Aerial View Eucalyi River, PeruAerial View Eucalyi River, Peru

Seismic View: 2 km Deep Meandering RiverSeismic View: 2 km Deep Meandering River

Overview of Seismic Overview of Seismic ImagingImaging

Jerry Schuster Jerry Schuster

KAUSTKAUST

OutlineOutline• Forward Acoustic Problem Forward Acoustic Problem

• Inverse Acoustic Problem Inverse Acoustic Problem

• Seismic Experiment Seismic Experiment

• Seismic Migration Seismic Migration

ZO Seismic SectionZO Seismic SectionD

epth

Dep

th

Tim

eT

ime

c c 2 2 2 2

c c 1 1 1 1

Monterey Optical Image Monterey Optical Image

Monterey Seismic Image Monterey Seismic Image 0 km0 km

2 km2 km

0 km0 km

0.1 km0.1 km

Acoustic Forward ProblemAcoustic Forward ProblemD

epth

Dep

th

cc22

cc11

Given:Given: dd + k + k dd = = oo22 22 k = k = cc

Find:Find: d(r)

Soln:Soln:

rorr )()(grd)(

dr

PressurePressure SourceSource

Goal: Compute ZO Goal: Compute ZO Seismic SectionSeismic Section

Dep

thD

epth

Tim

eT

ime

c c 2 2 2 2

c c 1 1 1 1

rorr )()(grd

)(

dr

rorr )()(grd

)(

Common Shot GatherCommon Shot GatherD

epth

Dep

thT

ime

Tim

e

Common Midpoint GatherCommon Midpoint GatherD

epth

Dep

th

MidpointMidpoint

Tim

eT

ime

Normal Moveout CorrectionNormal Moveout Correction

MidpointMidpoint

Dep

thD

epth

Tim

eT

ime

Stacked TraceStacked Trace

MidpointMidpoint

Dep

thD

epth

Tim

eT

ime

Stacked Seismic SectionStacked Seismic SectionD

epth

Dep

thT

ime

Tim

e

OutlineOutline• Forward Acoustic Problem Forward Acoustic Problem

• Inverse Acoustic Problem Inverse Acoustic Problem

• Seismic Experiment Seismic Experiment

• Seismic Migration Seismic Migration

What is the Problem?What is the Problem?

V/2V/2

Dep

thD

epth

Tim

eT

ime

Events Can Originate Updip Events Can Originate Updip

Incorrect location. You think Incorrect location. You think events originated directlybelow geophones.events originated directlybelow geophones.

D=

VT

/2D

=V

T/2

What is another Problem?What is another Problem?D

epth

Dep

th

Tim

eT

ime

Events Originate Pt. Diffractors Events Originate Pt. Diffractors

0 m 30 m0 m 30 m

0 km0 km

30 m30 m

cornercorner

ZO DataZO DataZO DataZO DataMigration Migration (Relocates Reflections back to Place of Origin)(Relocates Reflections back to Place of Origin)

0 km 7 km0 km 7 km

0 km0 km

3 km3 km

Given: Given: dd = L= LooSeismic Inverse ProblemSeismic Inverse Problem

Find: Find: o(x,y,z)o(x,y,z)

Soln: min || LSoln: min || Loo--dd || ||22

oo = [L L] L = [L L] L ddTT TT-1-1

‘‘

L L ddTT

migrationmigration

waveformwaveforminversioninversion

OutlineOutline• Forward Acoustic Problem Forward Acoustic Problem

• Inverse Acoustic Problem Inverse Acoustic Problem

• Seismic Experiment Seismic Experiment

• Seismic Migration Seismic Migration

2-w

ay ti

me

2-w

ay ti

me

(x-(x-xx ) + y ) + y 2222

.5.5ccssrrss ==

rrss + + TToo

ZO MigrationZO Migration SmearSmear Reflections along Fat Circles Reflections along Fat Circles

xxss

rr

d(d(xx , ) , )rrssss

2-w

ay ti

me

2-w

ay ti

me

ZO MigrationZO MigrationSmearSmear Reflections along Fat Circles Reflections along Fat Circles

rrssd(d(xx , ) , )ss

xx

& & SumSum

2-w

ay ti

me

2-w

ay ti

me

ZO MigrationZO MigrationSmearSmear Reflections along Circles Reflections along Circles

rrssd(d(xx , ) , )ss

rr

& & SumSum

ZO Migration ResolutionZO Migration ResolutionIntersection of Fresnel ZonesIntersection of Fresnel Zones

Intersection of Fresnel ZonesIntersection of Fresnel ZonesVertical Res. = Near-Offset TracesVertical Res. = Near-Offset Traces

ZO Migration ResolutionZO Migration ResolutionIntersection of Fresnel ZonesIntersection of Fresnel Zones

Intersection of Fresnel ZonesIntersection of Fresnel ZonesHoriz. Res. = Far-Offset Traces Horiz. Res. = Far-Offset Traces

Why is Pt. Scatterer Response of MigrationWhy is Pt. Scatterer Response of Migrationa Blurred Version of Point?a Blurred Version of Point?

MigrationMigration:: m = m = L L ddTT

MigratedMigratedSectionSection

DataData

butbut dd = = LL rrLL rr

Migration SectionMigration Section = = Blured ImageBlured Image ofof r r

Seismic Section Seismic Section

Tim

eT

ime

12 km12 km

0 km 7 km0 km 7 km

0 km0 km

3 km3 km

0 km 7 km0 km 7 km

0 km0 km

3 km3 km

Migration Least Squares MigrationMigration Least Squares Migration

Seismic Imaging CourseSeismic Imaging Course

• Kirchhoff & Beam MigrationKirchhoff & Beam Migration

• Phase Shift-Like MethodsPhase Shift-Like Methods

• Reverse-Time MigrationReverse-Time Migration

• Full Waveform InversionFull Waveform Inversion