Velocity estimation using prestack depth migration: field data trial (ps 4366K) (src 8321K)
**Etgen J. T.**

Velocity information extracted from prestack migrated data can be
used to update the interval velocity model by solving a filtered
tomography problem. Depth migration with the new velocity model
should yield an improved structural image that stacks better over
offset. Initial field data results indicate the promise of the method and
also point out some of the difficulties encountered when using it.

Prestack Partial Migration Analysis (ps 59K) (src 11K)
**Popovici A. M.**

Prestack partial migration (PSPM)
is a well-known process which
transforms the prestack data to zero offset.
I discuss several properties of the PSPM spreading operator
and of the equivalent PSPM summation operator
reflected by a transformation of coordinates from (*x*, *t*) domain
to (*p*, ) domain, where *p*=2*dt*/*dx* and is the NMO
correction. This transformation allows for a more general
representation for the PSPM operator and can explain the
apparition of triplications in the DMO curve in a
variable velocity medium.
Then I attempt to find a partial differential equation formulation
for the PSPM operator in the family of first order partial
differential equations using as characteristics the curves
defined by the new transformation of coordinates.

Refining the image of profile migration: residual moveout and residual migration (ps 106K) (src 362K)
**Zhang L.**

In complex geologic environments, imaging of seismic reflection data
requires model-driven depth migration. It is well known that such migration is
sensitive to velocity errors. If the velocity model used in
migration does not correctly model the travel-times of reflection events,
the images of reflectors on migrated shot profiles will be distorted
from the true images of the earth.
By solving the Eiconal equation, I find a residual-moveout equation that
can be used in estimating residual velocities, and a residual-migration operator
that can revise the distortion of the images on migrated shot profiles.
For a constant-velocity medium, these results are precise
in the kinematic sense.

Upwind finite-difference calculation of traveltimes (ps 245K) (src 379K)
**Trier J. v. and Symes W. W.**

Fluid flow is often described by conservation laws that
define the conservation of mass, momentum, or energy in a fluid.
In fluid mechanics, a standard technique for solving such
laws is upwind finite differencing, a numerical
method that uses different finite-difference operators depending on the
direction of the fluid flow. Upwind finite-difference methods
are more stable than centered finite-difference techniques because
they mimic the behavior
of fluid flow by only using information taken from upstream in
the fluid.
Seismic traveltimes can be computed with upwind finite differences
by solving a transformed eikonal equation.
The transformed equation is a conservation law that describes
the changes in the gradient components of the traveltime field among
points on the computational grid.
A first-order upwind finite-difference scheme proves accurate enough for
seismic applications. The method calculates
single-valued traveltime functions (i.e. first arrival times)
efficiently on a regular grid, and is useful both in Kirchhoff
migration and modeling and in seismic tomography.

Anisotropic finite-difference traveltimes (ps 74K) (src 90K)
**Dellinger J. and Trier J. V.**

Finite-difference traveltime methods are an efficient
way to calculate first arrival times at every point in a complex
heterogeneous isotropic model. We show that
Van Trier and Symes' algorithm can be extended
to include anisotropy by replacing the isotropic dispersion
relation inherent in their method with an anisotropic one.
Unfortunately, the upwind method they use
is difficult to implement in the anisotropic case, because
it requires high-accuracy solutions of derivatives of complex
anisotropic dispersion relations.
For our preliminary results we use instead an easy-to-implement
fixed-grid finite-difference method. This method works well in
homogeneous anisotropic models, but seems to have trouble
in heterogeneous ones.

Generalized adaptive deconvolution (ps 567K) (src 838K)
**Darche G.**

In signal processing, the lattice algorithms have been widely applied to
spectral analysis. Their best known example in geophysics
is Burg's filtering. In fact, lattice structures can be used to construct
algorithms solving any kind of prediction problems. In this paper, I derive
two of these algorithms. They generalize two classical adaptive algorithms
used in spectral analysis: the least-squares lattice (LSL) algorithm, and
Burg's adaptive algorithm. I will apply these algorithms to the
problem of multiples removal with non-stationary data; these applications
will show the superiority of Burg's algorithm.

Imaging to eliminate water-bottom multiples (ps 354K) (src 886K)
**Zhang L.**

On a common midpoint (CMP) gather, the water-bottom multiples
are characterized by their moveout of small stacking velocities. In this paper
I describe a new velocity discrimination method to eliminate these low velocity
events. The new method is similar in principle to the velocity
filtering method. First the CMP gather is transformed into a distorted image
by using a velocity-dependent operator.
The velocity of the operator is chosen in such a way that the
distorted images of the water-bottom multiples are separable
from the distorted images of other
events. Eliminating the images of the water-bottom multiples is
followed by the backward transformation, to give a CMP gather free
of the interference of the water-bottom multiples. The synthetic
example and field-data example show that the algorithm works
to a certain extent; however, several
problems remain to be solved.

