Application of azimuth moveout to the coherent partial stacking of a 3-D marine data set (ps 1198K) (src 5340K)
**Biondi B., Fomel S., and Chemingui N.**

The application of azimuth moveout (AMO) to a marine
3-D data set shows that
by including AMO in the processing flow
the high-frequency steeply-dipping energy
can be better preserved
during partial stacking over a range of offsets and azimuths.
Since the test data set requires 3-D prestack depth migration
to handle strong lateral velocity variations,
the results of our tests support the applicability
of AMO to prestack depth imaging problems.

Handling irregular geometry in wide-azimuth surveys (ps 972K) (src 4338K)
**Chemingui N. and Biondi B.**

The processing of seismic data for amplitude
inversion often neglects an important
issue which could be detrimental to amplitude preservation: the effect
of sparse and irregular geometry. The problem is severe in wide-azimuth
3-D surveys
acquired with the aim of studying the
azimuthal variations in the AVO gradient.
We present a new technique for processing
wide-azimuth surveys that accurately images 3-D seismic data while preserving
relative amplitudes describing the offset and azimuth-dependent reflectivity
function. The method focuses on both algorithm accuracy and proper handling
of irregular geometry and therefore allows for reliable
AVO analysis on migrated data.
The technique is based on organization of the data into common-azimuth
(CA) and common-offset (CO) cubes and allows
interpolation into a regular grid before imaging.
The regular CA/CO cubes are then migrated using an efficient true-amplitude
migration algorithm. We apply this technique in order to invert for a
synthetic reflectivity model
simulating a
real 3-D wide-azimuth land survey over a fractured reservoir.
Results show that, as expected, Kirchhoff migration
is very sensitive to uneven sampling, which creates
strong amplitude distortions. The azimuth moveout (AMO) transformation
succeeded in organizing the data as regular gridded cubes while preserving
its amplitude information for imaging.
We conclude that interpolating seismic data prior to migration is
effective in preserving amplitude information
and that AMO can effectively
correct for the irregular sampling in wide-azimuth surveys.

Revealing geological discontinuities by local plane wave suppression (ps 1009K) (src 32945K)
**Schwab M., Holden C., and Claerbout J.**

Interpreters
of migrated seismic image volumes
need to delineate
reflector discontinuities,
such as faults or buried channels.
To enhance these discontinuities
we applied local, data-adaptive Prediction Error (PE) Filters
to the migrated image.
We
restricted
the PE Filters
to local combinations of 2-D filters,
which
remove
local planar events
and
reveal
rapidly varying local features.
Unfortunately,
while the scheme
successfully enhanced
geological discontinuities
in one field data case,
it failed in two others.
In these two cases,
the PE Filters
erroneously
predicted (and consequently removed)
the geological discontinuities of interest.
We were unable to tune the PE Filters
to forgo a specific target bandwidth.
Such a tuning may be possible if we use a sequence of two
PE filtering steps of which the first filter prewhitens the
image.
In another case,
the PE filter
enhanced the image's acquisition footprint
and thereby obliterated any geological details.
Moreover,
we do not yet know how to combine optimally
the various PE Filter residuals to produce
a meaningful subsurface map.

Reservoir monitoring: A multi-disciplinary feasibility study (ps 1375K) (src 36622K)
**Biondi B., Deutsch C., GundesøR., Lumley D., Mavko G., Mukerji T., Rickett J., and Thiele M.**

Monitoring reservoir changes with time-lapse seismic holds the promise
to significantly improve reservoir characterization and reservoir
management. To relate time-dependent changes in seismic to the
underlying geological description and flow processes requires input
from a number of disciplines: (1) geological modeling/geostatistics,
(2) flow simulation, (3) rock physics, and (4) seismic imaging. This
paper documents the start of a project that brings these disciplines
together.
In this initial model study we have considered the forward problem,
i.e., create a detailed geological truth model, perform flow simulation,
relate the dynamic rock properties to seismic properties,
and, finally, image the reservoir at multiple times. We document this
forward modeling exercise on a single geological relization
and discuss opportunities for future work.

Modeling heterogeneous reservoirs using the first order Born Approximation (ps 151K) (src 178K)
**Rickett J., Biondi B., and Lumley D.**

This short-note is intended as a companion paper to
Biondo et al. 1996. It aims to examine the
validity of some of the assumptions necessary for the Born
elastic scattering method which we used to create the synthetic
seismograms, especially the assumption of weak scatterers which
allows the problem to be treated as linear.
Born generated synthetic seismograms for plane layer models are compared
with Zoeppritz reflection coefficients, and can be seen to give good
...

