Imaging complex structures with first-arrival traveltimes (ps.gz 902K) (pdf 781K) (src 2356K)
**Bevc D.**

I present a layer-stripping Kirchhoff migration algorithm which is
capable of obtaining accurate
images of complex structures by downward continuing
the data and imaging from a lower datum.
I use eikonal traveltimes in a Kirchhoff datuming algorithm for the
downward continuation. After downward continuation, I perform
Kirchhoff migration.
The method alternates steps of datuming and imaging. Because traveltimes
are computed for each step, the adverse effects of caustics, headwaves, and
multiple arrivals do not develop.
In principal, this method only requires the same number of
traveltime calculations as a standard migration.
Tests on the Marmousi data set produce excellent results.

3-D prestack depth migration of common-azimuth data (ps.gz 48K) (pdf 64K) (src 910K)
**Biondi B. and Palacharla G.**

We extended the common-azimuth 3-D prestack migration
method presented in a previous report
() to the important case
of imaging common-azimuth data
when the velocity field varies laterally.
This generalization leads to an efficient
mixed space-wavenumber domain algorithm
for 3-D prestack depth migration of common-azimuth data.
We implemented the method using a split-step scheme,
and applied it to the migration of two synthetic
data sets: the first data set was generated assuming a vertical velocity
gradient,
the second one assuming a velocity gradient with both
a vertical and a horizontal component.
Common-azimuth migration correctly imaged the reflectors in both cases.

The time and space formulation of azimuth moveout (ps.gz 582K) (pdf 643K) (src 1639K)
**Fomel S. and Biondi B. L.**

Azimuth moveout (AMO) transforms 3-D prestack seismic data from one
common azimuth and offset to different azimuths and offsets.
AMO in the time-space domain is represented by a three-dimensional
integral operator. The operator components are the summation path,
the weighting function, and the aperture. To determine the summation path and
the weighting function, we derive the AMO operator by cascading dip
moveout (DMO) and inverse DMO for different azimuths in the time-space
domain. To evaluate the aperture, we apply a geometric approach,
defining AMO as the result of cascading prestack migration (inversion)
and modeling. The aperture limitations provide a consistent
description of AMO for small azimuth rotations (including zero) and justify the
economic efficiency of the method.

Migration from a non-flat datum via reverse-time extrapolation (ps.gz 335K) (pdf 281K) (src 4089K)
**Palacharla G.**

Land surveys usually have elevation changes, and this irregular topography
distorts seismic data. For large topography changes and
near-surface velocity comparable to subsurface velocity, static-corrections
are inadequate, wavefield extrapolation is required in this situation.
I present a scheme for doing
migration directly from the irregular datum. The scheme can also be used for
redatuming data collected at a non-flat datum to a flat datum.
The reverse-time migration method is used to do the extrapolation,
because it is a boundary-value problem, which naturally accommodates an
irregular topography. It can handle steep dips and a general
velocity model. After describing the reverse-time algorithm, I apply it to a
post-stack example and show that static shifts are inadequate but migration from
a non-flat datum produces a good image. I also outline the
shot-profile implementation and its extension to 3-D.

Prestack migration by split-step DSR (ps.gz 407K) (pdf 366K) (src 730K)
**Popovici A. M.**

This document was generated using the
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Nikos Drakos,
Computer Based Learning Unit, University of Leeds.
The command line arguments were:

**latex2html** `-dir /net/sepwww/public/docs/sep84/mihai1/paper_html index.ltx`.
...

Evaluating the Stolt stretch parameter (ps.gz 94K) (pdf 108K) (src 251K)
**Fomel S.**

The Stolt migration extension to a varying velocity case (Stolt
stretch) implies
describing a vertical heterogeneity by a constant parameter
(*W*). This paper
exploits the connection between modified dispersion relations and traveltime
approximations to derive an
explicit expression for *W*. The expression provides theoretically the
highest possible accuracy
within
the Stolt
stretch framework. Applications considered include optimal partitioning
of the velocity distribution for the cascaded migrations and extension
of the Stolt stretch method to transversally isotropic models.

