Amplitude-preserved wave-equation migration (ps.gz 416K) (pdf 552K) (src 3797K)
**Sava P. and Biondi B.**

We analyze the amplitude variation as a function of reflection angle
(AVA) for angle-domain common image gathers (ADCIG) produced via
wave-equation migration.
Straightforward implementations of the two main ADCIG methods
lead to contradictory, thus inaccurate, amplitude responses.
The amplitude inaccuracy is related to the fact that
downward-continuation migration is the adjoint of
upward-continuation modeling,
but it is only a poor approximation of its inverse.
We derive the frequency-wavenumber domain diagonal
weighting operators that make migration a good approximation to
the inverse of modeling. With these weights, both ADCIG methods
produce consistent results.
The main applications that follow from this paper are
true-amplitude migration and pseudo-unitary modeling/migration,
usable for iterative inversion.
The two most important factors that degrade the accuracy of
wave-equation ADCIGs
are the limited sampling and offset range, combined
with the band-limited nature of seismic data.

Offset and angle domain common-image gathers for shot-profile migration (ps.gz 672K) (pdf 562K) (src 4081K)
**Rickett J. and Sava P.**

In order to estimate elastic parameters of the subsurface,
geophysicists need reliable information about angle-dependent
reflectivity.
In this paper, we describe how to image non-zero
offsets during shot-profile migration so that they can be mapped to
the angle domain with Sava and Fomel's 2000
transformation.
CIGs also contain information about how well focused
events are at depth, and so provide a natural domain for
migration-focusing velocity analysis.

*PS*-wave polarity reversal in angle domain common-image gathers (ps.gz 221K) (pdf 305K) (src 2079K)
**Rosales D. and Rickett J.**

The change in the reflection polarity at normal incidence is a
fundamental feature of converted-wave seismology due to the vector nature
of the displacement field.
The conventional way of dealing with this feature is to reverse
the polarity of data recorded at negative offsets. However, this
approach fails in presence of complex geology.
To solve this problem we propose operating the polarity flip in
the angle domain. We show that this method correctly handle the
polarity reversal after prestack migration for arbitrarily
complex earth models.

Amplitude analysis in the angle domain (ps.gz 4013K) (pdf 3541K) (src 24260K)
**Gratwick D.**

This paper discusses amplitude vs. angle (AVA) analysis using image gathers generated from a wave-equation
migration algorithm.
An AVA cross-plot muting algorithm is used to highlight parts of
an image corresponding to a Class III, low impedance, AVO sand.
Processing to eliminate surface multiples is used on the synthetic data, thereby enhancing
reflectors. Results show that our AVA muting algorithm is effective for both a synthetic and a real dataset.

The accuracy of wave-equation migration amplitudes (ps.gz 340K) (pdf 341K) (src 3347K)
**Gratwick D.**

When migrating seismic data for the purpose of reservoir characterization, it
is necessary to use a migration algorithm that preserves relative amplitude trends Scheriff (1995).
In the industry, this is usually attained using Kirchhoff methods
with asymptotic Green's functions Biondi (2000). This method
is useful in many geologic settings, but when a complex velocity Earth
introduces more complex wave propagation phenomena, ``wave-equation'' migration (WEM)
based on downward continuation becomes more attractive Prucha et al. (1999).
...

Amplitude behavior in angle gathers (ps.gz 83K) (pdf 133K) (src 1067K)
**Mora C. B.**

In a previous report, Sava and Fomel (2000)
presented a method for computing angle-domain common-image gathers
by a radial-trace transform in the Fourier domain.
The method converts offset-domain common-image gathers,
which are computed using 2-D prestack wave-equation migration
Prucha et al. (1999) into true reflection angle-domain
common-image gathers.
...

Model-space vs. data-space normalization for recursive depth migration (ps.gz 833K) (pdf 718K) (src 10102K)
**Rickett J.**

Illumination problems caused by finite-recording aperture and lateral
velocity lensing can lead to amplitude fluctuations in migrated
images.
I calculate both model and data-space weighting functions that
compensate for these illumination problems in recursive depth
migration results based on downward-contination.
These weighting functions can either be applied directly with
migration to mitigate the effects of poor subsurface
illumination, or used as preconditioning operators in iterative
least-squares (*L*2) migrations.
Computational shortcuts allow the weighting functions to be computed
at about the cost of a single migration.
Results indicate that model-space normalization can significantly
reduce amplitude fluctuations due to illumination
problems.
However, for the examples presented here, data-space normalization
proved susceptible to coherent noise contamination.