Passive seismic imaging applied to synthetic data (ps 148K) (src 195K)
**Rickett J. and Claerbout J.**

It can be shown that for a 1-D Earth model illuminated by random plane waves
from below, the cross-correlation of noise traces recorded at two points on the
surface is the same as what would be recorded if one location contained a
shot and the other a receiver. If this is true for real data, it could
provide a way of building `pseudo-reflection seismograms' from background
noise, which could then be processed and used for imaging.
This conjecture is tested on synthetic data from simple
1-D and point diffractor models,
and in all cases, the kinematics of observed events
appear to be correct.
The signal to noise ratio was found to increase as , where *n* is
the length of the time series. The number of incident
plane waves does not directly affect the signal to noise ratio; however,
each plane wave contributes only its own slowness to the common
shot domain, so that if complete hyperbolas are to be imaged
then upcoming waves must be incident from all angles.

Fluid-flow simulation concept of methane hydrate growth and decomposition (ps 609K) (src 983K)
**Ecker C.**

Bottom simulating reflectors (BSR) are associated with the base of the
stability zone of methane hydrates. The occurrence, stability and breakdown
of these BSRs is considerably dependent on the temperature and pressure
conditions in the sediment. Any P-T changes can affect the
hydrate stability significantly and thus influence the behavior
of the BSRs. I present
the theory and development of a three-dimensional finite-difference fluid-flow
simulator for hydrate decomposition/growth in porous media. I derive the
equation for a 3-phase/2-component isothermal gas-water-hydrate system
and discuss the
code development of a two-dimensional system. The code is still in a test phase
and is not working properly for all required cases. I show the results of
some preliminary code testing based on simple gas-water flow.
Furthermore, I discuss
how to include more realistic thermodynamics into the system.

Velocity space interpolation of aliased seismic data by preconditioning (ps 768K) (src 5403K)
**Crawley S.**

Sparsity and irregularity of spatial sampling are common problems in
seismic data.
Irregularity severely limits the types of processes which may be applied
to a data set, and any process will likely fail on data which are
overly sparse, as data and operator aliasing become a crippling problem.
Interpolation schemes seek to dealias data,
but are themselves challenged by aliasing,
because it is difficult for an algorithm
to pick exclusively the correct dip or dips to interpolate.
Transformation to velocity (or slowness) space is an attractive
basis for an interpolation algorithm, because the operator
is limited
to 'reasonable' directions, in that it operates only along centered
hyperbolas.
Since data can be organized so that it is symmetric, and largely
hyperbolic,
in CMP gathers,
this type of interpolation should greatly reduce the risk of interpolating
incorrect dips.
However, the velocity transform is not an exact
forward/inverse-transform pair, and the smoothness and/or noisiness
of the estimated velocity spectrum presents a new and serious pitfall.
While the original data space may be remodeled exactly, large
artifacts are likely to appear in alternate similar data spaces, such as are
appropriate for interpolation or regularization.
By preconditioning the inversion, the model may be made more parsimonious,
resulting in improved remodeling into a new data space.

Validation and update of 3-D velocity models by inversion of seismic and well-log data (ps 258K) (src 198K)
**Berlioux A.**

In this paper, I propose a new procedure for estimating the
validity of 3-D velocity models combining seismic data and
well-log information.
The method I describe gives the best least-square 3-D model for the
velocity. It has even more potential for
determining how accurate a velocity model is by estimating a
range of possible models and giving a measure of local uncertainty
about the velocity. I propose to use a 3-D prestack seismic survey
as well as the well-log curves available on the site of the survey
to evaluate and update a 3-D velocity model. Performing 3-D velocity
analysis on the 3-D prestack seismic data, I will get an initial
velocity model. From the well-log information, I plan to extract
velocities at the well locations. I will then employ two different
approaches to derive an accurate 3-D velocity model. The first is
based on the least-square inversion of the well-log-derived velocities
and uses the seismic velocities as a constraint, by applying for a
conjugate gradient method. The second approach is a simulation of the
velocity at each node of the 3-D model, using a sequential Gaussian
simulation algorithm based on a generalized least-square inverse
technique (kriging). I also intend to estimate local and global
uncertainties about the velocity model I have derived.

On nonhyperbolic reflection moveout in anisotropic media (ps 131K) (src 50K)
**Fomel S. and Grechka V.**

The famous hyperbolic approximation of *P*-wave reflection moveout is
strictly accurate only if the reflector is a plane, and the medium is
homogeneous and isotropic. Heterogeneity, reflector curvature, and
anisotropy are the three possible causes of moveout
nonhyperbolicity at large offsets. In this paper, we analyze the
situations where anisotropy is coupled with one of the other two
effects. Using the weak anisotropy assumption for transversely
isotropic media, we perform analytical derivations and comparisons.
Both the case of vertical heterogeneity and the case of a curved
reflector can be interpreted in terms of an effective anisotropy,
though their anisotropic effects are inherently different from the
effect of a homogeneous transversely isotropic model.