Multi-azimuth velocity estimation (ps.gz 134K) (pdf 147K) (src 459K)
**Clapp R. G. and Biondi B.**

It is well known that the inverse problem of estimating interval velocities from
reflection data is poorly constrained in 2-D.
We show that the interval velocity estimation problem in 3-D is much
better constrained when the velocity function is estimated by
jointly inverting the data collected along multiple offset-azimuth,
even when the azimuth range is fairly limited.
We extend to 3-D the linear operator presented by () for relating stacking velocities
with interval velocities. We then apply a Singular Value Decomposition (SVD)
analysis to the derived operator.
This analysis suggests that methods that take advantage
of the azimuth range in the data should yield
better velocity functions than currently used velocity estimation methods that
neglect the additional information provided by
multi-azimuth coverage.

Tomographic velocity estimation with planewave synthesis imaging (ps.gz 939K) (pdf 966K) (src 19527K)
**Ji J.**

In areas with structurally complex geology,
tomographic velocity analysis is required to estimate velocities.
This paper describes a tomographic velocity analysis algorithm
which uses planewave synthesis imaging as a prestack migration.
In reflection tomography, prestack migration is required
for both event picking and traveltime error computation.
Traveltime errors are often measured
in the form of residual moveout (RMO) velocity
in common surface location (CSL) gathers after prestack depth migration.
It is shown that we can measure the residual moveout (RMO) velocity
accurately with the help of reflector-dependent planewave synthesis imaging.

Velocity structure of the methane hydrate formation at the Blake Outer Ridge (ps.gz 951K) (pdf 1288K) (src 4939K)
**Ecker C.**

Seismic analysis of data from
the Blake Outer Ridge indicates the presence of hydrate-bearing sediments
overlaying gas-saturated sediments in this region. In an attempt to
determine possible lateral and vertical
variations of the hydrate and gas sediments, I performed a 2-D
velocity analysis along two approximately perpendicular seismic lines.
Subsequent determination of the seafloor and BSR reflection coefficients
along one of the lines resulted in additional zero offset P-wave
velocity and density constraints. Combining these with the average interval
velocity model of this line, I performed a 1-D
elastic amplitude modeling of zero
offset reflections using the Thompson-Haskell reflectivity method.
The results suggest that regions showing a continuous bottom
simulating reflection are characterized by a thick hydrate layer that has an
average velocity of 2.1 km/s overlaying low-velocity ( 1.6 km/s)
sediments of considerable thickness. This result agrees well with
results discussed in SEP80.
In regions of discontinuous BSR,
a less pronounced velocity contrast is visible, probably indicating a decrease
in the hydrate concentration of the sediments.

Amplitude-preserved processing and analysis of the Mobil AVO data set^{} (ps.gz 3474K) (pdf 3051K) (src 68651K)
**Lumley D. E., Nichols D., Ecker C., Rekdal T., and Berlioux A.**

Mobil Oil has released a comprehensive seismic and well-log data set
from the North Sea to benchmark AVO techniques.
We present our results on amplitude-preserved data processing and analysis
of the Mobil AVO data.
First, we apply a source and receiver consistent amplitude balancing
to the seismic data, which reduces source and receiver amplitude variance
from about 8% and 15% respectively, to within a few percent scatter.
Next, we apply a time-domain conjugate-gradient multiple-suppression technique
to remove multiple reflection energy and simultaneously preserve
and enhance primary-reflection AVO amplitudes.
We perform unmigrated AVO analyses and find that the multiple-suppressed
data correlate better with the well-log data than the unprocessed data.
A prestack migration/inversion of the multiple-suppressed data shows
a clear improvement over unmigrated AVO analysis, and reveals an undrilled
graben block in the center of the line that exhibits a positive hydrocarbon
indicator anomaly.

Amplitude preserving AMO from true amplitude DMO and inverse DMO (ps.gz 99K) (pdf 129K) (src 8051K)
**Chemingui N. and Biondi B.**

Starting from the definition of Azimuth Moveout (*AMO*) as the cascade
of *DMO* and inverse *DMO* at different offsets and azimuths, we derive
an amplitude-preserving function for the *AMO* operator.
This amplitude function is based on the FK definition of *DMO*
and the definition of its true inverse. Similar to Liner's formalism
of a true inverse for Hale's *DMO*,
we derive an asymptotically true inverse for Black/Zhang's *DMO*
and Bleinstein's Born *DMO*.
A numerical test is given that
compares amplitude preservation using kinematically equivalent
*DMO* operators cascaded
with their true inverses.
We define amplitude-preserved processing as the preservation of the
offset-dependent reflectivity after *AMO* transformation, where the
reflectivity is considered to be proportional to the peak amplitude
of each event.
We found that an *AMO* operator defined using
Zhang's *DMO* cascaded with its true inverse best reconstructs data amplitudes
after transformation to a new offset and azimuth.
The new amplitude function represents
an amplitude-preserving azimuth moveout.

