in interval velocity indicated in the lower part oi

this unit is real or not. The base of the unit is therefore put at the reflection disconfor-

mity. The upper part of this unit clearly correlates with the glacio-lacustrine Thorncliffe

Chapter 4: interpretation/cowefation

Chap t er 4: in t erpret a t ion/correla t ion 98

Formation. Xlthough there is no clear seismic evidence for i t . the lower part of t his unit

may be the Sunnybrook Formation which in this area is clearly identifiable in gamma

Logs .

Unit T is characterized by numerous high-amplitude reflectors at depths from 65-75 m

down to 80-Y5 m. The dipping and overlapping form of the reflectors in this unit is

believed to be an indication of foreset bedding. The interval velocity in this unit, ait hough

less certain than for higher units appears to range from '2000 m/s to 2200 m/s. It

correlates stratigraphically with the deltaic Scarborough Formation.

Unit 8 correlates stratigraphically with weathered bedrock. It is characterized by a pair of

flat-lying continuous reflectors occurring a t depths between 82 to 90 m which generally are

disconformable with the reflectors of unit 7. The interval velocity is probably about 2500-

2700 m/s. Below this unit the true interval velocity in the bedrock probably increases

rapidly to >3200 m/s much more quiclily than is shown in Figure 4. i 1. Two nearly Rat.

low amplitude reflectors a t depths -108 and -140 m can be identified ivithin the Whitby

shale bedrock.

An example view of the post-stack depth-migrated data along the in-line direction is pre-

sented in Figure 4.1-a. Different colors have been applied to dist inguish the seismofacies

units from each other. Figure 4.12b indicates the geological interpretation of the section.

The main geological sequences identified in Figure 4.1Zb correlate very well wit h t hose in

the most recent geological mode1 shown in Figure 4.9. The only exception is the absence

of the Sunnybrook Till. As seen in Figure 4.10, the Sunnybrook Till a t depth - 65-75

m has a niarkedly higher gamma emission rates t han upper and lower formations on the

gamma logs obtained from boreholes BH l T and BH-6. This suggests a clay rich lithology

for Sunnybrook Till than its neighbors but provides no information about their seismic

velocities.

Due to the st ratigraphic characteristic of the Scarborough Formation (i.e.. foreset bed-

ding) the Sunnybrook Till is not expected to be seen at this interval. I t must be identified

on the interval velocity model (e.g., Figure 4.1 1) some where at the lower part of the

Thorncliffe Formation. One possibility for not being able to distinguish the Sunnybrook

Till from Thorncliffe Formation could be the lack of enough velocity contrast betwveen

two units. The other possibility could be the thickness of the Sunnybrook Till which

perhaps was not sufficient to be seen as a separate unit on t h e veiocity model at this

depth.

CDP # O

50 El w

.fi a B

100

150 In-Line 44

figure 12. Seismofacics and concsponding Quatcmary lithofach (a) A ample d o n dong th m-line <tiriection of cbe depm

migratcâ data (sec Littic cube for appioximatc location). @) Geological hiapietation of ibc reirmr wcQn wi!h a m e

vclocitiea h cornparison, narural gamma and lithologic logs h m a n d y boicbolc (-350 m towmd no& of ibc spnicy a m )

are piesated W k c HT=Xaiton 'NI, ïS=htastodial Scdimaits, UNbUpper Nonhcm llll, Rn.. SU.Sunnyîmok

Ra, SC=Scpbomugh Ra, and-whitby Rn. (Me). Ihe logs han ban adaptcû bwi B o p ci ai. (1995).

Chapter 4: in terpreta tion/correlation 100

Because of the dense spatial sampling provided by the 3-D of data volume (trace bin of

3 x 3 m), and the much reduced lateral smearing provided by 3-D ChIP gathering and

3-D migration. the seismic mode1 presented here has higher horizontal resolution than

could be obtained with 2-D surveying techniques. It better delineates rninor structural

features within the till and lacustrine deposits which could be important in geological.

hydrogeological, and ot her similar investigations. Since such feat ures are smaller t han

the boreholes separation. their lateral extent can hardly be determined by the borehole

data.

4.6 Geological details

The dept h-migrated stacked data volume (Figure 4.8) provides important details regard-

ing the internal architecture of geological units belom P 1 and are discussed below.

In te r s t ad ia l u n i t

Figure 4.12 shows two closely-spaced reflectors a t depth about 113-20 meters which cor-

relate wi th sorted Interstadial sediments between the Halton and Northern tills. The

interstadial represents the uppermost aquifer in the study area mith an average thickness

of 5 m. A detailed image of the 3-D geometry of this unit below the survey area is shown

in Figure 4.13. The iipper and lower surfaces of the unit show low relief undulations

which reflect the erosional topography on the underlying 'lorthern Till surface. Step-like

features are also present mhich are believed to be due to cycle skipping during picking of

reflec tion eve~its.

