Visualization of multi-dimensional seismic datasets with CM-AVS (ps 834K) (src 791K)
**Biondi B. and Trier J. v.**

We have developed a visualizer for large 3-D prestack seismic surveys
that takes advantage of the data handling (memory and I/O)
and computational capabilities of SEP's CM-5.
The visualization application is a collection of AVS
and CM/AVS modules and networks.
The CM/AVS modules read, window, gain, and slice large multi-dimensional
(up to six dimensions) datasets on the CM-5 and then pass the images
to a workstation for displaying or 3-D rendering with standard AVS modules.
We demonstrate our application
by visualizing a 3-D prestack marine
survey and a 3-D migrated volume together with a 3-D velocity function.

Lateral prediction for noise attenuation by t-x and f-x techniques (ps 883K) (src 12118K)
**Abma R. and Claerbout J.**

Attenuating random noise with a prediction filter in the
time-space domain generally produces results similar to those of
predictions done in the frequency-space domain.
However, in the presence of moderate- to high-amplitude noise,
time-space, or t-x prediction passes less random noise than does
frequency-space, or f-x prediction.
The f-x prediction may also produce false events in the presence
of strong parallel events where t-x prediction does not.
These advantages of t-x prediction are the result of its ability to control
the length of the prediction filter in time.
An f-x prediction produces an effective t-x domain filter that is
as long in time as the input data.
Gulunay's f-x domain prediction, also referred to as FXDECON,
tends to bias the predictions toward the traces nearest the output trace,
allowing more noise to be passed, but this bias may be overcome by
modifying the system of equations used to calculate the filter.
The three-dimensional extension to the two-dimensional t-x and f-x
prediction techniques allows improved noise attenuation,
because more samples are used in the predictions,
and the requirement that
events be strictly linear is relaxed.

3-D data infill and extrapolation (ps 140K) (src 217K)
**Claerbout J. F.**

Here I deal with data given on a uniform 3-D mesh (or 1-D or 2-D).
I provide code for recovering missing data in
the interior of the cube or abutting one wall of the 3-D data cube
by a two-stage linear least squares process.
First I fit a 3-D prediction-error filter (PEF) to the extended cube
ignoring regression equations that involve missing elements.
Then I estimate those missing elements
by finding the data that minimizes the power out of the PEF.
As in my other work since SEP-73,
the volume can be broken into subcubes
in which separate problems are solved and pieced together.

Operator design for three-dimensional data extrapolation (ps 286K) (src 1515K)
**Abma R.**

In this paper,
extrapolation of data in three dimensions
is done in two steps.
First, a three-dimensional annihilation filter is calculated
from the available data.
Next, the result of filtering an extended volume with the
calculated annihilation filter from the first step
is then minimized by computing the missing data in
the extended volume.
This technique
suffers from a limited
extrapolation range and from edge effects.
By making predictions with purely lateral prediction filters,
the distance the data is extrapolated in the spatial directions is extended.
Also, although not well understood,
the use of multiple directional
prediction filters
appears to improve the extrapolation quality,
especially near the edges of the volume where very poor
predictions are made.
These three-dimensional directional filters are lateral filters with
the output on one corner of the three-dimensional filter.
While these results are preliminary,
the techniques presented here look promising.

Statics estimation by optimization of local slant stacks (ps 313K) (src 654K)
**Cole S.**

Estimating statics by maximization of stack power
presumes that NMO correction has flattened events.
For estimating statics prior to NMO correction, or
where a sufficiently accurate NMO correction is not
available, an alternative is to optimize the power
of local slant stacks. Long wavelength statics
present a problem, as with other algorithms, but
varying the number, size, and overlap of the local slant
stacks can help.

Reflection tomography: Kjartansson revisited (ps 543K) (src 951K)
**Claerbout J. F.**

I begin experiments with Kjartansson's data set with the
goal of constructing a near-but-below-surface velocity model.
I test lateral extrapolation of data before tomography
and propose an alternate definition of pilot trace.
Traditionally, a pilot trace is defined as a stack trace.
Here I define a pilot trace as
the output of a three-dimensional prediction filter.
This pilot trace is designed to be
insensitive to velocity, dip, and shot statics.
The crosscorrelation of this pilot trace with the observed trace
is highly sensitive to geophone statics
as well as deeper lateral velocity variations beneath the geophones.
This crosscorrelation function of midpoint and offset
is slant-stacked transforming offset to depth.
With suitable normalization the result is a volume
of coherency with axes of depth, midpoint, and slowness.
The strange ``footprint'' of the 3-D prediction filter
confuses the construction of a specific slowness model.
A less confusing alternate is a Snell wave approach.

