Seismic imaging using Riemannian wavefield extrapolation (ps.gz 23627K) (pdf 3056K) (src 41056K)
**Sava P. and Fomel S.**

Riemannian spaces are described by
non-orthogonal curvilinear coordinates.
We generalize one-way wavefield extrapolation to
semi-orthogonal Riemannian coordinate systems, which
include, but are not limited to, ray coordinate systems.
We obtain one-way wavefield extrapolation methods
which are not dip-limited,
and which can even be used to image overturning waves.
Ray coordinate systems can be initiated either from
point sources, or from plane waves incident at various
angles.
Since wavefield propagation happens mostly along the
extrapolation direction, we can use cheap
finite-difference or mixed-domain
extrapolators to achieve high angle accuracy.
The main applications of our method include imaging
of steeply dipping or overturning reflections.

Wavefield extrapolation in phase-ray coordinates (ps.gz 13927K) (pdf 3186K) (src 77388K)
**Shragge J. and Biondi B.**

A ray theoretic formulation is developed that allows rays to be
traced directly from existing solutions to the Helmholtz equation.
These rays, termed phase-rays, are defined by the direction normal to
surfaces of constant wavefield phase.
Phase-rays exhibit a number of attractive characteristics, including
triplication-free ray-fields, an ability to shoot rays forward or
backward, and an ability to shoot infill rays for ensuring adequate ray density.
Because of these traits, we use phase-rays as a coordinate basis on which to
extrapolate wavefields using the generalized coordinate system approach.
Examples of wavefields successfully extrapolated in phase-ray coordinates are
presented, and the merits and drawbacks of this approach,
relative to conventionally traced ray coordinates, are discussed.

Amplitude balancing of 3-D angle-domain common-image gathers (ps.gz 168K) (pdf 690K) (src 759K)
**Biondi B.**

The azimuthal resolution
of 3-D Angle Domain Common Image Gathers (ADCIGs)
strongly varies
with the reflection aperture angle.
This dependence
may cause severe distortions in the image
when 3-D ADCIGs
are averaged over azimuths.
To correct for these distortions,
I derive an effective weighting method
based on the jacobian of the transformation to angle domain.
The proposed method
avoids the underweighting of the reflections close to normal incidence
by properly taking into account the ``folding'' of the azimuth axis.
A simple scheme to limit
the range of the azimuthal averaging as a function of the opening angle
further attenuates noise in the image.
A synthetic example illustrates the practical application
of the proposed methodology .

Velocity sensitivity of subsalt imaging through regularized inversion (ps.gz 1926K) (pdf 653K) (src 4685K)
**Clapp M. L.**

The effects of inaccurate velocity models on migration are well known.
Accurate velocity models are most difficult to obtain in complex areas
where iterative inversion can provide a better image than migration.
This paper investigates the velocity sensitivity of a regularized inversion
scheme that explicitly assumes that the correct velocity is being used.
This inversion uses a regularization operator that assumes that there is
no moveout along the offset ray parameter axis. Experiments performed
with various incorrect velocity models indicate that this assumption
is valid for velocity models that can be reasonably produced by common
velocity analysis techniques. Velocity models that are very inaccurate
cause the inversion process to reject attempts by the regularization
to produce an image that is inconsistent with the data.

WKBJ and amplitude preserving one-way wave equation (ps.gz 19K) (pdf 70K) (src 5K)
**Shan G. and Biondi B.**

The standard one-way wave equation Claerbout (1971) produces the correct phase
of the wavefield, but it is not equivalent to the acoustic wave equation in terms of amplitude.
Zhang (1993) suggests that to improve the dynamics information of one-way wave equation,
an amplitude correction term should be included into the standard one-way wave equation.
Zhang et al. (2001) apply the one-way wave equation with the amplitude correction
to shot-profile migration and shows that it can provide the same amplitude
as an image produced by the true amplitude Kirchoff migration Hanitzsch (1997) by asymptotic analysis.
...

Kinematics of 3-D angle-domain common-image gathers for migration velocity analysis (ps.gz 467K) (pdf 876K) (src 974K)
**Tisserant T. and Biondi B.**

We extend the study of the kinematic properties
of 2-D offset- and angle-domain common-image gathers
to the general 3-D problem.
We examine how the use of an incorrect
migration velocity affects the behavior of the image in
the offset and angle domains.
We show that the general 3-D case with and without the correct
migration velocity can be cast into a 2-D formulation, making it
possible to apply existing theory from 2-D.
We illustrate both ray-tracing and plane-wave approaches to the
problem and verify our theoretical results with a synthetic model.

