Sediments with gas hydrates: Internal structure from seismic AVO (ps 1333K) (src 6102K)
**Ecker C., Dvorkin J., and Nur A.**

We use rock-physics-based synthetic seismic modeling to interpret AVO
data of methane hydrate structures.
Two micromechanical models of gas hydrate deposition are
examined: (1) the hydrate cements grain contacts and strongly reinforces
the sediment; and (2) the hydrate is located away from the grain contacts
and only weakly affects the stiffness of the sediment's frame.
We calculate the effect of pore fluid on seismic velocities from
Gassmann's equation. Synthetic seismograms are generated from 1-D elastic
modeling (Thompson-Haskell reflectivity method) and the AVO responses
at the BSR are obtained from Zoeppritz equations.
Comparison with real seismic AVO data from the Blake Outer Ridge, offshore
Florida and Georgia, shows that the second model of hydrate deposition
can reproduce the real AVO effect qualitatively.
The inferred topology
of hydrate deposition leads to two important conclusions:
(1) the sediment containing hydrate is uncemented and thus mechanically
weak, and (2) the permeability of this sediment is very low because
hydrate clogs large pore-space conduits. This second conclusion explains
the fact that free gas is trapped underneath the BSR at the Blake
Outer Ridge. The data furthermore
indicate the absence of strong reflections at the top of the hydrate. We
conclude that the high concentration of hydrate in the sediment immediately
above the BSR gradually decreases with decreasing depth.

4-D seismic steamflood monitoring (ps 1620K) (src 6108K)
**E. Lumley D.**

Six repeated 3-D seismic data sets are analyzed at a single steamflood site
in Indonesia. Migrated images and velocity analysis
illuminate fluid-flow features of the steamflood in time-lapse mode.
The steam front is visible seismically as large reflection and diffraction
responses, and velocity decreases of up to 40%, in a disk centered
at the steam injection well. The steam front intensifies in place
at a radius of less than 50 m for the first nine months of injection, and then
breaks out and rapidly propagates to the northwest of the injection pattern
at and beyond the 13-month survey. The steam movement mapped by time-lapse
seismic correlates with two temperature observation wells and oil
production data from the surrounding producing wells.
A thin annulus of hot water
(steam condensate) is visible in time slices and a 10% increase in velocity.
A transient pressure front is observed at 2 months of steam injection
to propagate towards the northwest, but not toward the southeast.
Mapping the early pressure front movement predicts where
the thermal and steam fronts will follow.
The steam front is shown to follow the leading pressure front movement
to the northwest one full year after the pressure front was initially mapped.

Equations of motion for isotropic porous media with multiple solid constituents (ps 83K) (src 75K)
**Berryman J. G. and Pride S. R.**

The volume averaging technique for obtaining macroscopic equations of motion
for materials that are microscopically inhomogeneous is extended to the
situation in which multiple solid constituents form a porous matrix while a
uniform fluid fills the pores.
Previous volume averaging efforts of Pride *et al.* (1992) and others
have concentrated on single solid constituent porous media. The analysis for
multiple solid constituents is complicated by the presence of internal
interfaces between the solid constituents within the averaging volume.
These interfaces are characterized by constants that measure the fraction
of the interface on which solid touches solid, fluid touches one solid, fluid
touches the other solid, or fluid lies on both sides of the interface.
These fractions are easily computed if the interface fractions are assumed
to be uncorrelated, but real materials may be expected to exhibit some
correlation.
On the other hand, these interface fractions do not appear in the volume
average equations at the macroscopic level.
To complete the analysis, it is found that the jacketed and unjacketed tests
of Biot and Willis (1957) together with the thought experiments of Berryman
and Milton (1991) for solid matrix composed of two constituents are required
in order to obtain definite results.
Results are found to be in complete agreement with earlier work of Brown
and Korringa (1975) concerning the most general possible form of the
quasistatic equations for volume deformation and therefore of the equations
of motion for wave propagation through such media.

