Th-04-14
Amplitude Inversion of Depth-imaged Seismic
Data from Areas with Complex Geology
S.H. Archer* (WesternGeco), X. Du (WesternGeco) & R.P. Fletcher
(WesternGeco)
SUMMARY
Conventional amplitude inversion assumes that the input migrated image has preserved relative amplitude
information and is free from the effects of illumination. Under this assumption, stretching a depth migrated
image back to time and applying inversion based on 1D convolutional modeling can produce reasonable
results.
However, illumination effects in complex geological settings (such as shadow zones in subsalt imaging)
pose a challenge to even the most advanced imaging algorithms such as reverse-time migration (RTM).
Traditional approaches to compensate for illumination effects in migrated images are difficult to regularize
in areas of very poor illumination.
We address this problem by using the modelled response of the acquisition and imaging process, defined
by Point Spread Functions (PSFs), to include these effects in forward modeling for inversion directly in
the depth domain. We demonstrate this approach for poststack inversion of synthetic, subsalt data and also
apply it to field data from the Gulf of Mexico.
75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013
London, UK, 10-13 June 2013
Introduction
Conventional amplitude inversion assumes that the input migrated image has preserved relative
amplitude information and is free from the effects of illumination. Under this assumption, stretching a
depth migrated image back to time and applying inversion based on 1D convolutional modeling can
produce reasonable results.
However, illumination effects in complex geological settings (such as shadow zones in subsalt
imaging) pose a challenge to even the most advanced imaging algorithms such as reverse-time
migration (RTM). Traditional approaches to compensate for illumination effects in migrated images
are difficult to regularize in areas of very poor illumination.
We applied a technique, proposed by Fletcher et al. (2012) for performing amplitude inversion in
these poorly illuminated zones to synthetic data and 3D field data from the Gulf of Mexico.
Method
Traditional approaches to migration/inversion regard the recorded data, d, as the result of a linear
modeling operator, M, applied to the reflectivity model, r. This can be either a discrete or continuous
(integral) operator. The least-squares inverse to this problem is

rˆ  M *M

1
M *d,
(1)
where M*, the adjoint of modeling, is the migration operator. The true model, r, and the migrated
image I=M*d are related through
I  Hr,
(2)
where the Hessian operator, H=M*M, can be thought of as demigration followed by migration, and is
often used as a measure of illumination that reflects the effects of velocity variation and the
acquisition footprint. If we relax the requirement that the modeling operator and the migration
operator are related to each other, then the operator, H, is still considered as an operator, defined by
the applied processing and imaging, that blurs the true reflectivity model to give the image.
Fletcher et al. (2012) describe how the H operator was included in a depth-domain amplitude
inversion for the elastic properties of a 3D earth model. In this work we compare the results of this
depth-domain inversion with conventional inversion on synthetic and field data in areas of complex
geometry.
Examples
(a)
(b)
Figure 1 The Sigsbee 2A model (a) stratigraphic model (b) imaging velocity model.
75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013
London, UK, 10-13 June 2013
A poststack inversion was applied to synthetic data from the constant density Sigsbee2A model, and
compared to the results of conventional inversion. The Sigsbee2A model (Figure 1a) and data are
made available by the Subsalt Multiples Attenuation and Reduction Joint Venture(SMAART JV). It is
described as representative of “…a geologic setting found in on the Sigsbee escarpment in the deep
water Gulf of Mexico” and having “…illumination problems due to the complex salt shape with
rugose salt top found in this area” resulting in “sub-salt structure that is difficult to image”.
Figure 1 shows the Sigsbee 2A model and Figure 2(a) displays the prestack RTM image from the
target zone defined in Figure 1(a), using the migration velocity model displayed in Figure 1(b). The
image clearly shows lateral variability in image amplitude and quality beneath the salt where the
velocity model does not indicate any corresponding changes in geology. Note that there are point
(
a)
(b)
c)
(d)
e)
(f)
(
(
Figure 2 Detailed zone of inversion. (a) the image, (b) PSFs, (c) true model acoustic impedance (after
removing the background prior model), (d) depth-domain inversion, (e) sequential inversion and (f)
simultaneous inversion.
reflectors added to this model in the subsalt sediments at depths of 17,000ft and 25,000ft. These also
show the lateral variability in the subsalt image.Our estimate of the H operator is obtained by
demigration followed by the prestack RTM workflow applied to point diffractors to give the point
spread functions (PSFs) in Figure 2b. For locations where we did not compute a PSF, we interpolate
one from the surrounding PSFs.
Poststack inversion of this image was computed using two conventional inversion processes:
simultaneous seismic inversion (Ma, 2002; Rasmussen et al. 2004) and sequential seismic inversion
75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013
London, UK, 10-13 June 2013
(Poggliagliomi and Allred 1994) for comparison with the proposed inversion algorithm outlined
above. Figure 2 compares the results of the three inversion approaches. Figures 2(c) to 2(f) show the
acoustic impedance after subtraction of the migration background model. The new inversion (Figure
2d) shows more continuous reconstruction of the model than either of the conventional inversions.
