Common-azimuth migration of a North Sea dataset (ps.gz 2261K) (pdf 9339K) (src 213062K)
**Vaillant L. and Sava P.**

3-D prestack common-azimuth depth migration has a strong potential for
imaging accurately complex media and handling multi-pathing. We apply
the technique to North Sea real data for imaging a salt dome. The
results obtained demonstrate the efficiency of the method in complex
media. A detailed analysis of common-image gathers shows
opportunities for improving the velocity model.

Offset plane waves vs. common-azimuth migration for sub-salt imaging (ps.gz 1508K) (pdf 9908K) (src 15470K)
**Biondi B.**

Offset plane wave migration and common-azimuth migration
are among the most promising wave-equation migration methods
for efficiently imaging 3-D marine data sets.
Offset plane wave migration has some computational advantages
over common-azimuth migration,
but common-azimuth is more accurate.
Sub-salt images produced by common-azimuth migration
are better focused than the corresponding
images produced by offset plane wave migration.
These differences can be attributed
to an approximation intrinsic to offset plane wave migration:
the offset plane wave components are downward continued
separately, instead of being allowed to mix
as they should be in media with laterally varying velocity.
Offset plane wave migration also approximates the
cross-line offset ray parameter of the plane-waves with zero.
A theoretical analysis of the migration errors
caused by this approximation is confirmed
by the imaging results.
The shallow reflectors
dipping at 45 degrees with respect to the acquisition
axes are poorly imaged by offset plane wave migration.

Iterative resolution estimation in Kirchhoff imaging (ps.gz 1690K) (pdf 2512K) (src 22932K)
**Clapp R. G., Fomel S., and Prucha M.**

We apply iterative resolution estimation to least-squares
Kirchhoff migration. Resolution plots reveal low illumination areas
on seismic images and provide information about image
uncertainties.

Enhancing common-image gathers with prestack Stolt residual migration (ps.gz 1841K) (pdf 12374K) (src 3261K)
**Sava P.**

Wave-equation migration velocity analysis is a two-step process:
first, we estimate the perturbation between a starting image and
a better-focused image, and then invert for the perturbation
in slowness that explains the perturbation in image obtained in the
first step. The key to success is to obtain a sharp image, with
flat common-image gathers at every location.
In this paper, I show how prestack Stolt residual migration and
common-image gathers come together, and lead to a successful
image enhancement procedure with which we can transform a given
image into a better-focused one.

On Stolt common-azimuth residual migration (ps.gz 253K) (pdf 2321K) (src 360K)
**Sava P.**

This short note presents the extension of the velocity-independent
Stolt residual migration introduced in a previous report
HREF="../paul2/paper_html/node5.html#Sava.sep.100.paul1">Sava (1999) to common-azimuth (CA) data.
The derivation is very similar to its 2-D equivalent and retains
the important feature of being independent of any assumption about
the velocity used to obtain the image being residually migrated.
Residual migration can be used for both image improvement and velocity
analysis. As was previously shown
...

On Stolt stretch time migration (ps.gz 3929K) (pdf 7576K) (src 9977K)
**Vaillant L. and Fomel S.**

We implement Stolt-stretch time migration with an analytical
formulation for the optimal stretch parameter and show how it improves
the quality of imaging.
By a cascaded *f-k* migration approach with this
algorithm, we manage to obtain time migration results on real data
comparable to Gazdag's
phase-shift method, with a high accuracy for steeply deeping events at
a computational cost dramatically lowered.

Interpolating missing data: convergence and accuracy, *t* and *f* (ps.gz 497K) (pdf 5931K) (src 955K)
**Crawley S.**

Prediction error filters (PEFs) can be used to interpolate seismic data, in
the time domain
HREF="../sean1/paper_html/node8.html#pvi">Claerbout (1992) or in the frequency domain
HREF="../sean1/paper_html/node8.html#spitzInterp">Spitz (1991).
The theory for PEFs assumes stationarity, so typically the data are
considered a little bit at a time in patches,
and assumed to be locally stationary within a patch.
An alternative is to use nonstationary filters, which
effectively sets the patch size to one sample (or slightly larger).
...

Applying SEP's latest tricks to the multiple suppression problem (ps.gz 292K) (pdf 1103K) (src 3376K)
**Clapp R. G. and Brown M.**

Two methods for suppressing multiples are proposed.
In the first,
multiple suppression is expressed as a signal to noise separation
problem. The problem is solved in the time domain using space-varying
Prediction Error Filters (PEFs).
The second method shows how greater separation between primaries
and multiples can be obtained by velocity space inversion using
a Huber functional rather than the standard *L _{2}* functional.
Early results of both methods are encouraging.