Thin b e d s

Generally. t ills are expected to be massive deposits lacking internal strat.ificat ion. How-

ever, strong, continuous reflectors are seen within the Northern Till a t depths betmeen

about 45-50 m. These reflectors can be correlated with sand and grave1 horizons in the

till which can be traced for several tens of meters in outcrops. These interbeds are how-

ever, often not recovered during drilling and are difficult to correlate in the subsurface

with borehole data alone. The 3-D stacked data volume (Figures 4.5 and 4.8) better

defines the geornetry and areal distribution of interbeds within the till and shows that

they have a lateral continuity of at least 150 m (see Figure 4.12). Interna1 reflectors are

also observed within the Halton Till which likely record the presence of similar sand and

Chap t er 4: int erpre t at ion/correlat ion

Figure 4.13: A detajled 3-D image of the boundaries of the uppermost aquifer, extracted from the cube of depth migrated stacked data.

gravel interbeds.

A less continuous sand and gravel body can also be identified within the Northern Till.

This deposit is elongated in the direction of ice flow (northeast-southwest ) and likely rep-

resents a thin &wedgeV of sand and gravels that perhaps deposited by meltwaters Aowing

in channels a t the ice base (Eyles et al., 1982 called this type of deposit a 'shoestring').

Figure 4.14 shows cross sections of the feature along several in-line depth migrated sec-

tions; Figure 4.15 displays constant dept h slices near its top and bot tom. As seen in the

figure it overs about fifth of the survey area.

Foreset bedding

The 3-D survey clearly shows a foreset bedding within the Scarborough Formation sed-

iments in the depth range 65 to 80 meters (see Figures 4.5a. 4.8, and 4.12a). Foresets

are prograding (dipping) towards the southwest and are consistent with deposition of

the Scarborough sands within a deltaic environment (Iiarrow, 1967; Boyce et al. 1995).

The dipping geometry of reflectors in Scarborough Formation is sharply contrasted with

flat-lying reflectors within the underlying bedrock. This suggests that foresets and less

Chapter 4: in terpretation/correlation

Figure 4.14: The top 50 rn of four depth migrated stacked sections along the in-line direction. They reveal a wedge of contrasting material within the Northern Till (high lighted with green coior).

Figure 4.15: Two depth slices extrzted from the cube of depth migrated stacked data. They are located at the top (depth 32 m ) and bottom (depth 39 m ) of the wedge material within the Northern Till. Light colors correspond to positive polarity.

Chapter 4: in t erpret at ion/correlation 1 03

regular patterns of discontinuity seen in overlaying deposits are real ieatures and not

data artifacts.

Unconformity surfaces

3-D seismic data can be used to better resolve the presence of sequence boundaries and

unconformi ty surfaces in Pleistocene and oider strata below P 1. Two major unconformity

surfaces are represeoted by the base of the Northern Till and the weathered bedrock sur-

face (Figure 4.12). These unconformities are characterized by a high amplitude reflectors

which provide part icularly useful seismic marker horizons for regional strat igrap hic cor-

relation. The unconformity marking the base of the Northern Till is rnarked by a gently

undulating reflector. The bedrock unconformity surface is in contrast, is relat ively Bat

below the P l survey site but often is characterized by the presence of broad channels

elsewhere (Karrow? 1967; Boyce et al. 199.5).

4.7 At t enuat ion

In section 2.2. assumptions were made about the Q of surficial formations and the res-

olution limit of the test survey was set so as not to encounter strong attenuation. In

shooting tests. i t was very hard to obtain seismograms containing much reflect ion energy

above 500 Hz. But it is worth checking whether the attenuation of the high frequency

seismic energy is due to near surface processes or is caused by bulk attenuation process.

4.7.1 Near-surface attenuat ion mechanisms

This section int roduces possible mechanisms for attenuation of the seisrnic energy at

shallow dept hs using the average amplitude spect ra of trace subsets selected from 3 -

D data set. Prior to spectral analysis and in order t o weight trace data appropriately,

frequency independent amplitude corrections were applied to compensate for the spherical

divergence. These were based on the stacking velocity model.

The analysis was carried out at two distinct steps. In the first step. reflection events from

shallow stratn are compared to reflection ewnts [rom deeper horizons. For this proposeo

a trace subset from a selected high SIN 3-D shot gather (traces 60-96 of record 3 ) were

used. The trace subset consisted of 36 traces with offset ranging from 60 to 95 m. The

reflection events are selected at time intervals of 50-80 ms and 130-160 ms respectively

Chap t er 4: in t erpret at ion/correla t ion 10-4

corresponding to a factor of two difference in the total travel path in wavelengths. Figure

4.16 indicates average amplitude spectra and average spectrum ratio of the reflection

events of given trace subset. Although the shallow event has a slight enhancement in

amplitudes around 250 Hz. in comparison with the deeper event. there is no sÿstematic

increase in attenuation a t higber frequencies. This suggests t hat most of the attenuation

must occur a t or near the earth's surface.