The simultaneous inversion (Figure 2f) method is similar to the new workflow, with the main
difference being that it uses a 1D spatially invariant wavelet in the time domain. This clearly prevents
this inversion from recovering the true reflectivity from zones where the image amplitudes are
distorted. Both of these methods use the same smooth prior model. The sequential inversion (Figure
2e) uses a prior model based on extrapolation of well data to determine the scalar for the contribution
of the seismic data to the inversion result. In this case we used the assigned well location shown,
along with horizon picks from the structural image to compute the prior model. This allows better
recovery of the true reflectivity for this method, although it relies heavily on constructing an accurate
prior model. The new inversion shows better
recovery of the model through the weak image zone
near the top centre of the zone shown in Figure 2
than either of the other two inversion methods. This
new approach uses the measured response of the
seismic imaging workflow, the PSFs, so it does not
rely on assumptions on the lateral stability of the
data or the accuracy of the prior model.
Field data application
Depth-domain inversion was applied to 3D field
data from a Gulf of Mexico survey. Data from the
selected area are shown in Figure 3 and poor
amplitude recovery can be seen beneath the salt
edges. The box shows the target zone for inversion.
Figure 3 Reverse-time migration image from the
Gulf of Mexico survey. The box shows the target
zone for our inversion. Courtesy of WesternGeco.
The shots contributing to the target zone were identified and processed through RTM imaging to
generate an image for inversion (Figure 4a).
(
a)
(b)
(
c)
(d)
Figure 4 The target zone inversion results (a) The reverse-time migration image, (b) the PSFs,
(c) acoustic impedance from simultaneous inversion (d) acoustic impedance from depth-domain
inversion. Courtesy of WesternGeco.
75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013
London, UK, 10-13 June 2013
Synthetic data for these shots were then generated for a grid of point scatters in the imaging velocity
model and these were processed through RTM imaging to generate the point spread functions
required for the inversion (Figure 4b). The inversion results are compared to conventional
simultaneous inversion results in Figure 4.
The simultaneous inversion (Figure 4c) was run after converting the data to the time domain using a
wavelet extracted at the well location. The depth-domain inversion (Figure 4d) was calibrated at the
well location by generating synthetic data by convolving the PSFs with a model constructed using the
well data and then designing a match filter to refine and scale the PSF synthetic to match the image at
the well location. This is somewhat similar to the wavelet estimation for conventional inversion, but
represents a refinement to the PSFs, rather than the complete definition of the wavelet.
Acoustic impedance from simultaneous inversion (Figure 4c) shows a close correspondence with the
amplitudes in the image as would be expected due to the invariant wavelet used. The depth-domain
inversion (Figure 4d) shows some extension of the events into the poorly illuminated zone. It is able
to do this by using the measured variation of the wavelet inherent in the PSFs (Figure 4b). Both of
these inversions used the same prior model, derived from the imaging velocity model and correlations
between velocity and density.
Discussion and conclusions
We demonstrated improved inversion of seismic data, directly in the depth domain, accounting for
illumination effects in the image by replacing the 1D wavelet in conventional inversion with the point
spread function of the depth imaging processing. The synthetic and field data examples we presented
inverted RTM images using PSFs generated from finite-difference wave-equation propagation.
However, the inversion algorithm could be applied using PSFs (or a complete calculation of the
Hessian) and images generated using less-expensive propagators for geologies that do not warrant a
full-wave solution.
Whilst we have shown an example of poststack acoustic impedance inversion, this workflow has been
extended to perform AVO inversion of angle stacked depth images.
Aknowlegements
We thank Juan Paulo Perdomo Tellez and many other colleagues from WesternGeco for assistance
with this case study and WesternGeco Multiclient Services for providing wide-azimuth seismic data
from the area. This work includes data supplied by IHS Energy Log Services, Inc; Copyright (2012)
IHS Energy Log Services, Inc.
References
Fletcher, R.P., Archer, S.H., Nichols, D. and Mao, W. [2012] Inversion after depth imaging. 82nd
Annual International Meeting, SEG, Expanded Abstracts,1-5.
Ma, X-Q. [2002] Simultaneous inversion of prestack seismic data for rock properties using simulated
annealing. Geophysics, 67, 1877-1885.
Poggliagliomi, E, and Allred, R.D. [1994] Detailed reservoir definition by integration of well and 3-D
seismic data using space adaptive wavelet processing. The Leading Edge, 749-753.
Rasmussen, K.B., Bruun, A. and Pedersen, J.M. [2004] Simultaneous Seismic Inversion. 66th EAGE
Conference & Exhibition, Extended Abstracts.
75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013
London, UK, 10-13 June 2013