Angle-dependent reflectivity recovery by planewave synthesis imaging (ps.gz 168K) (pdf 170K) (src 427K)
**Ji J.**

In this paper I compared imaging conditions
of three different prestack migrations
in terms of angle-dependent reflectivity recovery.
The imaging conditions compared are shot profile migration
with conventional imaging condition,
de Brduin's imaging condition, and planewave synthesis imaging.
The conventional imaging condition can be applied to any reflector
geometry and to arbitrary velocity, but it recovers
only diagonal component of the reflectivity matrix.
de Bruin's imaging condition recovers full reflectivity matrix
but has difficulty in implementing for arbitrary reflector geometry
and under variable velocity.
Planewave synthesis imaging takes advantages from both conventional
and de Bruin's imaging condition.

Amplitude preserving offset continuation in theory Part 1: The offset continuation equation (ps.gz 111K) (pdf 97K) (src 124K)
**Fomel S.**

This paper concerns amplitude-preserving kinematically equivalent
offset continuation (OC) operators. I introduce a revised partial
differential OC equation as a tool to build
OC operators that preserve offset-dependent reflectivity in prestack
processing. The method of characteristics is applied to reveal the
geometric laws of the OC process. With the help of geometric
(kinematic) constructions, the equation is proved to be
kinematically valid for all
offsets and reflector dips in constant velocity media.
In the OC process,
the angle-dependent reflection coefficient is preserved, and the
geometric spreading factor is transformed in accordance with the laws
of geometric seismics independently of the reflector curvature.

Amplitude-preserved low velocity noise suppression (ps.gz 3898K) (pdf 3339K) (src 17175K)
**Urdaneta H.**

Low velocity noise can contaminate reflections and distort AVO
amplitude information. I explore different inversion methods for
suppressing low velocity noise while simultaneously preserving
amplitudes along reflections. A velocity-stack inversion process is
used for recreating models in velocity space that can reconstruct the
reflections and the low velocity noise. Velocity-stack inversion is
the process of creating a velocity space model that can correctly
reconstruct the measured data. This is usually implemented by
minimizing the *L _{2}* norm of the data misfit and the

Seismic monitoring of reservoir fluid flow: Fundamental theory and examples^{} (ps.gz 320K) (pdf 306K) (src 823K)
**E. Lumley D.**

Time-lapse 3-D seismic monitoring of subsurface rock property changes
incurred during reservoir fluid-flow processes is an emerging new
diagnostic technology for optimizing hydrocarbon production.
I discuss the physical theory relevant for three-phase fluid flow
in a producing oil reservoir, and rock physics transformations of
fluid-flow pressure, temperature and pore-fluid saturation values
to seismic P-wave and S-wave velocity. I link fluid-flow physical
parameters to seismic reflection data amplitudes and traveltimes
through elastic wave equation modeling and imaging theory.
I demonstrate with synthetic and field data examples that changes in fluid flow
can be monitored and imaged from repeated seismic surveys acquired at
varying production calendar times.

4-D seismic monitoring of an active steamflood (ps.gz 922K) (pdf 815K) (src 34837K)
**E. Lumley D.**

3-D migrations of time-lapse seismic monitor data acquired
during steam injection show dramatic
and complex changes in the reservoir zone over a wide area, compared to
baseline seismic data recorded prior to steam injection.
Anticipated large decreases in seismic P-wave velocity *V*_{p}
near the injection well correlate with the presence of a
hot desaturated steam zone. Unanticipated large *increases* in *V*_{p}
in an annulus around the steam zone may correspond to a high-pressure
cold oil front, in which residual free gas in pore space crosses the bubble
point and dissolves into liquid oil.
Horizontal and vertical anisotropy in flow directions inferred
from these seismic observations correlate with two temperature monitor wells,
and in situ measurements of upper and lower reservoir permeability.
Since the pressure front propagates out from the injector an order
of magnitude faster than either the thermal or steam fronts,
monitoring it may be useful for predicting future fluid-flow paths of
heated oil, months in advance of actual production.

