florence delprat-jannaud and patrick lailly · the insidious effects of fine scale heterogeneity in...

Florence Delprat-Jannaudand

Patrick Lailly

The insidious effects of fine scale heterogeneity in reflection seismology IMA05

Exploration seismology (1)

– acquisition– seismic imaging– interpretation

(explo, reservoir)


Exploration seismology (2)

3500 6500

P impedance S impedance

(g/cm3.m/s) 1300 3500(g/cm3.m/s)

essential to evaluate the reservoir properties


Reflection seismology and prospection for hydrocarbons

• Target– down to 10 Km– burried beneath a complex overburden (rocks are

very heterogeneous materials)• Horizontal and vertical resolution

– a few tens of meters (???????)– a remarkable performance

• 3D reflection seismology: an essential tool for the prospection for hydrocarbons


Specificity of our problem

• Looking for a 3D high resolution image (and, if possible, quantitative) image

• Propagation takes place within quite a heterogeneous medium


P and S velocities, density,...

• Undergo large range variations (1 to 3)

• At very different scales


Imaging in exploration seismology

• Modern sophisticated imaging techniques– require the P and S velocity distributions to be

determined accurately geometrical optics based techniques generally used

– quantitative imaging achieved by prestack depth migration (linear inversion procedure)

• All these techniques rely on a very simple conceptual wave propagation model The exploration seismologist’s standard model


The exploration seismologist’s standard model (Ray + Born)

• Propagationdownwards

• Reflection or diffraction

• Propagationupwards


Goal of the paper

• To raise doubts about the relevance of the exploration seismologist’s standard model especially when we look for:– high resolution quantitative imaging – targets buried beneath a rough and thick overburden

some challenges

• Restriction to acoustic wave propagation


Outline

• Introduction• The exploration seismologist’s standard model • A 1D benchmark of the exploration

seismologist’s standard model• The parameters that govern 1D wave

propagation• 2D wave propagation• So what ?


A simple idea for a complex problem ?

Field data measured with dz =15cm

Velocity (m/s)

2.0D

epth

(km

)

20000.0

4.0

6000 2.0 2.4 2.8

Density (g/cm3)

• We want the background to be – smooth in order to

make use of geometrical optics

– close to the quite unsmooth actual medium (Born approximation)

• How can we conceive an appropriate background medium ?


A simple idea for a complex problem ?

• The single scattering assumption :

Can we really neglect the superposition of the innumerable multiple scattered events ?

Let’s have a look ...

Field data measured with dz =15cm

Velocity (m/s)

2.0D

epth

(km

)

20000.0

4.0

6000 2.0 2.4 2.8

Density (g/cm3)


Outline

• Introduction• The exploration seismologist’s standard model :

a simple idea for a complex problem ? • A 1D benchmark of the exploration

seismologist’s standard model • The parameters that govern 1D wave



Why a restriction to 1D wave propagation?

• Such a restriction allows to get rid of concerns associated with the use of geometrical optics...

• ...and to concentrate on the single scattering assumption (that underlies “Born approximation” )


Wave propagation and standard model

• 1D model and 1D seismic excitation• Wave equation

with boundary conditions

and initial conditions

21 1 02( ) ( )PP

z z z ztκ ρ� �∂ ∂∂ − =� �∂ ∂� �∂

0(0, ) ( )P t P t=

( ,0) 0

( ,0) 0

P zP zt

=��

∂� =� ∂�


The 1D wave equations

• Standard depth variable

• Depth measured in terms of the traveltime

– waves propagate at a velocity equal to 1

2

2

1 ( ) 0( ) ( ) ( )

P c z Pz c z t z z zσ σ

� �∂ ∂ ∂− =� �∂ ∂ ∂� �

2

2

1 1 0( ) ( )

P Ptσ τ τ σ τ τ

� �∂ ∂ ∂− =� �∂ ∂ ∂� �

τ

z


Linearization in the 1D wave equation

• Chosen backgroundWave propagation in the background : just according to

geometrical optics!• Linearization procedure : linearization with respect to the

reflection coefficient time series• Standard model: convolution of the reflection coefficient

(two-way) time series with the seismic wavelet• The linearization error reflects the “multiple scattering”

effects Can we really neglect the superposition of the

innumerable multiple scattered events ???

