Florence Delprat-Jannaud and Patrick Lailly
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
Exploration seismology (1)
– acquisition– seismic imaging– interpretation
(explo, reservoir)
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
Specificity of our problem
• Looking for a 3D high resolution image (and, if possible, quantitative) image
• Propagation takes place within quite a heterogeneous medium
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
P and S velocities, density,...
• Undergo large range variations (1 to 3)
• At very different scales
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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 insidious effects of fine scale heterogeneity in reflection seismology IMA05
The exploration seismologist’s standard model (Ray + Born)
• Propagationdownwards
• Reflection or diffraction
• Propagationupwards
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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 ?
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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 ?
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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)
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
propagation• 2D wave propagation• So what ?
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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” )
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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 insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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=
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
First geological environment
• Field velocity and density profiles measured with vertical step dz =15 cm.
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
Comparison between seismic
responses
The standard model works fine !
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
-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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
Third geological
setting
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
Third geological setting
density
velocity
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
Third geological
setting
Again, for large times we cannot find any match between the standard model and reference seismic responses
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
Third geological
setting
Who can foresee the presence of a perfectly reflecting basement looking at the reference ?
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
What is happening?
VSP Acquisition
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
What is happening?
VSP Acquisition
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
propagation• 2D wave propagation• So what ?
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
Parameters that govern wave propagation
• The depth of the target (propagation time) The multiple scattering phenomenon is
cumulative
• The roughness of the overburden
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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 insidious effects of fine scale heterogeneity in reflection seismology IMA05
The homogenized model fordifferent smoothingvelocity density
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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…
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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)
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
propagation• 2D wave propagation• So what ?
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
Beyond the 1D propagation
• 2D wave propagation in the 1D model
• Propagation in a 2D model for a plane wave excitation
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
Beyond the 1D propagation
• 2D wave propagation in the 1D model
• Propagation in a 2D model for a plane wave excitation
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
Propagation in the 1D and 2D models
� The differences between the two seismic responses are due to 2D lateral variations.
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
Propagation in the 2D model� The total reflection is hardly visible.
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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.
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
propagation• 2D wave propagation• So what ?
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
So what ?
• A critical view of quantitative seismic imaging
• A more constructive view
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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!
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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)
• ...
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
Sensitivity of the solution to errors in the wavelet
• Errors accumulate with depth!
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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)
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
Inversion of VSP data: an interesting framework for applications (2)
• An application (Macé and Lailly, 1986)• computed impedance profile
•computedNeumann BC
The insidious effects of fine scale heterogeneity in reflection seismology IMA05
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!