Wave-equation MVA: Born, Rytov and beyond (ps.gz 1409K) (pdf 480K) (src 2761K)
**Sava P. and Biondi B.**

The linearized wave-equation MVA operator can be used for
velocity analysis using both Born and Rytov approximations.
The distinction arises from the method used to compute
the image perturbations.
Both approximations suffer from limitations that limit
their practicality:
the Born approximation is usable only for small anomalies,
while the Rytov approximation requires phase unwrapping.
Differential image perturbations can be used for arbitrarily
large slowness anomalies and do not require phase unwrapping,
but their accuracy decreases with
increasing deviation from the background image.
For simple cases, the differential image perturbation method
is equivalent with phase-unwrapped Rytov.

Dip-dependent residual moveout (ps.gz 62K) (pdf 137K) (src 12040K)
**Shan G. and Biondi B.**

Residual moveout is an effective tool for interval velocity analysis for depth migration.
However, the conventional residual moveout method assumes that the reflectors in the
subsurface are all flat, and thus estimates curvature parameters for velocity analysis
that are inaccurate for steeply dipping reflectors.
In this paper, we develop a dip-dependent residual moveout method,
which is performed in the Fourier domain and handles dip effects.

Velocity estimation for seismic data exhibiting focusing-effect AVO (Part 3) (ps.gz 294K) (pdf 234K) (src 551K)
**Vlad I., Biondi B., and Sava P.**

Given a satisfactory image perturbation, Target Image Fitting
(TIF) Wave Equation Migration Velocity Analysis (WEMVA) successfully produces
a velocity model that completely eliminates focusing-effect AVO
anomalies through prestack depth migration. However, TIF WEMVA ceases
to converge to the desired result when the Born approximation is not
fulfilled because the starting guess is too far from
the correct velocity. Fortunately, there are several possible remedies to
this problem. Extracting the image perturbation proves somewhat more
complicated than expected, but new possible solutions based on differential semblance
have been identified.

Reflection tomography with depth control (ps.gz 523K) (pdf 349K) (src 1426K)
**Chen W., Clapp R. G., and Biondi B.**

Reflection tomography Clapp (2001); Stork and Clayton (1991); Stork (1992) is one of the most effective and widely used velocity estimation methods. However, reflection tomography has velocity-depth ambiguity problem (we do not know how much a traveltime error is due to a velocity error and how much is due to a reflector misposition) because of insufficient source-receiver offset and lateral velocity changes Bickel (1990); Lines (1993); Ross (1994); Tieman (1994).
From borehole data, we can obtain the correct reflection positions around the borehole. The normal shift between the correct reflection positions and the apparent reflection positions can be linearly mapped to the traveltime perturbation along the normal ray van Trier (1990). However, from borehole data, we can only obtain the correct position for only a few reflection points along the borehole. In this paper, we assume all the reflection points within a local area around the borehole have the same normal shift. The normal ray traveltime perturbation for all these reflection points are then backpropagated simultaneously with the reflection traveltime perturbation. We applied this scheme on a synthetic model and obtained a better inversion result than using reflection tomography without this control. We further discuss how to improve this method for more complex datasets.
...

Frequency-dependent velocity analysis? (ps.gz 561K) (pdf 171K) (src 969K)
**Vlad I.**

There are two reasons for exploring imaging and
velocity analysis with a frequency-dependent velocity model. First,
significant dispersion may occur naturally in the volume of rock
investigated by the seismic experiment. Second, the goal of Wave Equation
Migration Velocity Analysis (WEMVA, Biondi and Sava (1999)) is
image optimization, which some successful approaches
Pratt (1999) perform by inverting one frequency at a time, from
lower to higher frequencies. The velocity model that optimizes the
...

Interval velocity estimation using edge-preserving regularization (ps.gz 629K) (pdf 362K) (src 23325K)
**Valenciano A. A., Brown M., Sacchi M. D., and Guitton A.**

We test two edge-preserving forms of model regularization in a least-squares implementation of Dix formula that leads to interval velocities with sharp edges in the plane. This characteristic in the interval velocity may be desirable in geologic environments with abrupt changes in velocity, like: carbonate layers, salt bodies, and strong faulting.