In the second step, the average amplitude spectra of two trace subsets containing reflec-

tions from shallow strata (- 25 m ) are compared. The trace subsets have the same zero

offset time window (20-65 ms) but they were selected from different shot-receiver offset

range. The offset for the short-offset trace subset was ranged from 50 to 60 m. But for

the long-offset trace subset the offset range was 65 to 75 m. Both trace subsets were

selected from the same shot gat her used in step one. Figure 4. Li indicates the average

amplitude spectrum and spectrum ratio (long offset to short offset) of the trace subsets.

The results obtained in this step confirms the suggestion that was made in the previous

step. .As shown in the figure. there is frequency dependent attenuation mechanisrn at

near surface materials. The shooting mechanism in my survey was able to generate a

useful seismic signal up to 500 Hz. In the frequency bandwidth of up to 500 Hz. traces

in the longoffset subset indicates an amplitude loss up to 8 db higher than traces in

the short-offset subset. This suggests either that the Halton Till is relatively highly

absorptive. or possibly the overall reflection coefficient of the interstadial sediments t hat

produced the event analysed is frequency dependent.

For the short-offset trace subset. the larger amplitude of frequencies below 100 Hz is

probably due to the contamination of the first few traces by the surface wave arrivals

and/or head waves. In this comparison it was assumed that the variations in amplitude

spectra due to the different physical conditions of the receiver stations are negligible.

This is supportable because similar results were observed in a variety of gathers (where

shot and receiver locations differ).

4.8 Summary

In this chapter after presenting a summary of the regional geology, previous works a t or

near the site PZ were discussed. The various 3-D reflectivity data cubes and :3-D sub-

surface velocity mode1 were presented. Selected sections along the in-line and cross-line

directions through the cubes were used to show the correlation of the seismofacies with

Chapter 4: interpretation/correlat ion

SPECTRUM RATIO (deep/shallow)

FREQUENCY (KHz)

AMPLITUDE SPECTRUM

Figure 4.16: Average spectrum ratio ( top ) and average amplitude spectra ( bo t tom) of two trace subsets of different two-way-tirne windows. The trace subsets included traces 60-96 of one of the shot records. The travel-time windows were selected at 50-80 ms (solid line) and 130- 160 ms (dot ted Iine) respectively.

Chapter 1: in terpretation/correlat ion

SPECTRUM RATIO (long/short)

FREQUENCY (KHz)

A M f LITUDE SPECTRUM

long off. . .. .; .. .. . . .. . , .... ....-..._.. ... ... .

FREQUENCY (KHz)

Figure 3. Il': -Average spectrum ratio ( top) a n d average ampIitude spec t ra ( bot tom) of two trace subsets with the same time window (20-6.5 ms) but different shot-receiver offset range. T h e shot-receiver offset range for solid line was 50-60 m (i.e. traces 45-55) and for dotted line was 65-75 m (i.e. traces 71-8 1 ). Traces were selected frorn the same shot ga ther as in Figure 4.16).

Chapter 4: interpretation/correlation 107

corresponding geological units. Detailed seismic images of the local features extracted

from dept h-migrated st acked data volume were presented. Results correlate well with al1

that is known about the geology of t he survey site.

Chapter 5

Conclusions

Near large industrial urban centers. water supply. sewage, and solid waste disposa1 have

become major issues. A detailed understanding of the st ratigraphy and sedimentology of

near-surface (< 100 m) formations in these areas is of increasing importance for hydroge-

ological and engineering assessments. S tate-of- t he-art engineering seismology current ly

employs a simplified version of the two-dimensional multi-fold seismic reflection methods

used in petroleum seismology. Hoivever, the resolution of very local structures by 2-D

seismic surveys can be insiifficient to identify possible local hydrogeological and engineer-

ing problems.

Since 3-D seismic survey methods that have been developed in petroleum exploration

generally provide a much higher spatial resolution than comparable 2-D surveys. i t was

nat ural to consider IV het her:

1. 3-D seismic methods are technically and logistically feasible for near-surface studies.

2. 3-D surveying techniques yield beneficial results in the shallow environment compaïa-

ble to those found in the petroleum case.

To address these questions, in my Ph.D. program I have investigated the iniaging ca-

pability of 3-D multifold high-resoiution reflection seismology in near-surface complex

deposits and I developed and tested a form of three-dimensional seismology suitable

for environmental, geotechnical, hydrogeological, and other similar surficial exploration

purposes.

.As a consequence of this work, and for the geological condition of the greater Toronto

area, the 3-D shallow seismic survey was practical and led to a subsurface image with

higher spatial resolution. 1 can answer both questions in the affirmative.

Chap ter 5: Con cl usions

Survey technique

Different field configurations can be use to conduct an areal seismic reflection survey.

This study sought to find a forrn of 3-D seisrnology that is capable of providing an

optimum balance betrveen the survey cost. field efforts. and quali ty of the final subsurface

image. Among three acquisition geometries t hat were considered. the orthogonal line

configuration tvas found operationally satisfactory. lt was used to conduct a test small

scale (about 2 0 x 2 0 m ) 3-D seisrnic s u r v e . The following are some advantages of

utilizing the orthogonal line survey geometry:

1. Simplicitj- of the geornetry was t h e major factor for its feasibility. It required minimum

field efforts and a srnall field crew (3-4 persons).