Imaging under salt edges: A regularized least-squares inversion scheme (ps.gz 1605K) (pdf 1597K) (src 14552K)
**Prucha M. L., Clapp R. G., and Biondi B. L.**

We introduce a method for improving the image in areas of poor illumination
using least-squares inversion
regularized with dip penalty filters in one and two dimensions.
The use of these filters helps to emphasize
the weak energy that exists in poorly illuminated areas,
and fills-in gaps by assuming lateral continuity along
the reflection-angle axis and/or the midpoint axes.
We tested
our regularized inversion method on synthetic and real data.
The inversion employing one-dimensional filters along
the reflection-angle axis generated prestack images
significantly better than the images obtained
by simple migration and unregularized inversion.
The inversion employing two-dimensional filters
reduced the frequency of the image
but also increased reflectors' continuity and reduced noise.

Narrow-azimuth migration: Analysis and tests in vertically layered media (ps.gz 382K) (pdf 597K) (src 1636K)
**Biondi B.**

Analysis of common-azimuth migration
for vertically layered media shows
that downward continuing the data in
a narrow strip around the zero crossline offset
should yield a kinematically correct migration scheme.
I introduce two migration methods
that exploit the common-azimuth equations
to define an optimal range of crossline-offset wavenumbers
and thus to minimize the number of crossline offsets
that are necessary to sample adequately the crossline-offset dips.
Tests on synthetic data generated assuming
a vertically layered medium confirm the theoretical
analysis and suggest further testing
on data sets with complex velocity functions.

Analysis of the damping factor in phase-shift migration (ps.gz 1160K) (pdf 1083K) (src 5522K)
**Rosales D.**

Cosmetic processes, the use of different parameters in
standard seismic data processing in order to improve the appearance of the data, are generally not considered
in the mathematical formulation of migration algorithms,
even though they are physically and
mathematically related to the wave propagation process. The
inclusion of
causality and viscosity
in phase-shift migration as a damping factor will take
care of these ``superficial'' features and numerical instability
due to evanescent energy.

Acoustic daylight imaging: Introduction to the underlying concept: A prospect for the instrumented oil field (ps.gz 119K) (pdf 117K) (src 293K)
**Claerbout J.**

Why and how it is that the autocorrelation of natural noise
gives us a reflection seismogram.

Preliminary results from a small-scale 3-D passive seismic study in Long Beach, CA (ps.gz 226K) (pdf 133K) (src 626K)
**Kerr B. and Rickett J.**

While helioseismologists routinely crosscorrelate stochastic acoustic
noise to produce time-distance curves Duvall et al. (1993) that
look like active-source seismograms, terrestrial geophysicists have
had less success.
Baskir and Weller (1975) describe the first published attempt to use
passive seismic energy to image subsurface reflectivity. They briefly
describe crosscorrelating long seismic records to produce correlograms
that could be processed, stacked and displayed as conventional seismic
...

Multiple realizations: Model variance and data uncertainty (ps.gz 1812K) (pdf 2440K) (src 16001K)
**Clapp R. G.**

Geophysicists typically produce a single model, without
addressing the issue of model variability.
By adding random noise to the model regularization
goal, multiple equi-probable models can be generated that
honor some *a priori* estimate of the model's second-order
statistics. By adding random noise to the data, colored by
the data's covariance, equi-probable models can be generated
that give an estimate of model uncertainty resulting from
data uncertainity. The methodology
is applied to a simple velocity inversion problem with
encouraging results.

A least-squares approach for estimating integrated velocity models from multiple data types (ps.gz 153K) (pdf 349K) (src 3212K)
**Brown M. and Clapp R. G.**

Many exploration and drilling applications would benefit from a robust method of
integrating vertical seismic profile (VSP) and seismic data to estimate interval
velocity. In practice, both
VSP and seismic data contain random and correlated errors, and integration methods
which fail to account for both types of error encounter problems. We present a
nonlinear, tomography-like least-squares algorithm for simultaneously estimating
an interval velocity from VSP and seismic data. On each nonlinear iteration of
our method, we estimate the optimal shift between the VSP and seismic data and
subtract the shift from the seismic data. In tests, our algorithm is able to
resolve an additive seismic depth error, caused by a positive velocity
perturbation, even when random errors are added to both seismic and VSP data.

A differential scheme for elastic properties of rocks with dry or saturated cracks (ps.gz 86K) (pdf 214K) (src 223K)
**Berryman J. G., Pride S. R., and Wang H. F.**