( ) (0)bg trueτσ σ=


Evaluation of the standard model Experimental protocol

• Comparison between the seismic responses according to– the standard model– a reference solution (F.D. waveform modeling)

• Seismic acquisition :• seismic source : Ricker wavelet with a central

frequency of 30 Hz• receiver located at z = 30 m

• Models: velocity and density well logs at a fine scale


First geological environment

• Field velocity and density profiles measured with vertical step dz =15 cm.


Comparison between seismic

responses

The standard model works fine !


0.0

0.6Ti

me

(s)

0.2

0.8

1.0

0.4

1.0

1.6

1.2

1.8

2.0

1.4

Second geological

setting

Beyond 1 s, it becomes impossible to find any match between the standard and reference seismic responses


-10 0 10ReferenceReference

-10 0 10Standard

1.6

2.0

2.4

Tim

e (s

)

-0.2 0 0.2Reflection coefficients

0.0

2.0

Dep

th(k

m)

Not yet convinced ?

Who can foresee the presence of a perfectly reflecting basement looking at the reference ?

1.0

3.0

4.0

5.0


Third geological setting

• A synthetic sedimentary sequence– described at a fine scale– inspired from a real situation– including lithologic and velocity logs– from 0 to 4.4 km depth

• Motivations– no confidentiality– avoid errors in well logging


Third geological environmentConstruction of a synthetic model

• Geological interpretation of an actual well log– identification of macro-sequences– for each of them, determination of the percentage

of the different occurring facies, of the range of thickness of the beds associated with these facies

• Simulation of a synthetic well that matches the statistical properties

• For each macrosequence, identification of velocities corresponding to each lithology from the field sonic log

• Estimation of the density from Gardner ’s law


Third geological

setting


Third geological setting

density

velocity


Third geological

setting

Again, for large times we cannot find any match between the standard model and reference seismic responses


Third geological

setting

Who can foresee the presence of a perfectly reflecting basement looking at the reference ?


What is happening?

VSP Acquisition


In summary

• We have observed:– that the multiple scattering phenomenon can be far

from negligible– this, to an extent that may disturb many exploration

geophysicists– the reason may lie in the fine scale heterogeneity

which is (almost) always ignored• Let ’s now try to understand


Outline






Parameters that govern wave propagation

• The depth of the target (propagation time) The multiple scattering phenomenon is

cumulative

• The roughness of the overburden


Parameters that govern wave propagation

• The depth of the target (propagation time)

• The roughness of the overburden a feature that may be eliminated through 1D

homogenization theory depending on …

• … the considered seismic frequency band


Homogenization theory (1)

• Aim to simplify a given medium while keeping the

seismic response unchanged• Procedure (1D, quasi-static)

Adequately (?) smooth the medium by computing moving averages. Given a sampling interval dz, compute, on each interval, the – harmonic average of the bulk modulus

– arithmetic average of the density

( 1) 1( )

h dz

h hdz

dz dζκ κ ζ

+

= �( 1)

( )h dz

hhdz

dz dρ ρ ζ ζ+

= �


The homogenized model fordifferent smoothingvelocity density


Homogenization theory (2)

• The important question : to what extent can we simplify a medium while

keeping its seismic response unchanged ?• It depends on the considered seismic

frequency band (Bamberger, 1977):– a lot for a low frequency source– possibly very little for a high frequency source


Homogenization in standard / reference models

• Standard model :– you can filter the reflection coefficient time series as

long as you do not enter the seismic frequency band– this filter can be defined a priori: it does have to

depend on the considered propagation time and on the considered medium

• Reference model:– the filtering procedure is more complex– the allowed amount of smoothing does depend on the

considered medium and on the considered propagation time


Homogenization for a 30 Hz central frequency (1)

• Homogenized model obtained with dz = 4m has an almost identical seismic response

• The base of the homogenized model is deeper in traveltime

• The medium has been simplified but the remaining heterogeneitymaintains the complexity of wave propagation


Homogenization for a 30 Hz central frequency (2)

• Can we simplify further ?• No, for dz =16m we

observe significant discrepancies

• Standard resolution criterion– holds for the standard model– but does not apply in our

situation• A super-resolution

phenomenon (Fink,1996) shows up


First conclusions

• Bad news– for standard seismic frequencies the remaining

heterogeneity can be so strong that multiple scattering remains quite important

– we must take this nonlinear effect into account• Good news

if we are able to do so, we can take advantage of the super-resolution phenomenon


What happens for other frequencies ?