2 . Uniformit- of the overall fold across a considerable portion of tlie survey area ( -

75%).

3. The recording patch configuration provided enough direct and head waves in each

field record to establish an acceptable near-surface mode1 suitabie for estimation and

correct ion of s t a t ics.

However. problems arose. mostly at tlie processing stage. because of the simplicity of the

geornetry and from the asymmetric distribution of the shot lines over the active seisniic

patch. These problems are as follows:

1. For velocity analysis. the seismic traces in each super-CLIP gather contained an

acceptable range and distribution of shot-receiver offsets so that reliable velocity analysis

could be performed. However. i f t hey tvere sorted into sub gathers wit li different azimut h

ranges. the offset distribution of the traces w w not uniform enough to perform azimuth-

dependent veloci ty analysis. in case of appreciable dipping reflectors or s t rong lateral

velocity variations. t his aspect of the acquisition geornetry would need to be improïed

(see suggestions),

2. Despite a relatively uniform offset distribution in both common-shot and cornrnon-

receiver gathers. the distribution of offsets and azimut hs in the CMP gathers rvas irregu-

lar. This can variably affect the character of the CMP stacked trace over the 3-D voliirne

of stacked data. because the noise rejection characteristics achieved by the stack depend

on tlie offset/azimuth distributions.

In spite of the simplicity of orthogonal Line geometry. the 3-D d a t a set provided a good

Chap t er 5: Con cl usions 110

mode1 of subsurface interval velocity. A dense grid of super CkfP gathers (24 x36) over

the entire survey area. selection of the super CMP gathers at the crossing points of the

shot-receiver lines ( to get a broad range of shot-receiver offset ), and refining of the velocity

mode1 after each iteration of velocity analysis were some of the criteria for establishing

such an interval velocity rnodel.

The velocity model was used to perform post-stack depth migration. Although depth

migration did not show severe stratigraphic changes on the seismic sections. its main

usefulness was in providing confidence in the accuracy of the utilized velocity rnodel (i-e..

lack of push downs and pull ups of events on depth migrated sections). The velocity

rnodel was also found to be extremely helpful in identifying reflectors on CSIP stacked

sections and correlating them with lithofacies during interpretation of the final results.

The following is a general point arising from my esperience wit h this survey:

Surface ivave and air rrTave filtering is a major issue in engineering seismology (both 2-D

and 3-D) . .Ml engineering scale seismic surveys employ a single shot and receiver at each

point which generates strong surface waves that must be removed in the data process-

ing stage. In my 3-D survey some of t h e field records had strong air waves and highly

dispersed and scattered surface waves. Their processing required the implenientation of

some special techniques which ma) not be cornmonly used for this purpose. Of sereral

methods tested. the most effective were a I i -L ( Iiarhunen-Loeve) deconiposition tech-

nique to eliminate air waves and a 3-D local slant stacking technique to attenuate surface

waves.

stratigraphic details

Closer esamination of the final 3-D stacked data volume. revealed the following strati-

graphie featiires at the test site:

1. Although previous studies have found evidence that the Late Wisconsin Tills (Halton

and Northern) are separated by an interstadial deposit. this survey provided a 3-D image

of the interstadial unit beneath the 3-D survey site.

2. Generallj-. tiiis are expected to be a massive deposits lacking interna1 stratification.

Hoivever. strong. highly continuous. reflectors are seen within the Northern Till. They are

of much greater continuity and extent than has previously been realized (From outcrops

and/or drilling). Also a disconformable. local wedge of apparently different material

Chap t er 5: Con c h i o n s 11 1

(probably sand and gravel) was iound in the middle Northern Tiil elongated in the

direction of ice flow (nort heast-southwest ). It likely deposited by meltwaters flowing in

channels at the ice base.

3. In addition to the clearly recognizable packages of the Late Wisconsin Tills. Middle and

Early Wisconsin lacust rine sediments. and Paleozoic bedrock format ion on the st acked

data volume, a south-westerly dipping ioreset bedding was identified within the deltaic

Scarborough sediments.

In general. the results of the test survey including better lateral resolution. 3-D image

of locai ieat ures. 3-D su bsurface veloci ty model, etc.. indicated t hat the orthogonal line

geometry is a suitable field configuration to conduct a Iow-cost small scale 3-D seis-

mic reflection survey to obtain detailed image of subsurface geology for hydrogeological.

envi ronment al. and engineering assessment.

Suggestions

Xs mentioned eariier. some of the CMP bins have traces with only two or three different

azirnuths (see bins 27-30 in Figure 2.7). This happened due to the asymmetric distribu-

tion of shot lines over the patclieç of the designed 3-D survey geometry (i-e.. not including

shot points along the third shot line in the patch). Figure 5.1 indicates the distribution

of new offsets and azimuths for the same CMP bins alter including the shot points along

the third shot line.

As seen in the figure. the overall fold distribution rernained uniform but the maximum

fold rose t o 18. Implementation of t his survey geometry increases the total shot numbers

40% compared to the orthogonal geometry used to collect 3-D seismic data. This in turn

will increase the survey cost and field efforts.