Plane wave prediction in 3-D (ps.gz 487K) (pdf 3696K) (src 4075K)

The theory of plane-wave prediction in three dimensions is described by Claerbout (1993, 1997). Predicting a local plane wave with

Predictive signal/noise separation of ground-roll-contaminated data (ps.gz 801K) (pdf 12609K) (src 1536K)

Coherent noise contamination is a first order problem plaguing the imaging of seismic data acquired in both land and marine environments. We present a new method for the predictive separation of coherent noise from prestack data which operates in the

On non-stationary convolution and inverse convolution (ps.gz 30K) (pdf 192K) (src 13K)

Recursive inverse filtering with non-stationary filters is becoming a useful tool in a range of applications, from multi-dimensional inverse problems to wave extrapolation. I formulate causal non-stationary convolution and combination and their adjoints in such a way that it is apparent that the corresponding non-stationary recursive filters are true inverse processes. Stationary recursive inverse-filtering is stable if, and only if, the filter is minimum-phase. I show that recursive inverse-filtering with a filter-bank consisting of minimum-phase two-point filters is also unconditionally stable. However, I demonstrate that, for a more general set of minimum-phase filters, stability of non-stationary recursive inverse-filtering is not guaranteed.

Revisiting the half-derivative filter (ps.gz 416K) (pdf 3042K) (src 1099K)

A primary goal in designing an iterative optimization method for inversion is to minimize the number of iterations necessary for convergence. Often, we tackle this by applying an appropriate filter. When conjugate gradient (CG) methods are applied to a problem like velocity transform in 2-D, the principal artifact faced is the half-integration waveform Claerbout (1993, 1995). ...

Estimating rock porosity and fluid saturation using only seismic velocities (ps.gz 67K) (pdf 1568K) (src 146K)
**Berryman J. G., Berge P. A., and Bonner B. P.**

Evaluation of the fluid content in deep earth reservoirs
or of fluid contaminants in shallow earth environments
has required the use of geophysical imaging methods such as seismic reflection
prospecting. The processing of these seismic data has involved
meticulous care in determining the changes in reflected seismic amplitude
as the point of observation for the received signals at the earth's
surface is moved away from the seismic source (Ostrander, 1984). The now
commonly used method called AVO
(for Amplitude Versus Offset) is based on theories of fluid-saturated
and partially saturated rocks that have been available since the 1950's.
Here we present a new synthesis of the same physical concepts that
uses some of the same data as AVO (compressional wave velocities)
together with some different data (shear wave velocities)
in a scheme that is much simpler to understand and apply, yet
yields the desired information about porosity and fluid saturation.
The method is designed especially for near surface applications
and for use with crosswell and VSP data,
but it can also be applied to reflection seismic data assuming
that reliable interval velocities are available.
Since the new method does not require hard-to-obtain
wave amplitude information, it can be used
for a wider range of seismic source-receiver configurations, including
crosswell seismic transmission tomography (well-to-well),
vertical seismic profiling (well-to-surface), as well as
seismic reflection profiling (surface-to-surface),
since reflection data can be used but are not a necessity.

Seismic attribute sensitivity to velocity uncertainty (ps.gz 893K) (pdf 11070K) (src 108853K)
**Mora C. and Biondi B.**

This paper explores the relationship between velocity uncertainty and
AVO-related seismic attributes in a dataset from the Blake Outer Ridge,
offshore from Florida and Georgia.
From an initial velocity model, several realizations were generated
that are perturbations of the original velocity model. Prestack wave-equation
migration was applied to the data for each velocity realization.
In the migrated
CMP gathers, velocity coherence was measured by applying semblance analysis.
Also, several seismic attributes were calculated in the migrated CMP gathers,
including AVO intercept, AVO gradient, and near - far offset stack.
Preliminary results from attribute versus velocity coherence crossplots
at the range of CMPs studied suggest that,
for the case of maximum semblance coherence measurements, attribute
values are more dispersed for lower coherence values and more localized for
higher coherence values.
These results are not definitive, and further work is needed to improve
the velocity coherence measures.