Fast parabolic transforms (ps 573K) (src 947K)
**Darche G.**

I improve here an already existing method of multiples elimination
by parabolic transforms. It is based on the approximate parabolic
shape of the multiples after NMO correction, and uses a parabolic
transform similar in concept to the hyperbolic and slant-stack transforms.
This parabolic transform is easy to express in the frequency
domain. More important, I will show that its least-squares inverse can also
be computed easily, because it requires only the inversion of a Toeplitz
matrix. This property
makes the transformations especially fast to compute, and is still valid
for special cases, like irregular space sampling, or offset-dependent
weighting. I will recall the interest of this method for multiple
elimination, and extend it to interpolation processes to illustrate the
practical advantages of the Toeplitz structure.

Snell-driven beam-stack (ps 56K) (src 9K)
**Filho C. A. C.**

Combining the concepts of Snell-rays and beam-stack, I define a
transform that maps prestack data from the offset-traveltime
domain into the vertical-traveltime-Snell-parameter domain.
The transform is defined for a common-mid-point (CMP) gather, and
it requires the basic assumption that the earth can be well
approximated by a stack of horizontal layers.
Each output
trace represents the reflections associated with the
propagation of a Snell beam through the layers of the medium.
Energy is summed up, inside the beam, along the reflections, and
divergence effects for either a point or line source are
properly compensated for by the transform.

Coupled wave propagation (ps 1104K) (src 2790K)
**Karrenbach M.**

Coupled wave propagation phenomena have been observed in laboratory
measurements for a long time; however in field experiments observations have
been less convincing. In this paper coupled wave equations allow us to model
such coupling by combining elastic
stress and strain, electric field strength and displacement, entropy and
temperature. For piezoelectric media slowness surfaces show changes in
propagation velocity and particle motion when coupling is included in the
computation. Average properties of such media can be computed using the
Schoenberg and Muir group theory. Possible applications of coupled
wave propagation, besides earthquake prediction and mineral exploration, might
be the 3D monitoring of oil fields during enhanced oil recovery.
Accurate rock parameter estimation seems to be sensitive to coupling effects.

Putting Schoenberg-Muir to the test (ps 1618K) (src 3004K)
**Dellinger J., Muir F., and Etgen J.**

The Schoenberg-Muir averaging technique is a powerful method for calculating
the bulk properties of layered and fractured elastic media. The theory is
exact only for infinite layers and infinitely low frequency waves. It is
already known that the approximations are accurate for infinite flat layers
if the wavelength of the slowest elastic wave is long enough to contain
a representative sample of the layers at any position in the medium.
In this paper we run models testing the infinite flat layers assumption.
We find that if the layers are much longer than they are thick this
approximation is a good one and Schoenberg-Muir averaging is applicable.

A perturbation method for elastic-isotropic inversion--a proposal (ps 55K) (src 7K)
**Filho C. A. C.**

Several methods for elastic inversion have been applied in
recent years, based on the optimization of either the fitting between
the predicted and recorded data, or the fitting between the
model-predicted and data-retrieved reflectivity series.
In both cases, the model is
usually described by a stack of layers that controls the kinematics and
the dynamics of the physical process. I propose a method in which
geometrical and physical effects are decoupled, so that the part of
the model responsible for the dynamics can be modified without introducing
any change on the kinematically-related part of the model.
The model is characterized by a background medium,
with smoothly-varying elastic properties,
and an arbitrary number of perturbation layers. Each perturbation
layer is responsible for the introduction of two reflections, whose
amplitudes depend only on the contrast between the properties of the
layer and the local properties of the background model. In addition to
the kinematics-dynamics uncoupling, the number of unknown parameters
necessary to describe the two reflections of a layer (top and bottom)
is reduced to less than a half of the number required by usual
model-description methods.

Design considerations for experiments using novel seismic sources (ps 47K) (src 11K)
**Cole S.**

Two experiments using unconventional seismic sources have been studied
recently at SEP, a passive seismic experiment and an experiment using a
drill-bit source.
The differences between these novel sources and conventional seismic
sources place some added constraints on the experiment design.
For instance, the ability to resolve the arrival direction
of a wave in 3-D is
essential if we are to discriminate the relatively weak
(compared to conventional sources) source energy
in the presence of nearby surface noise sources.
From considerations such as this,
I evaluate the design of the two experiments conducted to date
and see how they could be improved upon.

Comparison of different approaches to processing ambient noise data (ps 351K) (src 1257K)
**Vanyan L. and Cole S.**

Various methods of processing ambient noise data and
teleseismic coda waves, recorded by seismic arrays, have been developed
by different groups.
The main goal of these investigations is to
locate endogenous sources
of microseisms beneath the array (in the ambient noise case)
or to detect scattering (in both cases).
In the simplest processing scheme, semblance is used to measure
the coherent energy exhibiting hyperbolic moveout arriving
from sources (primary sources or scatterers) in the medium.
The processing reveals some possible sources at depth, but the
results are strongly influenced by surface sources.
To eliminate the influence of these sources, a least-squares
method in the frequency domain has been applied, but the method
is hampered by the problem of estimating a source signal,
which is required by the algorithm.