Searching the Sea of Galilee (ps.gz 990K) (pdf 868K) (src 5832K)
**Fomel S. and Claerbout J. F.**

We applied the inverse linear interpolation method to process a
bottom sounding survey data set from the Sea of Galilee in Israel.
Non-Gaussian behavior of the noise led us to employ a version of the
iteratively reweighted least squares (IRLS) technique. The IRLS enhancement
of the method was able to remove the image artifacts caused by the
noise at the cost of a loss in the image resolution. Untested
alternatives leave room for further research.

The interpolation of a 3-D data set by a pair of 2-D filters (ps.gz 151K) (pdf 138K) (src 1037K)
**Schwab M. and Claerbout J. F.**

Seismic 3-D field data is often recorded as a set of
relatively sparse and often irregular 2-D lines.
Under the assumption that the data consists of the superposition
of local plane waves,
such data can be interpolated by prediction-error techniques
using a set of two 2-D filters instead of the
conventional single 3-D filter.
The two 2-D prediction-error filters are found
by two independent linear minimization problems along sets of
parallel linearly-independent lines. A third linear minimization
yields the missing data.
Fortunately, such an approach avoids the nonlinear minimization
that is required when trying to find simultaneously the missing data
and the 3-D filter on a sparse 3-D
data set.

Multigrid nonlinear SeaBeam interpolation (ps.gz 154K) (pdf 146K) (src 351K)
**Crawley S.**

A multigrid nonlinear algorithm was applied to the April 18 SeaBeam data set to
fill in the large regions of missing data,
obtaining an image superior to those
obtained with linear methods, and more quickly
than is possible with a normal, single grid nonlinear interpolation.
The model may be chosen to contain any number of points; here models
with gradually increasing numbers of points are solved for in succession,
each providing the initial guess for the next.
The algorithm is unstable in some cases, but in general converges
quickly to a detailed solution.

An example of inverse interpolation accelerated by preconditioning (ps.gz 81K) (pdf 72K) (src 2475K)
**Crawley S.**

This document was generated using the
**LaTeX**2`HTML` translator Version 97.1 (release) (July 13th, 1997)
Copyright © 1993, 1994, 1995, 1996, 1997,
Nikos Drakos,
Computer Based Learning Unit, University of Leeds.
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**latex2html** `-dir /net/sepwww/public/docs/sep84/sean2/paper_html index.ltx`.
...

Flying over the Ocean Southeast of Madagascar (ps.gz 657K) (pdf 606K) (src 10686K)
**Ecker C. and Berlioux A.**

Satellite measurements from the Southwest Indian Ridge provide information
about the local ocean topography
along both ascending and descending tracks. We present a weighted
least-squares approach to combine the information given along these
two measurement directions, thus obtaining a dense altitude coverage.
High-frequency, spiky noise along the tracks is eliminated by additional
weighting of the derivatives of the initial residuals. After having obtained the
optimal altitude fit to the crossing data, we illuminate the local seafloor
features using a set of first-order derivative filters. The results
show high image resolution, indicating effective noise removal.

2-D phase unwrapping (ps.gz 1864K) (pdf 1520K) (src 7309K)
**Chemingui N., Clapp R. G., and Claerbout J.**

We present a method for unwrapping the phase of a satellite data
set that maps Mt.Vesuvius in Italy.
The method finds a solution for
a partial differential
equation by redefining the problem as a system of regressions that we
solve using linear inversion techniques with iterated reweighting.
We show three different
techniques for eliminating the noise bursts from the raw
data and fitting it to a linear model.
The first process is a two-step solution in which the data is
first cleaned up and then fitted to a model by phase unwrapping.
In the second approach, starting from a raw noisy data, we solve the
inversion problem as a system of regressions using iterative weighting
based on the residual. The third technique attempts to resolve a discontinuity
in the data by solving a different system of regressions with weights
based on the model.
In the three processes, the inversion successfully unwrapped
the phase of the radar image and
produced an altitude map of the volcano region.
We were able to accelerate the convergence of the solution by
a smart preconditioning substitution. This transformation
changes the problem-formulation variable
using a leaky integration operator as a preconditioner. The substitution
reduced the number of iterations in
the least square-inversion by two orders of magnitude and provided a solution
after very few iterations.
The method, however,
did not help resolve a presumed discontinuity in the model, and we may
have to determine an optimal function for the iterated reweighting.