Differential effective medium (DEM) theory is applied to the problem
of estimating physical properties of
elastic media with penny-shaped cracks, filled either with air or liquid.
These cracks are assumed to be randomly oriented.
It is known that such a model captures many of the
essential physical features of fluid-saturated or partially saturated
rocks. By making the assumption that the changes in
certain factors depending only on
Poisson's ratio do not strongly affect the results, it is possible to
decouple the equations for bulk (*K*) and shear (*G*) modulus,
and then integrate
them analytically. The validity of this assumption is then tested
by integrating the full DEM equations numerically.
The analytical and numerical curves
for both *K* and *G*
are in very good agreement
over the whole porosity range of
interest. Justification of the Poisson's ratio approximation is also
provided directly by the theory, which shows that,
as porosity tends to 100%,
Poisson's ratio tends towards small positive values
for dry, cracked porous media and tends to one-half for liquid
saturated samples.
A rigorous stable fixed point is
obtained for Poisson's ratio, , of dry porous media,
where the location of
this fixed point depends only on the shape of the voids being added.
Fixed points occur at for spheres,
and for cracks, being the
aspect ratio of penny-shaped cracks. Results for the elastic
constants are then compared and contrasted with results predicted by
Gassmann's equations and with results of Mavko and Jizba,
for both granite-like and sandstone-like examples.
Gassmann's equations do not predict the observed liquid dependence
of the shear modulus *G* at all. Mavko and Jizba predict the observed
dependence of shear modulus on liquid bulk modulus for small crack
porosity, but fail to predict the observed behavior at higher porosities.
In contrast, the analytical approximations derived here give very
satisfactory agreement in all cases for both *K* and *G*.

oclib: An out-of-core optimization library (ps.gz 39K) (pdf 64K) (src 49K)
**Sava P.**

This paper introduces a `Fortran90` out-of-core
optimization library designed for large-scale problems.
The library is centered around the filtering operators and
gradient solvers currently in use at SEP.

Coherent noise attenuation: A synthetic and field example (ps.gz 1365K) (pdf 1319K) (src 9123K)
**Guitton A.**

Noise attenuation using either a filtering or a subtraction scheme
is achieved as long as the prediction error filter (PEF), which
(1) filters the coherent noise in
the first method and (2) models the noise in the second one, can be
accurately estimated. If a noise model is not known in advance, I
propose estimating the PEF from the residual of a previous inverse
problem. At this stage, the filtering and subtraction method give similar
results on both synthetic and real data. However the subtraction
method can more completely separate the noise and signal when both are
correlated.

A pattern-based technique for ground-roll and multiple attenuation (ps.gz 1964K) (pdf 1794K) (src 5726K)
**Guitton A., Brown M., Rickett J., and Clapp R.**

We present a pattern-based method that separates coherent noise
from signal. This method finds its mathematical foundation
in the work conducted by Nemeth (1996) on coherent noise attenuation
by least-squares migration. We show that a similar inverse problem
can be formulated to attenuate coherent noise in seismic data.
In this paper, we use deconvolution with prediction error filters
to model the signal and noise vectors in a least-squares sense.
This new formulation of the noise separation problem has been tested
on 2-D real data for ground-roll and multiple attenuations.
So far, it achieves similar results to the
approach used by Brown and Clapp (2000) and Clapp and Brown (2000).
However, we show that the main strength of
this new method is its ability to incorporate regularization
in the inverse problem in order to decrease the correlation
effects between noise and signal.

Adaptive multiple subtraction with non-stationary helical shaping filters (ps.gz 1640K) (pdf 1474K) (src 5798K)
**Rickett J., Guitton A., and Gratwick D.**

We suppress surface-related multiples with a smart adaptive
least-squares subtraction scheme in the time-space domain after
modeling multiples with a fast but approximate modeling algorithm.
The subtraction scheme is based on using a linear solver to estimate a
damped non-stationary shaping filter. We improve convergence by
preconditioning with a space-domain helical roughening filter.

Solutions to data and operator aliasing with the parabolic radon transform (ps.gz 1193K) (pdf 1059K) (src 3320K)
**Guitton A.**

Focusing in the radon domain can be affected by data
and operator aliasing. Antialiasing conditions can be imposed on the
parabolic radon transform (PRT) operator by dip limiting the
summation path. These dip limits in time translate into
frequency limits in the Fourier domain. Consequently, antialiasing the
PRT enables better focusing in the radon domain. If the radon domain
is computed *via* inverse theory, a regularization term
in either the time or frequency domain can reduce data aliasing effects.
The frequency domain regularization has the advantage of being
noniterative, but needs to be applied in patches in order to improve focusing.

Multiple suppression with land data: A case study (ps.gz 6305K) (pdf 6028K) (src 23936K)
**Alvarez G.**

Some of the most important methods for multiple suppression
are based on the *moveout* difference between the hyperbolas
corresponding to primary and multiple reflections in a CMP gather. This
moveout difference is exploited by means of the
Parabolic Radon Transform. In this case study I review the methodology and
show the result of its application to a 2-D land seismic line are.
Of particular importance are the results that show that
without the suppression of multiples a distorted image is obtained of the
Paleozoic and
its stratigraphic terminations against basement, which constitute the
exploratory objective in the area. This is partly due to the improved
stacking velocities afforded by the suppression of the multiples.

4/29/2001