Offset and azirnuth distribution ranges a t each CMP bin can be further improved by

shifting every other shot line about half a shot spacing ( 3 m) along the cross-line direction.

Figure 5.2 indicates offset and azirnuth distributions for the same CDP bins as in Figure

rj.1 after shifting every other shot line along the cross-line direction. The improvement

is seen most clearly dong CMP line 50 in Figure 5%.

Data processing brought to light several problems related to the use of a simple orthogonal

line geornet ry.

Chapter 5: ConcIusions


IN-LINE BIN NUMBER


IN-UNE BIN NUMBER

Figure 5.1: Orthogonal 3-D survey geometry after including shot points d o n g the third shot line in the patch. (a) Fold distribution over survey area. ( b ) Offset-azimuth distribution over the same area as in Figure 2.ïa. Note that shorter lines may be hidden by longer ones in t h e same direction.

Chapt er 5: Con clusions


IN-LINE BIN NUMBER


Fold

18

15

12

IO

9

8

6

5

4

3

2

1

IN-LINE BIN NUMBER

Figure 5.2: Orthogonal 3-D survey geometry after shifting of every second shot line about half a shot spacing (3 m) dong the cross-line direction. (a) Fold distribution over survey area. ( b ) Offset-azimuth distribution over the same area as in Figure5.la. Note that shorter Lines may be hidden by longer ones in the same direction.

Chap ter 5: Condusions 114

1. Generally, shooting a t single point generates strong surface waves. These must be

removed in processing. This can be facilitated by use of straight lines of uniformly and

relatively closely spaced shots and detectors.

2. To obtain a uniform SIN ratio and trace character over the 3-D volume of stacked data.

the distribution of offsets and azimuths in the CMP bins should be as uniform as possibie.

This could have been achieved with a less linear shot and receiver distribution, but would

have conflicted with 3 above. It is recommended that in the future. some research should

be devoted to design an acquisition geometry that is an optimum compromise between

L and 2.

Referen ces

References

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Born. W.T.. 19-11? Attenuation constant of eart h niaterials: Geophysics. 6. l X - L-LS.

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R eferen ces 116

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Appendix A

Seismic wave at tenuat ion

The importance of at tenuat ion in down scaling a convent ional (pet roleum scale) survey

geometry to an engineering scale has been discussed in chapter 2 (see section 2.1.1 ). This

appendix provides definitions of absorption coefficient (a). quality factor (Q). and t heir

relations hi p.

The strong attraction of shallow seismic reflection method as a geophysical tool is its

potential for high spatial resolution. The shorter the duration of the seismic pulse. the

greater the resolu t ion achievable. Minimum pulse widt hs are O btains by maximizing the

frequency bandwidth of the signal (Bracewell. 1986). X Iarge nurnber of seismic attenua-

tion mechanisms present in the earth (Sheriff, 1975), each of which having some frequency

dependence, but toget her producing a form of attenuation t hat is nearly linear wit h fre-

quency. This frequency dependence causes the pulse shape to change as it propagates

t hrough the eart h.

Seismic waves propagating through the earth are attenuated by conversion of some Irac-

tion of their energy to heat. At two different distances from the source (e.g. r, and x )

the amplitude for a wave propagating in a homogeneous medium can be described by

where A ( x ) and A(x,) are the amplitudes at the distances x and x, from the source

point respectively. and cr is the absorption coefficient. The ratio (%)" is a general terrn

of amplitude loss due to geometrical divergence. The exponent n is determined by the

geometry of the wave propagating, n = O for plane waves, n = f for cylindrical waves.

and n = 1 for spherical waves.

Appendix A: At tenuation

In the case of plane waves. Equation A. 1 becomes

furt hermore, assuming xo = 0. and A(x0) = -4, as initial amplitude a t the source position

(or any arbitrary reference point). Equation A.2 is changed into

which can be derived lrom general plane wave equation in a homogeneous medium by

introducing a complex wave number.

From Equation A.'. the absorption coefficient for two different positions is

In Equation A.4 if x - x, = A, then CI will show the loss in amplitude per cycle ( Equation

A.5) which is used to define a new quantity called logarithrnic decrement 6 (Equation

X.6)

where r is t h e velocity of wave propagation. and f the Irequency.

.An alternative measure of the ability of a rock to attenuate the seismic waves is the

specific dissipation funct ion defined by

where Q is quality factor. In this definition A E is the amount of energy dissipated per

cycle of a harmonic excitation in a certain volume. and E is the stored elastic energy in

the system in the same volume.

Appendix A: At tenuation 123

As the absorption coefficient a is the fractional loss of amplitude per unit distance (Equa-

tion A.4) and % is the fractional loss of energ-y per wavelength. t he two quantities are

related by the wavelength X

Ignoring small changes of phase velocity 27 with frequency f . Q is approximately

Experimental da ta show that Q is nearly independent of frequency over a broad frequency

range especially for dry rocks (Born 1941; McDonal et al. 195s; Attewell and Ramana

1966; Iijartansson, 1979; Nur and Winkler 1980; and Tittmann e t al. 19Sl). Unconsoli-

dated sediments generally have highest attenuation properties among rocks. This means

that a significant amount of the seismic energy is consumed when waves pass through

this sediments (on the way down and again on the way up).