Book additions preface (ps 27K) (src 1K)
**Claerbout J. F.**

Additions to my third book in preparation include
(1) a picking algorithm based on the operator ,(2) examples and code for a missing data program,
(3) prediction-error filter estimation along with missing data estimation,
(4) discussion of trace interpolation beyond aliasing
as an optimization problem,
and
(5) a pixel-precise method of velocity computation.

Univariate problems (ps 82K) (src 91K)
**Claerbout J. F.**

Model fitting by least squares (ps 61K) (src 24K)

Nonlinear problems (ps 70K) (src 54K)

- OPTIMUM FILTER WITH MISSING DATA
- References
- INTERPOLATION BY PLANE WAVE DESTRUCTION
- PLANE WAVE IDENTIFICATION BEYOND ALIASING
- References
- DIP FILTER DEFINITION
- INTERPOLATION WITH P.D.E. DIP FILTERS
- INTERPOLATION WITH SPATIAL PREDICTORS
- CLASH IN PHILOSOPHIES

Hyperbola tricks (ps 76K) (src 74K)

Data examples of pixel-precise velocity analysis (ps 36K) (src 493K)
**Ottolini R.**

Velocity resolution is different using the pixel-precise analysis
method on field data than using conventional analysis.
The spectra do not smear out laterally.
However, the signal-to-noise level can be lower.

Velocity Analysis on the Connection Machine (ps 52K) (src 7K)
**Kneib G.**

Implemented in slightly different ways on one of the new massively
parallel computers, the Connection
Machine, the performance of Jon Claerbout's
pixel-precise
velocity analysis algorithm
can differ by much more than one order. The performance depends strongly
on the way the Fortran programmer maps the data on the machine.

Anisotropic Velocity Analysis (ps 41K) (src 4K)
**Ji J.**

This paper examines the meaning of the anelliptic terms in relation to the
processes of approximating the ray velocity surface of transversely isotropic
media recently introduced by Muir (1985) and Byun et al. (1989).
Compared with stacking velocity obtained by simple hyperbolic velocity analysis,
the additional parameters estimated by the non-hyperbolic method contain more physically meaningful geologic information regarding the anisotropy of the subsurface.
Synthetic ¶-wave model experiments demonstrate that the non-hyperbolic moveout formulas yield an excellent fit to time-distance curves over a wide range of ray angles.
Thus the measurement parameters adequately reflect the characteristics of velocity dependence on ray angle, in other words, velocity anisotropy.

Estimation of missing data by least squares (ps 839K) (src 1628K)
**Nichols D.**

I formulate the problem of estimating missing data using least squares. The operators that I use are error operators that have as output that part of the interpolated data that does not fit some parametric model of the data.
If all the parameters of the model are known the problem is a linear least squares problem. If the parameters of the model must be estimated at the same time as the missing data the problem is non-linear.
I use a model based on local linear events to interpolate aliased data. This procedure depends on good initial estimates of the dips which can be obtained from a smoothed version of the data.

Wavelet decomposition of seismic data: examples and interactive XView program (ps 6K) (src 187K)
**Ottolini R.**

Seismic data may be decomposed into localized basis functions called wavelets.
Wavelets resemble Fourier decomposition in the ability to distinguish
frequency ranges and are invertible.
Wavelets beat Fourier analysis in computation cost and locality.
Wavelets may be inferior to the Fourier domain for propagating waves.
The wavelet studied here decomposes signals by octaves.
It is too coarse for studying seismic data.
It might be useful for signal detection.
I wrote an interactive, multi-dimensional wavelet-based bandpass application
using the XView toolkit.
XView combines the strengths of SunView and XWindows:
powerful set of command objects, simple programming interface,
portable, and network transparent.

An interactive processing environment (ps 47K) (src 8K)
**Cole S.**

I have
written an interactive software package that allows all SEP
batch-oriented software to be used
in an interactive manner, with no programming required of
the end user. One can ``build'' a processing sequence, interactively modify
the parameters for the various process, and see the result of
each modification displayed on the workstation screen.
The processing sequence and all associated parameters can be
saved to a file so that the user can exit, then return at any
time and pick up where he left off.
With this environment it is much easier to experiment with different
parameter values than in traditional batch processing.
My software is written using XView, a freely-distributed X Windows
toolkit developed by Sun Microsystems. Thus, like any X application,
it can be ported to many machines.

Seismic movies on the XView graphics system (ps 39K) (src 41K)
**Ottolini R.**

XView is a graphical interaction toolkit derived from the SunView toolkit
and running on top of X Windows.
It allows portable seismic display software with an easy-to-use control
interface.

1/13/1998