Toward estimating near surface lateral velocity variations (ps 145K) (src 10913K)
**Bevc D.**

Near surface velocity irregularities distort the seismic wavefield and
cause focusing anomalies in the data. These anomalies can be detected
by examining plots of trace power in midpoint-offset coordinates.
I generate synthetic data by upward continuing a synthetic wavefield
through a *v*(*x*,*z*) model. The location of the velocity anomaly is
determined by analyzing a plot of trace power in midpoint-offset coordinates.
By performing iterative slant stacks of the power plots, I can image the
velocity anomaly. Finally, I downward continue the wavefield through
the velocity anomaly in order to remove distortions from the data.

A parallel implementation of Kirchhoff DMO (ps 225K) (src 230K)
**Blondel P.**

In this paper I compare two parallel algorithms
for three-dimensional (3-D) Kirchhoff dip moveout (DMO)
in a constant velocity medium.
In the case of 3-D land data,
the highly irregular offset geometry pleads for
an algorithm where data are processed in time slices.
This mapping of the data into processor memory
minimizes the cost of communication, which is reduced
to nearest neighbor communication of time slices,
and achieves load balance, keeping eighty percent of the
processors busy throughout the process. The time aliasing
of the operator is solved by a spatial convolution with
dip-dependent triangles in a two-dimensional parallel implementation.

How variable velocity dip moveout improves post-stack migration (ps 361K) (src 500K)
**Blondel P.**

Nowadays, a standard industrial seismic processing almost always involves
the constant-velocity dip moveout correction. Two main features make the
process attractive. First, the computational cost is low compared to
prestack migration in both two-dimensional and three-dimensional
processings. Secondly, because constant-velocity dip moveout is
``independent of velocity'', it may come before velocity analysis,
removing the effects of dip Forel and Gardner (1988).
...

3-D Hale-McClellan migration: A salt intrusion example (ps 808K) (src 37016K)
**Palacharla G. and Biondi B.**

McClellan transformation offers a computationally efficient scheme
for 3-D post-stack depth migration. The accuracy of the response of
the McClellan filter is improved by rotating and averaging the
filter. We have implemented the
McClellan migration with the improved circular response
and tested it on real data, a salt intrusion example.
The migration collapses the diffractions, thereby
delineating the salt and fault boundaries.
The migration results obtained using different McClellan filters show
only slight differences because of the limited dip and frequency range
in the dataset we used for testing the algorithm.

Prestack slant stack migration and its application in AVO analysis (ps 340K) (src 1112K)
**Lin J.**

One synthetic and one field dataset from the Gulf of Mexico were used to test a program of
prestack slant stack migration with phase shift plus
interpolation (PSPI). The migrated section showed
a correct image with this algorithm, even with lateral velocity
variations. I also took advantage of this migration to do
amplitude-versus-offset (AVO)
analysis on the migrated field dataset. The prestack slant stack migration
collapses diffractions, and focuses bright spots, thus increasing
confidence in AVO analysis.

Prestack phase-shift migration for separate offsets (ps 251K) (src 451K)
**Popovici A. M.**

The straightforward implementation of the double square root
(DSR) equation in common midpoint and offset coordinates
for prestack migration
produces notable
artifacts that are routinely attributed to Fourier domain wraparound
in the offset wavenumber space. These artifacts usually
preclude the use of DSR for separate constant-offset sections.
I show that the artifacts are not
due to Fourier wraparound. I present two phase-shift
constant-offset migration algorithms free of offset artifacts.
The first algorithm migrates
each individual constant-offset at a time, but is slower
overall than the second algorithm which
requires all the constant-offset sections
to be migrated at the same time. Depending on the problem to
be solved one method could be more convenient than the other.

Controlled illumination by wavefront synthesis (ps 1202K) (src 3788K)
**Ji J.**

Controlled illumination by wavefront synthesis is
a depth migration which is tuned
by adopting the wavefront synthesis technique.
This imaging method provides several advantages
over conventional prestack depth migration.
One is computational efficiency,
the second is the quality of the images,
and the third is that it provides
more information about reflectors, such as
angle dependent reflection coefficients.

Four-pass technique for 3-D omega-x-y migration (ps 346K) (src 396K)
**Teng L. and Palacharla G.**

This paper tests Ristow's four-pass method of 3-D migration as an
improvement on the conventional two-pass finite-difference migration.
The four-pass
technique consists of applying the forty-five degree
finite-difference operator along the inline and
crossline directions and along the other two directions at forty-five
degree azimuth to the inline and crossline directions.
We have derived the dispersion relation
and differential equations
for the four-pass technique and implemented the four-pass
technique. The results
show that the four-pass operator is more isotropic than the two-pass
one.