Seismic pattern recognition via predictive signal/noise separation (ps.gz 424K) (pdf 1026K) (src 7248K)
**Brown M. and Clapp R. G.**

Manual stratigraphic interpretation of modern 3-D seismic images is a tedious
and time-consuming process.
We present a method based on nonstationary predictive signal/noise
separation for automatically recognizing the occurence of an arbitrary, predefined
pattern, or *facies template*, in seismic images.
Similarity of local data windows to the facies template is measured by an attribute
which has an easily interpretable physical meaning.
The method is tested on 2-D synthetic and real seismic images, and is shown to
reliably detect the presence of unconformities in both.
An extension of the method to 3-D should be quite straightforward, and early performance
assessments hint that the extension will not be hindered severely by computational
issues.

Origin of Gassmann's equations (ps.gz 28K) (pdf 165K) (src 10K)
**Berryman J. G.**

A short tutorial on the derivation of Gassmann's equations is provided.

Seismic velocity decrement ratios for regions of partial melt near the core-mantle boundary (ps.gz 31K) (pdf 204K) (src 13K)
**Berryman J. G.**

For regions of partial melt in the lower mantle,
both compressional and shear wave
velocities
decrease monotonically with increasing melt volume
fraction.
It has been observed
that regions close to the core-mantle boundary thought to contain
partial melt have a velocity decrement ratio (relative change in
shear velocity over relative change of compressional velocity)
of about 3. This is certainly a high value for this ratio and
arguments based on effective medium theories have been given to show that
such values are predicted for partial melt systems. The present work
confirms the value of 3 near the core-mantle boundary.
It is shown, furthermore,
that the velocity decrement ratio can be estimated without detailed
knowledge of, or assumptions about, the microstructure of the partial melt
system by using Gassmann's equation of poroelasicity together with some
reasonable assumptions about the change (or lack of change) of the
density and bulk modulus for lower mantle pressure and
temperature conditions.

Additions to SEPlib (ps.gz 28K) (pdf 269K) (src 12K)
**Clapp R. G.**

The release of this report coincides with the release of new version of the
SEP software "SEPlib". The new version of SEPlib contains a significant number
of new features that allows better handling of 3-D data. The release also
includes support for running Seismic Unix (SU) programs with SEP data, a new
installation mechanism, and machine independent makefile rules that should
allow easy building of SEP reports.

SEP's data library (ps.gz 9901K) (pdf 18283K) (src 19771K)
**Clapp R. G., Brown M., Vaillant L., Mora C., Prucha M., and Zhao Y.**

One of the requirements for graduation at SEP is to prove that a student's
ideas will work on real seismic data.
SEP sponsors have been very generous over the years in providing SEP with
real seismic datasets.
In the past we have kept these datasets on a variety of different tape formats
and with decidedly mixed levels of documentation. This summer
SEP organized a mini-seminar in an
attempt to organize these datasets. This paper, and the accompanying
web page^{},
...

Testing Linux multiprocessors for seismic imaging (ps.gz 55K) (pdf 4858K) (src 6903K)
**Biondi B., Clapp R. G., and Rickett J.**

Benchmarks of our ``production'' codes show that Pentium-based
multi-processors computers running the Linux operating system
are attractive options for SEP's next computational server(s).
A four-processor SGI 1400 L (500 Mhz Pentium III Xeon)
has consistently performed as well as, or better than,
our SGI Origin 200 (180 Mhz R10000).
We used the Portland Group's `pgf90` compiler to compile
our benchmarking codes,
that are parallelized with OpenMP directives.
This compiler has proven to generate efficient code,
though the support of some F90 and OpenMP features is still immature.

Reproducible research - results from SEP-100 (ps.gz 8K) (pdf 41K) (src 2K)
**Prucha M. L., Clapp R. G., Fomel S., Claerbout J., and Biondi B.**

SEP has been striving to create reproducible research for many years.
Our first attempts at reproducible documents began with the introduction
of interactive documents
HREF="../marie2/paper_html/node7.html#Claerbout.sep.67.139">Claerbout (1990). We then moved on
to putting SEP reports on CDROMs and using ``cake''
HREF="../marie2/paper_html/node7.html#Nichols.sep.61.341">Nichols and Cole (1989)
so that the results could be recreated using the author's own processing
flow. Later we updated to the GNU make system
HREF="../marie2/paper_html/node7.html#Schwab.sep.89.217">Schwab and Schroeder (1995).
Now SEP reports are available online and can be downloaded.
...

10/26/1999