Basis pursuit for geophysical inversion (ps.gz 702K) (pdf 458K) (src 2239K)
**Artman B. and Sacchi M.**

Accepting an inversion principle, it is possible to
design an algorithm to meet any requirements or
constraints. Given the context of representing a signal with an
arbitrary overcomplete dictionary of waveforms within the
signal, one can design an inversion algorithm that will focus
energy into a small number of model space
coefficients. With this principle in mind, an analogy to linear
programming is developed that results in an algorithm with: the
properties of an *l ^{1}* norm, a small and stable parameter space,
definable convergence, and impressive denoising capabilities. Linear
programming methods solve a nonlinear problem in an interior/barrier loop
method similar to iteratively reweighted least squares (IRLS) algorithms,
and are much slower than a least squares solution obtained with a
conjugate gradient method. Velocity scanning with the hyperbolic
radon transform is implemented as a test case for the methodology.

Deblurring using edge-preserving regularization (ps.gz 288K) (pdf 310K) (src 970K)

In this short note, we test various edge-preserving regularization schemes in the context of deblurring a text image with random noise. The blurred text image was created by Nagy and O'Leary (2003a) as a test case. Even if the blurring filter is known exactly, as it is in this case, sharp features are nearly in the nullspace of the filter which we must ``invert'', or deblur. Those eigenvalues of the filter matrix corresponding to edges may be well below the noise level, and thus difficult or impossible to resolve. We know that letters should be homogeneous for intervals (piecewise constant), thus it makes sense to impose model smoothness using a regularization operator. But letters also have abrupt discontinuities, thus using a regularization operator that imposes model smoothness considerably degrades our ability to discern the letter edges. ...

AMO regularization: Effective approximate inverses for amplitude preservation (ps.gz 319K) (pdf 396K) (src 96772K)
**Clapp R. G.**

Most downward continuation methods require that the data lie on
a regular mesh.
To map the irregular recorded seismic data onto the regular mesh
is a far from trivial exercise.
A common approach in industry is to think of the problems in the same
way we approach Kirchhoff migration,
namely to loop over data space and spread into our regular
model space. The spreading operation is governed by something
like AMO Biondi et al. (1998), which maps data from one offset vector to
...

More fitting equations for PEF estimation on sparse data (ps.gz 285K) (pdf 218K) (src 3595K)
**Curry W.**

Prediction-error filters (PEFs) can be used to interpolate data
Claerbout (1999); Crawley (2000); Spitz (1991). In order to generate a PEF, a least-squares
problem is solved where regularly-sampled data is convolved with an
unknown PEF. When estimating a PEF with missing data, the equations
that contain missing data can be eliminated from the inversion. When
dealing with sparse data, however, all equations may contain missing data, so
...

Dip estimation from irregularly-sampled seismic data (ps.gz 331K) (pdf 410K) (src 3457K)
**Brown M.**

The geometry of reflection seismic experiments rarely conforms to an idealized,
or nominal geometry. This is especially true in regions with unavoidable
surface obstructions like rivers, towns, or existing offshore oil platforms.
Such deviations from nominal geometry render many computer seismic processing
applications ineffective. It is therefore of considerable importance to 1)
accurately map irregularly-sampled seismic data onto a regular grid with
sufficient spatial resolution, and 2) to interpolate any missing trace locations
with reasonable values.
Any interpolation method fills missing traces using a prior estimate of the
...

Prediction-error filter estimation on irregular traces (ps.gz 39K) (pdf 103K) (src 73K)
**Curry W.**

Regularly-sampled data is normally required to estimate a prediction-error filter (PEF). I
show how a small PEF can be estimated when the data is irregularly sampled
in one dimension. I then estimate a PEF on an irregularly-sampled 2D
examples, and discuss extension to 3D.

Image segmentation for tracking salt boundaries (ps.gz 83K) (pdf 179K) (src 178K)
**Lomask J. and Biondi B.**

Image segmentation can be used to track salt boundaries when the salt boundary amplitude is greater than any other local reflections. We apply a modified version of the normalized cut image segmentation method to partition seismic images along salt boundaries. In principle our method should work even when the boundaries are not continuous, and conventional horizon tracking algorithms may fail. Our implementation of this method calculates a weight connecting each pixel in the image to each pixel in a local neighborhood. The magnitude of the weight is inversely proportional to the size of the maximum instantaneous amplitude along the shortest path between the two pixels. This method is demonstrated to be effective on two simple models and 2D seismic section.