Stacking fundamentals (ps 270K) (src 282K)
**Claerbout J. F.**

Velocity increasing with depth causes
moveout curves to cross.
Here we begin from the modeling operator and its adjoint,
the stacking operator.
Weighting functions can be used both before and after NMO.
We find that weighting functions that make the operator
quasi-unitary also sharpen the stack.

AVO analysis of methane hydrate seismic data (ps 1272K) (src 40105K)
**Ecker C. and Lumley D.**

Marine seismic data from the Blake Outer Ridge offshore Florida show strong
``bottom simulating reflections'' (BSRs) associated with methane hydrate
occurrence in deep marine sediments. We use a detailed amplitude versus offset
(AVO) analysis of these data to explore the validity of two models regarding
the origin of bottom simulating reflectors. After careful
preprocessing steps including source wavelet deconvolution, nonlinear trace
interpolation, amplitude and moveout traveltime calibration, and velocity
analysis, we estimate the P and S impedance contrasts at all subsurface
positions. This is done by applying a least-squares elastic parameter inversion
method to the preprocessed CMP gathers. Our results suggest that the Blake
Outer Ridge BSR is compatible with a model of methane hydrate in sediment,
overlying a layer of free methane gas-saturated sediment.

Time-lapse seismic reservoir monitoring: The petrophysical basis (ps 2634K) (src 12362K)
**Lumley D., Dvorkin J., and Nur A.**

Time-lapse seismic monitoring of subsurface rock property changes
incurred by reservoir production processes is increasingly being proposed
as a new diagnostic tool in efficient reservoir characterization
and management. We perform a model study to simulate waterflood production
in a light oil reservoir of Ottawa sand, and generate synthetic
time-lapse monitor seismic data both pre-flood, and at two subsequent
waterflood
phases. Pore pressure and oil/water pore saturation levels are simulated
in the reservoir due to two water injection well galleries by diffusive
fluid-flow modeling. The pressure and saturation data are converted to rock
density and both bulk and shear moduli, using rock physics
calibration curves derived from laboratory data. Synthetic seismic
reflection data are generated from the resulting spatially variable
rock physics properties at three separate waterflood stages. In the presence
of realistic noise levels, stacked and prestack migrated reflection images
clearly show the extent of the water-invaded zone after production.
Furthermore, we apply a prestack seismic impedance inversion method and
accurately track the relative P and S elastic impedance changes in the
reservoir
rock caused by the varying petrophysical conditions associated with the
waterflood production process.

Angle-dependent reflectivity estimation by Kirchhoff migration/inversion: Theory (ps 98K) (src 39K)
**Lumley D. and Beydoun W. B.**

We derive a new Kirchhoff forward and inverse theory for modeling and
estimating P-P angle-dependent reflectivity. We replace conventional
reflecting surface excitations by *equivalent body force* volumetric
excitations, and then linearize the divergence of the elastic stress
tensor wavefield with respect to smooth background material properties.
To obtain the reflected wavefield, we perform a volume integral over the
equivalent body force distribution, and interpret this result as a hybrid of
Zoeppritz plane-wave reflection and Rayleigh-Sommerfeld elastic diffraction.
We pose the inverse problem as a least-squares optimization to
estimate angle-dependent reflectivity, including the reflection angles,
by minimizing the squared error between the forward theory predictions and
the observed seismograms. The resulting coupled normal equations
are decoupled by the method of stationary phase, and then the uncoupled
equations are solved by a classical Gauss-Newton gradient method with
an approximate diagonal Hessian operator. The estimation for angle-dependent
reflectivity requires a simultaneous calculation of four differently weighted
Kirchhoff prestack depth migrations, which combine to compensate for
limited acquisition aperture and enhanced reflection amplitude recovery.

Preconditioning (ps 30K) (src 2K)
**Claerbout J. and Nichols D.**

Explicit schemes for estimating elastic properties of multiphase composites (ps 418K) (src 395K)
**Berryman J. G.**

Explicit schemes of Mori-Tanaka and Kuster-Toksöz for estimating
elastic properties of multiphase composites are compared and contrasted.
Both methods are known to have a limited range of validity. Reexamination
of the theories and comparisons to experiment lead to
the conclusion that these explicit schemes should not be used
to estimate properties of systems in which the host material occupies
less than of the total volume.
A unified approach to derivation of these explicit
methods, as well as some implicit methods, is also presented.