Tying well information and seismic data (ps.gz 53K) (pdf 57K) (src 108K)
**Berlioux A.**

Well log information and seismic data for a given horizon may not
tie properly. I address the problem by formulating a least-square
inverse problem for a synthetic dataset. The aim of my regression
equations is to find a model with a regular grid by simultaneously
linear interpolating the well data and mapping the trend of the
seismic information. I have scaled the second regression equation to
decrease the dominance of the seismic over the well data. First I
determine a prediction-error filter (PEF) from the seismic data and
then run a conjugate gradient solver with the PEF to create the final
map of the horizon. With this new method, the final map matches the
wells more accurately.

Compensating for irregular sampling and rugged topography (ps.gz 121K) (pdf 122K) (src 284K)
**Bevc D.**

Artifacts arise when irregularly
sampled data are input to a Kirchhoff datuming algorithm.
The irregular sampling occurs because of uneven sampling of the recording
surface and rugged topography. To ameliorate these artifacts,
I combine wave-equation datuming with model-space filtering
to resample data onto a regular grid. The filtering can be a simple
Laplacian operator or a nonstationary prediction error filter
with unknown filter coefficients.
Synthetic examples demonstrate that the method is successful for unevenly
sampled data along a flat datum.
The best result is achieved by using a Laplacian filter in the
inversion.

Trace balancing with PEF plane annihilators (ps.gz 37K) (pdf 49K) (src 71K)
**Crawley S.**

This document was generated using the
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Copyright © 1993, 1994, 1995, 1996, 1997,
Nikos Drakos,
Computer Based Learning Unit, University of Leeds.
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**latex2html** `-dir /net/sepwww/public/docs/sep84/sean3/paper_html index.ltx`.
...

Enhanced random noise removal by inversion (ps.gz 200K) (pdf 229K) (src 5746K)
**Abma R.**

Noise attenuation by prediction filtering breaks down
in the presence of high-amplitude noise when the prediction filter
is corrupted by noise and the filter response to the noise
overwhelms the signal.
Spurious events are generated and the amplitude of the signal
is reduced by prediction filtering under these circumstances.
To reduce these undesired effects,
the separation of signal and noise is posed as an inversion
problem.
The inversion process preserves signal amplitudes and attenuates
spurious events.

Enhanced prestack noise removal (ps.gz 121K) (pdf 111K) (src 388K)
**Abma R.**

This document was generated using the
**LaTeX**2`HTML` translator Version 97.1 (release) (July 13th, 1997)
Copyright © 1993, 1994, 1995, 1996, 1997,
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Computer Based Learning Unit, University of Leeds.
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...

Variational structure of inverse problems in wave propagation and vibration (ps.gz 90K) (pdf 126K) (src 59K)
**Berryman J. G.**

Practical algorithms for solving realistic inverse problems may often
be viewed as problems in nonlinear programming with the data serving
as constraints. Such problems are most easily analyzed when
it is possible to segment the solution space into regions
that are feasible (satisfying all the known constraints) and
infeasible (violating some of the constraints). Then, if the feasible
set is convex or at least compact, the solution
to the problem will normally lie on the boundary of the feasible
set. A nonlinear program may seek the solution by systematically
exploring the boundary while satisfying progressively more constraints.
Examples of inverse problems in wave propagation (traveltime tomography)
and vibration (modal analysis) are presented to illustrate
how the variational structure of these problems may be used to create
nonlinear programs using implicit variational constraints.

Errors in SEP-81 (ps.gz 14K) (pdf 16K) (src 1K)
**Nichols D.**

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SEP World-Wide Web update (ps.gz 96K) (pdf 77K) (src 145K)
**Berlioux A. and Claerbout J.**

This document was generated using the
**LaTeX**2`HTML` translator Version 97.1 (release) (July 13th, 1997)
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...

CD-ROM versus The Web (ps.gz 12K) (pdf 14K) (src 4K)
**Claerbout J. and Schwab M.**

SEP has learned how to deliver reproducible research on CD-ROM.
Publication via the Internet's World Wide Web may in the future
offer a more flexible and efficient alternative.

SEP AVS User Guide (ps.gz 357K) (pdf 249K) (src 885K)
**Clapp R. G.**

The last 10 years has seen a steady increase in the number of 3-D seismic
surveys. This increase has led to a
push to develop
innovative tools to deal with the unique challenges that 3-D data present.
SEP has chosen to work
within the framework provided by Advanced Visual Systems (AVS) for its 3-D
work.
This paper attempts to summarize current status of SEP's AVS environment;
provide some useful hints when problems are encountered running AVS; and
give a brief overview of where we are headed in the near future.

5/9/2001