Appendix B

Karhunen-Loeve t ransform

The Iiarhunen-Loeve (K-L) transform was found to be an effective method of attenuating

the air-wave energies from the 3-D data set (see section 3.3.2). To understand better the

technique, its basic mat hemat ical formulation is discussed here.

The Iiarhunen-Loeve (K-L) transform optimaliy extracts coherent information from mul-

tichannel input data in a least squares sense. This approach has a different number of

applications in seisrnic data processing (Levy et al., 1983; Ulrych et al.. 1YS3: Jones and

Levy. 1987).

In the field of image processing the K-L transform bas been widely applied to digital image

enhancement (Ahmed and Rao. 1975) and data transmission and analysis ( Kramer and

Mat hews. 19.56).

Prior to presenting t h e mat hematical formulation for I i-L transformation. it is desirable

to see what conceptually the 1;-L transformation does.

For a given rnultichannel data set with n seismic traces -G( t ) , at each instant in time (say

t o ) da ta samples of the n seismic traces -Yi(to) can be considered as the coordinates of a

point in n dimensional space. As time progresses the point will trace out a pattern in n

dimensional space. The patterns obtained from well correlated portions of the input data

set will tend to concentrate in some particular areas. Figure B.1 schematically indicates

a pattern obtained by a data set with two traces.

Since the K-L transformation is merely an spatial rotation of the coordinate axis, it is

tried to choose the rotation coefficients in such a wvay that a few number of rotated axis

correspond to the major dimensions of the above mentioned patterns. Consequently,

these few rotated axis will contain most of the information about input data set and ne-

rlppendix B: K-L transform

Figure B. 1: Representation of data samples for a case with two traces. Ases S 1 and .Y2 are t lie original input traces but Y 1 and Y2 are the new set of traces t hat form an orthogonal Lasis for rotated coordinate.

glecting the rest of axis during reconstruction of the input data. will result in a minimum

error.

B. 1 Mat hemat ical formulation

Given a set of n real signals (e-g. seismic traces) .Yi(!) and an ( n x n ) transformation

(rotation) mat ris A. a set of alternative data can be constructcd as a linear coinbination

of the input signals

where a;, are elements of the transformation matrix and O 5 t 5 T. The signals \ ' i ( t )

are chosen such that they form an orthogonal basis. These basis functions are referred

to as the principal components. Consequent ly, using the inverse transformation matrix

B with elements biJ one may reconstruct the original data set frorn a linear combination

of the Y$) .

Appendix B: K-L transform

Figure B.?: Schematic representation of the K-L transformation. where Si( t ) are input seismic traces, k;(t) are the principal components, and .<-;(t) are reconstructed seismic traces.

where .qi(t) is the it h reconstructed signai. and rn is the nurnber of basis functions used

in reconstruction. Figure B.?. In case of rn = rz the reconstructed signal will be esactly

sarne as the input one (.C,(t) = -t-'(t))' but when rn < n the Si([) will approxirnate the

input signal S i ( t ) .

The question arises here is what choice of aij and bij coefficients will give the best ap-

proximation of the input signals.

Kramer and 3Iathews (1965) showed that for a given rn the transformation matrices A

and B will be t hose that rninimize the least-square error:

to satisfy this. according to their results the rows of the transformation matrix A consist

of the normalized eigenvectors of t h e covariance matrix C of the input da ta

t O represen t t hese eigenvectors. consider a spectral decomposi t ion O t

trix C as:

( B . 4

the covariance ma-

where R is an ( n x n ) matrix whose columns contain the normalized eigenvectors r,,

( C r = A r ) The matrix A is an n-length diagonal matrix containing the eigenvalues

of the expression in descending order Al 2 X2 . - - 5 A,. The eigenvalues are significant

in tliat they indicate the relative strength of each basis function in reconstructing of the

input data set.

Finally, by finding the eigenvectors of C . the transformation matrices A and B can

be determined. To satisfy the condition given by Equation B.3. it can be shown that

B = A?

Appendix C

Slant stack

The local slant st.acking technique was a successful method to attenuate the strongly dis-

persed surface waves effectiveiy (see section 3.3.2). To understand better the technique.

its mat hematical formulation is given here.

When an explosive source explodes. seismic wave propagates nt al1 angles. each angle s tn ( i ) corresponds to a certain ray parameter p = . According to the Snell's Law. seismic

ray ivith a certain p value changes its direction of propagation a t each layer boundary.

and generates a family of reflected ray paths. As seen in Figure C.1. for a given seismic

ray ivit h a particular p value the signal is recorded at al1 offsets. In other words. receivers

a t al1 offsets record a plane mave \vit h a p value same as original ray. If this is the case.

then each shot record can be considered as a superposition of plane ivaves of man- p

values.