Elements of an exact kinematic theory for wavefronts traveling through layered anisotropic media (ps 36K) (src 2K)
**Muir F.**

Most conventional seismic processing steps assume either that the velocity
function, *v*(*z*), is known, or that it can be determined from the data.
A further, related, assumption is that the earth is isotropic. This is a
major convenience and allows the use of simple, ray-based arguments for
developing processes such as **DMO**. This **Isotropic Paradigm** is
clearly useful where it is backed up by well control, but is unnecessary
and may be quite misleading in frontier areas where surface seismic is the
sole information source.
In case of surface seismic data all processing steps up to and including
...

Extending Stolt migration to general dispersion relations (ps 260K) (src 804K)
**Ecker C. and Muir F.**

Nowadays, most data processing methods use depth dependent parameters that can
not be determined in a direct way but have to be estimated indirectly. On the
other hand, data processing in time requires only the knowledge of parameters
that can be measured on the surface such as time, offset and horizontal velocity
Muir (1993).
This is of advantage especially in the case of anisotropy as the vertical
velocity does not need to be estimated any longer.
...

Comparison of different interpolation methods for Stolt migration (ps 260K) (src 313K)
**Lin J., Teng L., and Muir F.**

In Stolt migration, it's very important to select a good algorithm for
interpolation in the frequency domain.
Incorrectly migrated events caused by a bad interpolator
can badly distort the correctly migrated events. Harlan
1982 showed some of the artifacts produced by different
interpolators.
In this paper we compare the following five different interpolation methods:
nearest-neighbor, linear, linear plus cork-screw, Harlan's 10-point scheme, and
...

Interpolation in Stolt migration (ps 46K) (src 3K)
**Popovici A. M., Blondel P., and Muir F.**

Downward continuation and imaging in the isotropic
case (Gazdag, 1978) can be written as

...
(1)

Parallel computing exhumes slow Fourier transform in Stolt migration (ps 233K) (src 300K)
**Blondel P. and Muir F.**

Stolt migration is a remapping of the data in the frequency-wave-number
domain. The mapping function may be an expression of the wave equation
either in isotropic media or in anisotropic media
Dellinger et al. (1993); Ecker and Muir (1993).
Both cases require a frequency-domain interpolation that can be a source
of many numerical artifacts Harlan (1982);
...

Modeling, adjoint modeling, and migration in V(z) media, using mono-frequency Green's functions (ps 290K) (src 587K)
**Nichols D.**

Modeling and migration are very simple to implement if
pre-tabulated Green's functions are available. I use Green's
functions, calculated at a few frequencies to estimate, the
Green's functions for all frequencies. In a V(z) medium the
Green's function is independent of surface location therefore only
one set needs to be calculated. I calculate this set by one way
extrapolation in polar coordinates. They are then used to perform
prestack modeling and migration of data. Because they are
calculated in polar coordinates they can be used to model and
image overturned waves.

Modeling nonlinear source-surface interactions (ps 550K) (src 551K)
**Karrenbach M.**

The interaction of a seismic source device
with the free surface of the earth
changes the radiation characteristic to be different from that of the
equivalent body point source.
Usual seismic sources are built to give enough energy
to penetrate a few kilometers in the earth.
It is not guaranteed that when the source is activated
the surface material behavior stays within a region that
can be appropriately described using infinitesimal stress
strain relationships. Finite differences can easily model
radiation characteristics and wave propagation when the
equations of motion are no longer linear.
I compare two nonlinear elastic wave equation to model such
source behavior.

3-D Eikonal equation for time migration (ps 45K) (src 3K)
**Berlioux A.**

In the short-note I wrote in the previous SEP report Berlioux (1993b),
I presented a new method to perform depth migration in 3-D, starting from
time-migrated maps. Since time migration does not always produce properly
migrated images or maps in areas where velocity variations are present
Hatton et al. (1981), the method I proposed consists of two parts: first
undo the time migration by a principle of *de-migration*, and then perform
the depth migration.
...

3-D grid with GOCAD (ps 526K) (src 2732K)
**Berlioux A.**

The aim of this article is two-fold. First, a small program has
been developed to build a 3-D grid and fill it from geological or
geophysical models using the GOCAD library of functions. This 3-D grid
program has been tested in many cases and has produced good results
even with very complex structural models. Second, a proposal is made
to elaborate a new implementation of the `GRID3_t` object of
GOCAD in a manner more convenient for geophysical and/or geological
purposes.

11/16/1997