• For a low frequency source, we can expect a substantial simplification of the medium dz=8m for a 10 Hz central

frequency• Therefore we can expect

the total reflection to show up as predicted by the standard model…


Influence of the central frequency

1.0

1.5

2.0

Tim

e (s

)

30 Hz 20 Hz 10 Hz 5 Hz

Comparison between the standard and reference seismic responses (second geological setting)


What happens for other frequencies ?

Conversely the use of a high frequency source may turn the standard model wrong in apparently simple situations – first geological setting– source with a 50 Hz

central frequency


Outline






Beyond the 1D propagation

• 2D wave propagation in the 1D model

• Propagation in a 2D model for a plane wave excitation


2D wave propagation in the 1D model

• We are still left with the difficulties associated with multiple scattering

• A standard NMO stack will not remove multiple scattering effects

1D p

ropa

gatio

n 2D propagation


Beyond the 1D propagation

• 2D wave propagation in the 1D model

• Propagation in a 2D model for a plane wave excitation


2D synthetic model


Propagation in the 1D and 2D models

� The differences between the two seismic responses are due to 2D lateral variations.


Propagation in the 2D model� The total reflection is hardly visible.


Beyond the 1D propagationTest with a total reflection

Receiver at x =100 m x =500 m x= 900 m

1500 m

� As in the 1D context, the total reflection is hardly visible in the seismic response.


Outline






So what ?

• A critical view of quantitative seismic imaging

• A more constructive view


A critical view of quantitative seismic imaging

• Dramatic conclusions in a context where the industry desires to extract sharp details from seismic information:– In general, no illusion to have regarding quantitative

imaging as it is implemented today– Even worse : loss of resolution (depth spreading of

"reflections")• In fact the above conclusions are case dependent


What can we propose in such a context ?

• Keep the standard model and estimate the actual resolution in the context of such a clutter :

practitioners might be strongly disturbed• SRME: an original but limited solution• Upgrade the physical model so that it accounts

for multiple scattering (estimate simultaneously the clutter and the scatterers!)

difficult but candidate for the super-resolution award!


An original but limited solution

• Surface related multiple elimination (Berkhout, Verschuur,…)– such multiple reflections can be eliminated from the

data themselves!– the technique requires

• a complete coverage in sources and receivers• the seismic wavelet to be known or determined…

• However the main problem is not surface related multiples but the whole series ofinternal multiples


Upgrade the physical model: a possiblysound starting point

• The NL inverse problem in the 1D waveequation (Bamberger et al.,70's)– is perfectly understood from a mathematical

standpoint (unicity, resolution)– but reveals important practical difficulties

• tremendous sensitivity in the poorly known seismic wavelet w(t) (Delprat-Jannaud & Lailly, 2004)

• ...


Sensitivity of the solution to errors in the wavelet

• Errors accumulate with depth!


Upgrade the physical model: a possiblysound starting point

• The inverse problem in the 1D wave equation– is perfectly understood from a mathematical

standpoint (unicity, resolution)– reveals important practical difficulties

• tremendous sensitivity in the poorly known seismic wavelet w(t)

• …

• a practical success: 1D inversion of VSP data


Inversion of VSP data: an interesting framework for applications (1)

• VSP data for close to 1D media– provide a reasonable

framework for a purely 1D wave propagation model

– provide enough information to determine the impedance profile and the Neumann BC (seismic wavelet)


Inversion of VSP data: an interesting framework for applications (2)

• An application (Macé and Lailly, 1986)• computed impedance profile

•computedNeumann BC


From the sound basis to practicalapplications ?

Upgrade the simplistic 1D wave propagation model : e.g. use of the 3D acoustic wave equation for the 3D imaging of a portion of the subsurface with gentle lateral variations– a critical parameter comes in: the velocity distribution...– … which is known to be very difficult to estimate accurately– a proposal: invert for impedances and remove the sensitivity to velocities

by considering small offsets only use vertical traveltime as depth coordinate and make use of an

approximately known velocity profile– keep in mind the sensitivity in the poorly known seismic wavelet

integrating other data (VSP,…) is essential!

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