Migration and velocity analysis by velocity continuation (ps 633K) (src 919K)
**Fomel S.**

Residual and cascaded migration can be described as a continuous
process of velocity continuation in the post-migration domain. This
process moves reflection events on the migrated seismic sections
according to changes in the migration velocity. Understanding the laws
of velocity continuation is crucially important for a successful
application of migration velocity analysis. In this paper, I derive the kinematic
laws for the case of prestack residual migration from simple
trigonometric principles. The kinematic laws lead to dynamic theory
via the method of characteristics. The main theoretical result is a
decomposition of prestack velocity continuation into three different
components corresponding to residual normal moveout, residual dip
moveout, and residual zero-offset migration. The contribution and
properties of each of the three components are analyzed separately.

Azimuthal behavior of P-waves in horizontal transverse isotropy (ps 919K) (src 974K)
**Urdaneta H.**

The behavior of P-wave reflection varies with azimuth for rocks whose
material properties vary with azimuth. I study the effects of
horizontal transverse isotropy in P-wave reflection patterns on a
simple homogeneous model, a finely fractured shale overlying an
isotropic chalk with varied amounts of fracturing. I have produced
2-D reflectivity maps that clearly illustrate the azimuthal
behavior of P-waves as the aspect ratio, volume density and filling
material of the cracks are varied.

Amplitude preservation for offset continuation: Confirmation for Kirchhoff data^{} (ps 71K) (src 13K)
**Fomel S. and Bleistein N.**

Offset continuation (OC) is the operator that transforms common-offset
seismic reflection data from one offset to another. Earlier papers by
the first author presented a partial differential equation in midpoint
and offset to achieve this transformation. The equation was derived
from the kinematics of the continuation process. This derivation is
equivalent to proposing the wave equation from knowledge of the
eikonal equation. While such a method will produce a PDE with the
correct traveltimes, it does not guarantee that the amplitude will be
correctly propagated by the resulting second-order partial
differential equation. The second author (with J. K. Cohen) proposed
a dip moveout (DMO) operator for which a verification of amplitude
preservation was proven for Kirchhoff data. It was observed that the
solution of the OC partial differential equation produced the same DMO
solution when specialized to continue data to zero offset.
Synthesizing these two approaches, we present here a proof that the
solution of the OC partial differential equation does propagate
amplitude properly at all offsets, at least to the same order of
accuracy as the Kirchhoff approximation. That is, the OC equation
provides a solution with the correct traveltime and correct
leading-order amplitude. ``Correct amplitude'' in this case means
that the transformed amplitude exhibits the right geometrical
spreading and reflection-surface-curvature effects for the new offset.
The reflection coefficient of the original offset is preserved in this
transformation. This result is more general than the earlier results
in that it does not rely on the two-and-one-half dimensional
assumption.

Conjugate-direction Huber regression (ps 60K) (src 26K)
**Claerbout J.**

A straight-forward way to make conjugate-direction regressions
robust (insensitive to bursty data noise)
is based on the objective function of Huber
(least squares for small residuals and
least absolute values for large ones).
The gradient is based on the
clipped residual instead of the residual itself.
Likewise the clipped residual
is used to define the
plane of the gradient and previous step (plane search).
This method does not apply to the deconvolution problem
because there noisy field data enters into the *operator*
for the determination of the prediction-error filter.

Medians in multivariate regression (ps 58K) (src 24K)
**Claerbout J.**

Here I design filters and models of hyperbola superposition
based on medians.
Let *r*_{i} be a residual and be a residual
perturbation caused by a change
in the model
.With ,choosing gives us residuals where as many components as possible
...

Nonlinear least squares and regularization (ps 58K) (src 9K)
**Berryman J. G.**

I present and discuss some general ideas
about iterative nonlinear output least-squares methods.
The main result is that, if it is possible to do forward
modeling on a physical problem in a way that permits
the output (*i.e.*, the predicted values of some physical
parameter that could be measured) and the first derivative of
the same output with respect to the model parameters
(whatever they may be) to be calculated numerically, then
it is possible (at least in principle) to solve the inverse
problem using the method described.
The main trick learned in this analysis comes from the realization
that the steps in the model updates may have to be quite
small in some cases for the implied guarantees of convergence to
be realized.