2-D Fourier transform is one way to decompose a shot gather into its plane-wave com-

ponents. each ivith a unique frequency and each traveling a t a unique angle from the

vertical direction. The domain of two-way travel time and ray parameter ( r - p), where

each trace corresponds to a particular ray parameter p. is another way to decompose the

wave field into its plane-ivave components. This can be done by T - p transform or slant

stacking.

The T - p transform is simply looking on seismic records (in t - x domain) for events of

some particular ray parameter p. This amounts to scanning records to find the places

ivhere the events are tangent to a straight line of dope p. The search and analysis will

be easier if the data is replotted with linear moveout (LMO).

Two steps typically are used in synthesizing plane waves. First, a linear moveout correc-

Appendix Cr Slant stack

Figure C.l: a) Schematic representation of seismic rays that propagate at different angles away from the source. 6 ) Some raypat hs for a part icular p value. corresponding to a single trace in the ( r . p) dornain.

tion is applied to the data (Claerbout. 1985):

where p is the ray parameter. x is the sliot-receiver offset. t is the two-way travel tirne.

and T is the linearly moved out time. After LMO. an event with slope p on input seisrnic

record is flat. Next. the data are summed over the offset axis to obtain

where .+(r. p ) represents a plane wave with ray parameter p. This is the same as summing

(or stacking) the amplitudes along slanted line in ( t . x ) domain

by repeating the Là10 for various values o l p and performing the sumrnation. the cornpiete

slant-stack gather is constructed.

in r - p domain seismic events are well separated. In particular. ground-roll transfers

to a point a t time zero, refractions transfer to points at their zero offset intercept times

Appendix Cr Slant stack 130

and reflect ion hyperbola t ransform to ellipses. Significant ly, the ellipses do not cross one

another, even if the reflection hyperbola do cross each other in input seismic record.

.4n inverse transform from the T - p domain back to t - x space can be easily constructed. d r This is accomplished by a similar siant stack on the r - p record along siopes corre-

sponding to a particular x. Thus. the same algorithm is used in performing the inverse

transform t hat is applied in const ructing the forward transform.

C .1 Mat hemat ical formulation

The proper implementation of the r -p method for seismic data excited by a point source.

requires the computation of a Cylindrical slant stack. Usually. the Cartesian slant stack

is computed instead as an approximation to the geometrically correct procedure. Here

a formulation of the Cartesian slant stack (for both line and point sources) in a uniform

medium is described. For more details about Cylindrical formulation of the slant stack

see Chapman (197s) and ( 1981).

C.1.1 Line source

This section discusses the theory of slant stack technique for a line source in a uniform

medium. The source is assurned to be along the y axis of a Cartesian coordinate. The

acoustic wave eqiiation in t his case reduces to

A continuous plane wave propagating away from the y-axis can be expressed as

where g is the expansion coefficient. p and q are horizontal and vertical slowness respec-

tively. Superposition of such waves each with frequency w and a horizontal slowness p

can be written as

Appendix C: Sfant stack 1:31

By definition the slant stack of data recorded at the surface ( 2 = O ) for a particular

slowness p' is given by

+m

@(r. pl) = / u(r + p'r. r. O)& -Ca

the rest of computation helps to obtain a mathematical expression for inverse slant stack

(i.e. reconstruction of u ( t . x . 2 ) ) . Let us first substitute Equation (C.1) into Equation

The factor sgn(w) = arises from the change of variable in the innermost integral from Iwl

x to

Equation C.4 is an inrerse Fourier transform and its Fourier transform yields

from Equation ( ( 2 . 5 ) the expansion coefficient G(w, p ) is determined as Fourier transform

of the slant stacked data,

For the rest of computation in order to perform inverse Fourier transform the term s g n ( ~ )

requires to invoke the Hilbert transform. By definition the Hilbert transforrn of d' is

- l +" $ ( t 7 P ) ~ ~ "('7 P) = r - t

After taking the Fourier transform of Equation (C.7)

Appendix C: Slant stack 1 :3'2

and changing variables to y = &*(r - t ) in the inner integral.

substituting Equation ((2.9) back into Equation ( C S ) gives

After sitbstititting of Equation (C. IO). the inverse Fourier transform of Equation (C.6)

becomes

Equation (C. 1 ) after substituting g from Equation (C. 11) changes to

and by substituting Equation (C.12) it yields

(C. 1 3 )

Equation (Ci. 13), with z = O is the inverse siant stack for line source in a uniform medium.

Appendix C: Slant s t ack

C.1.2 Point source

In this section slant stack and inverse slant stack formulations for a point source case

are determined. The source assumed to be at the ongin of a Cartesian coordinate in the

uniform medium. The acoustic ivave equation for this case is

and superposition of generated plane waves at point (t.s.y.z) looks like

- i u ( t - p , r - p y y - q : ) d u ( t , X . y. 2) - - J-, Je, J-, W. pz. P , PY (C. 14)

Generalization of slant stack Equation (C.2) for point source can be erpressed as

Substituting Equation (C. 14) into Equation (C. 15). and perforrning the same integrations

as in Equation (C.3) for both pairs (3. p,) and (y, p,) yields

wliere two s g n ( d ) factors have canceied. The inverse Fourier transform of Equation

(C.16) is

and its inverse Fourier transform leads to

Appendix C: Slan t stack 134

Finally. the inverse slant stack for a point source is obtained by substituting both y and

C; into Equation (C.14).