Automatic discontinuity extraction for 3-D seismic images (ps.gz 2988K) (pdf 976K) (src 6621K)
**Ji J.**

A goal of seismic processing is to verify the spatial characteristics of the subsurface.
Achieving this goal often requires human analysis to interpret
geologically meaningful discontinuities from the seismic image.
This interpretation is a challenging task even for an experienced interpreter if the image is 3D.
This paper introduces an automatic method
to extract seismic event discontinuities
from a 3D seismic image.
The proposed method consists of three steps.
The first step is to evaluate the coherency of seismic events from the seismic image.
The second step is to express the regions where discontinuities may exist in a binary image form.
The third step is to locate the discontinuity surfaces by thinning the region found in the second step.

Elastic and poroelastic analysis of Thomsen parameters for seismic waves in finely layered VTI media (ps.gz 67K) (pdf 179K) (src 64K)
**Berryman J. G.**

Layered earth models are well justified by experience, and provide a
simple means of studying fairly general behavior of the
elastic and poroelastic characteristics of seismic waves in the
earth. Thomsen's anisotropy parameters for weak elastic and poroelastic
anisotropy are now commonly used in exploration, and can be
conveniently expressed in terms of the layer averages of Backus.
Since our main interest is usually in the fluids underground, it would
be helpful to have a set of general equations relating the Thomsen
parameters as directly as possible to the fluid properties. This end
can be achieved in a rather straightforward fashion for these layered
earth models, and the present paper develops and then discusses
these relations. It is found that, although there are five
effective shear moduli for any layered VTI medium, one and only one
effective shear modulus for the layered system contains all the dependence of
pore fluids on the elastic or poroelastic constants that can be observed
in vertically polarized shear waves in VTI media. The effects of the
pore fluids on this effective shear modulus can be substantial (as
much as a factor of 5 in the examples presented here) when
the medium behaves in an undrained fashion, as might be expected at
higher frequencies such as sonic and ultrasonic waves for well-logging
or laboratory experiments, or at seismic wave frequencies for low
permeability regions of reservoirs, prior to hydrofracing. The
results presented are strictly for velocity analysis, not for amplitude or
attenuation.

Scale-up in poroelastic systems and applications to reservoirs (ps.gz 43K) (pdf 116K) (src 17K)
**Berryman J. G.**

A fundamental problem of heterogeneous systems is that the macroscale
behavior is not necessarily well-described by equations familiar
to us at the meso- or microscale. In relatively simple cases like
electrical conduction and elasticity, it is true that the equations
describing macroscale behavior take the same form as those at the
microscale. But in more complex systems, these simple results do not hold.
Consider fluid flow in porous media where the microscale behavior
is well-described by Navier-Stokes' equations for liquid in the
pores while the macroscale behavior instead obeys Darcy's
equation. Rigorous methods for establishing the form of such
equations for macroscale behavior include multiscale homogenization
methods and also the volume averaging method. In addition, it has
been shown that Biot's equations of poroelasticity follow in a
scale-up of the microscale equations of elasticity coupled to
Navier-Stokes. Laboratory measurements have shown that Biot's
equations indeed hold for simple systems but heterogeneous systems
can have quite different behavior.
So the question arises whether there is yet another level of scale-up
needed to arrive at equations valid for the reservoir scale? And if so,
do these equations take the form of Biot's equations or some other form?
We will discuss these issues and show that the double-porosity
equations play a special role in the scale-up to equations describing
reservoir behavior, for fluid pumping, geomechanics, as well as seismic
wave propagation.

Seismic attenuation due to wave-induced flow (ps.gz 221K) (pdf 356K) (src 352K)
**Pride S. R., Berryman J. G., and Harris J. M.**

Analytical expressions for three P-wave attenuation mechanisms in
sedimentary rocks are given a unified theoretical framework.
Two of the models concern wave-induced flow due to heterogeneity
in the elastic moduli at ``mesoscopic'' scales (scales greater than
grain sizes but smaller than wavelengths). In the first model, the
heterogeneity is due to lithological variations (*e.g.*, mixtures of
sands and shales) with a single fluid saturating all the pores. In
the second model, a single uniform lithology is saturated in mesoscopic
``patches'' by two immiscible fluids (e.g., air and water). In the
third model, the heterogeneity is at
``microscopic'' grain scales (broken grain contacts
and/or micro-cracks in the grains) and the associated fluid response
corresponds to ``squirt flow.'' The model of squirt flow derived here
reduces to proper limits as any of the fluid bulk modulus,
crack porosity, and/or frequency is reduced to zero. It is shown that
squirt flow is incapable of explaining the measured level of loss
(10^{-2} < *Q ^{-1}* < 10

10/14/2003