Least-square inversion with inexact adjoints. Method of conjugate directions: A tutorial (ps 381K) (src 3054K)
**Fomel S.**

This tutorial describes the classic method of conjugate directions:
the generalization of the conjugate-gradient method in iterative
least-square inversion. I derive the algebraic equations of the
conjugate-direction method from general optimization
principles. The derivation explains the ``magic'' properties of
conjugate gradients. It also justifies the use of conjugate
directions in cases when these properties are distorted
either by computational errors or by inexact adjoint operators. The
extra cost comes from storing a larger number of previous search directions
in the computer memory. A simple ratfor program and three examples
illustrate the method.

Stacking operators: Adjoint versus asymptotic inverse (ps 367K) (src 1968K)
**Fomel S.**

The paper addresses the theory of stacking operators used in
seismic data processing. I compare the notion of asymptotically
inverse operators with the notion of adjoint operators. These two
classes of operators share the same kinematic properties, but their
amplitudes (weighting functions) are defined differently. I introduce
the notion of the *asymptotic pseudo-unitary* operator, which possesses
both the property of being adjoint and the property of being
asymptotically inverse. The weighting function of the asymptotic
pseudo-unitary stacking operator is completely defined by its
kinematics. I exemplify the general theory by considering such
stacking operators as Kirchhoff datuming, migration, offset
continuation, DMO, and velocity transform.

Tieman's conversion of common-midpoint slant stacks to common-source (ps 58K) (src 25K)
**Harlan W. S. and Claerbout J.**

We derive equations for transforming slant stacks
at common midpoint to plane wave stacks, i.e.
slant stacks at common shotpoint or common geophone point.

Results of Tieman's conversion of common-midpoint to common-source point slant stacks on synthetic data (ps 300K) (src 1821K)
**Holden T. C.**

I became aware of Hans Tieman`s curious method of transforming slant stacks
of midpoint gathers into slant stacks of common
shot gathers in January of 1996 during a presentation he
gave to SEP. Inspiration to write this paper also comes from William
Harlan and Jon Claerbout who expressed interest in Tieman`s work. Harlan and
Claerbout presented a derivation of the Tieman transform equations during
an SEP seminar soon after Tieman`s visitHarlan and Claerbout (1996).
Tieman's transformation holds promise in providing an accurate method of
...

Test of wavelet-based seismic data compression software (ps 1257K) (src 2067K)
**Sun Y. and Biondi B.**

In this paper, we test a new wavelet-transform based seismic data compression
technique developed by Chevron. We apply this technique
to two synthetic datasets and one field dataset.
Our results show that this new compression approach can virtually retain all of
the important seismic information at high compression ratios.
We summarize several empirical rules which will help the high performance of
this software.

Making scientific computations reproducible (ps 207K) (src 317K)
**Schwab M., Karrenbach M., and Claerbout J.**

To organize computational scientific research
and hence to conveniently transfer our technology,
we impose a simple filing discipline on the authors in our laboratory.
A document's makefile includes laboratory-wide standard rules
that offer readers these four standard commands:
`make burn` removes the document's result figures,
`make build` recomputes them,
`make tube` displays the figures, and
`make clean` removes any intermediate files.
Although we developed these standards to aid readers
we discovered that authors are often the principal beneficiaries.

SEPlib90: SEPlib for 3-D prestack data (ps 1146K) (src 4617K)
**Biondi B., Clapp R., and Crawley S.**

We developed a generalization of the SEPlib software package
capable to handle data with irregular spatial sampling,
such as 3-D prestack seismic data.
The new SEPlib, dubbed SEPlib90, is layered on the top
of the old SEPlib, and shares with it the flexibility of use and
the efficiency in accessing large amount of data.
These attractive characteristics derive from
two principles at the basis of SEPlib90 design:
separation of the geometry information from the data traces,
and exploitation of existing regularity, if any, in the data geometry.

Fortran90: Introduction and use in 3-D geophysical problems (ps 105K) (src 71K)
**Clapp R. G. and Crawley S.**

There is a general consensus in the scientific community that object oriented
programming is the correct way to perform research. The object oriented
approach allows much more
complex ideas to be explored by allowing the scientist to concentrate on
ideas rather than algorithms.
This feature is especially attractive in problems such as we encounter in
3-D processing, where dealing with the huge
data size and irregularity
is extremely cumbersome and prone to errors, in traditional
languages such as Fortran77.
We use Fortran90, built upon the existing SEP90 accessors
routines, as the building blocks to an object oriented processing environment.
Our initial efforts indicate that a Fortran90 base can provide the
flexibility of C++, while maintaining the simplicity of Fortran,
to effectively
solve complex
geophysical problems.

11/12/1997