Appendix D

Migration

In a conventional CSIP stacking, no matter where in space the refiection actually occurs.

each event on a stacked section is plotted directly beneat h the source-receiver midpoint.

In order to get an accurate subsurface image from seismic data one needs to move dipping

reflectors into th& true subsurface positions and collapse diffractions. Seismic migration

techniques are usually used to construct the reffector surface from the recorded seismic

data.

Seismic migration consists of two steps: extrapolation and imnging. E'ct rapolation means

reconstruction of the wave field a t any depth from seismic data recorded a t the earth's

surface. Imaging is a principle which allows one to obtain local reflectivity from estrap-

olated data. Since imaging is a trivial task. migration schemes differ in their approach

to the wave extrapolation problems (Stolt and Benson, 19S6; Yilmaz. 1987).

Since phase-shift migration technique was used to perform 3-D time and dept h migrations

on the 3-D slmthetic zero-offset stacked data set (see section 3.4.2). fundamentals of the

technique is reviewed in this appendix.

D. 1 Phase-shift migration

Phase-shift migration technique (Gazdag, 1975) is based on the idea that downward

continuation arnounts to a phase shift in the frequency-wavenumber domain. The imaging

principle is inïoked by summing over the frequency components of the extrapolated wave

fields nt each depth step.

The theory of wave extrapolation is based on the assumption that the zero-offset com-

Appendin Dr Seismic migration 1 :36

pressional wave data. defined in the (x.t) domain, satisfy the scalar u-ave equation

with u = u ( x . 2 , t ) , where x is the midpoint variable, z is depth. t is two-way traveltime.

and c is the half relocity. To obtain a better understanding of Equation D.1. i t is helpful

to express P as a 2-D Fourier series

where I;, is the midpoint wavenumber and u is the temporal frequency. Substituting

Equation D.2 into Equation D. 1 yields

which has an analytic solution

for each C,, where k, can be espressed as

which often is called the dispersion relation of scalar wave equation. Since the downward

estrapolation of recorded seismic data is an inverse process. the positive sign in Equation

D.5 is used

which corresponds to waves moving in the reverse-time direction. Substituting Equation

D.6 into Equation D.4, one obtains the desired expression for waves extrapolation

A ppendix D: Seismic migration

Equation D.7 also is the solution of the lollowing one-way wave equation

which is the evac t extrapolation equat ion for constant veloci ty. Veloci ty variations wi t h

respect to the depth variable are accommodated by simply varying the velocity with z

in Equation D.7.

Under the horizontally layered veloci ty assumption. the simple analytic solution expressed

by Equation D.7 is the basis of the phase-shift migration method. Its accuracy is due

to exact dispersion relations (Equation D.6) and the esistence of analytic solution to

Equation D.8 which is unconditionally stable in both two and three dimensions.

D. 1.1 P hase-shift plus interpolation migration

If the migration veloci ty has no horizontal variations. the extrapolation of the zero-offset

data can be expressed by an exact wave-extrapolation equation in the wavenumber-

frequency domain (Equation D.8). The analytic solution of this equation calls for a

phase shift applied to the Fourier coefficients of the zero-offset data.

In the presence of lateral velocity variation. the exact ivave extrapolation equation is

no longer valid. To circumrent this problem. the exact expression can be approximated

by some series expansion (Hatton et al.. 1981; Gazdag, 1980) which can accornmodate

horizontal velocity variations. These equat ions are t hen solved numerically in ( x,t ) or

(x.&) domains.

Gazdag and Sguazzero ( l98-L) generalized the phase-shift met hod to handle lateral ve-

locity variations. which is called Phase-shift plus interpolation migration ( PSPI). The

PSPI extrapolation rnethod consists of two steps. In the first step, the wave field is

estrapolated by the hase-shift method using n laterally uniform velocity fields. The

intermediate results are n reference wave fields. In the second step, the actual migrated

wave field is computed by interpolation from the reference wave fields.

Using two vetocities pi and vz. which are defined as the extrema of a ( r . z )

Appendix D: Seismic migration 138

The phase-shifted wave fields Lrl(k,. 2 + A-.;) and 1Y2(kr, z + A=. d) are computed

t hen inverse t ransformed. resulting in the reference wave fields Cil (x. : + 0 2 . &) and

/T2(x7 z + A:. d). which serve as reference data from which the final result i ' ( x . 2 + Az, &)

is obtained by interpolation in the following manner.

According to Gazdag and Sguazzero (1984). first. the Fourier coefficients are expressed

in terms of their modulus and phase angle:

Second, the modulus and phase of the end results are obtained by means of linear inter-

polat ion:

from which the phase shift expression for laterally variable velocity can be written

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