Azimuth moveout: the operator parameterization and antialiasing (ps 999K) (src 5842K)
**Fomel S. and Biondi B. L.**

A practical implementation of azimuth moveout (AMO) must be both
computationally efficient and accurate. We achieve computational
efficiency by parameterizing the AMO operator with the help of a
transformed midpoint coordinate system. To achieve accuracy, the AMO
operator needs to be carefully designed for antialiasing. We propose
a modified version of Hale's antialiasing algorithm, which switches
between interpolation in time and interpolation in space depending on
the operator dips. The method is applicable to a vide variety of
integral operators and compares favorably with the triangle filter
technique. A simple synthetic example tests the applicability of the
method to the AMO case.

Amplitude preserving offset continuation in theory Part 2: Solving the equation (ps 145K) (src 471K)
**Fomel S.**

I consider an initial value problem for the offset continuation (OC)
equation introduced in Part One of this paper (SEP-84). The solutions
of this problem create integral-type OC operators in the time-space
domain. Moving to the frequency-wavenumber and log-stretch domain, I
compare the obtained operators with the well-known Fourier DMO
operators. This comparison links the theory of DMO with the advanced
theory of offset continuation.

Velocity model building in AVS (ps 299K) (src 287K)
**Mora C. B., Clapp R. G., and Biondi B.**

For the last three years SEP has been developing tools
within Advanced Visual System (AVS), to better handle 3-D
seismic data.
Our newest
module attempts to include the
entire velocity model building
process within our AVS environment.
It combines some of the best elements of GOCAD with the higher level
of flexibility offered by AVS.
An interactive model building process was tested by combining the new module,
along with other AVS modules
developed at SEP, to build a 3-D velocity model from
a land survey dataset provided by INTEVEP S.A.

Flexible seismic traveltime tomography applied to diving waves (ps 443K) (src 1010K)
**Harlan W. S.**

To prepare for 3D anisotropic applications of traveltime
tomography I found it
necessary to reformulate the estimation of raypaths
and the parameterization of velocities. Raypaths should
be efficient to calculate and store in memory without
recalculation.
Velocities should be able to change with angle when necessary.
Ray relaxation can optimize ray paths through an anisotropic
medium described only by group velocities.
Three parameters adequately describe transversely
isotropic group velocities with a vertical axis of symmetry.
One parameter changes most arbitrarily, one changes only
along the vertical axis of symmetry, and one remains a constant.
3D raypaths are described as sums of smooth curves with
a small number of coefficients. A generic Gauss-Newton
algorithm perturbs these coefficients
to minimize traveltimes between endpoints.
A small number of coefficients are saved in memory to
describe paths efficiently.
Diving wave tomography can use conventional traveltime tomographic
algorithms to model and invert the traveltimes of direct arrivals.
Early synthetic tests minimized
the complexity of velocity anomalies necessary to explain the data.
Raypaths robustly converge to their appropriate distribution.

Iterative least-square inversion for amplitude balancing (ps 623K) (src 1476K)
**Berlioux A. and Harlan W. S.**

Variations in source strength and receiver amplitude can introduce
a bias in the final AVO analysis of prestack seismic reflection data.
In this paper we tackle the problem of the amplitude balancing of
the seismic traces from a marine survey. We start with a 2-D energy
map from which the global trend has been removed. In order to balance
this amplitude map, we first invert for the correction coefficients
using an iterative least-square algorithm. The coefficients are
calculated for each shot position along the survey line, each receiver
position in the recording cable, and each offset. Using these
coefficients, we then correct the original amplitude map for amplitude
variations in the shot, receiver, and offset directions.

Linearized elastic inversion in the domain (ps 248K) (src 390K)
**Bernasconi G., Drufuca G., and Rocca F.**

We present an algorithm for elastic linearized inversion in the
wavenumber-frequency domain.
The medium is considered to be composed of a known constant background plus
an unknown small variation of P-impedance, S-impedance and density.
The linearized approach enables us to use the tools of linear algebra to
analyze the ill-conditioning of the inversion.
Operating in the wavenumber-frequency domain, we gain the advantage
of the simplicity of the theory,
as the scattering process becomes the interaction of monochromatic
plane waves with sinusoidal variations of the elastic parameters.
Inversion and analysis of the information give a smoothed but reliable
image of the original model.
We test the algorithm on synthetic data. Because of the ill-conditioning
of the inverse problem, we find that even small numerical errors cause
deterioration of the quality of inversion: P-P reflections allow an accurate
estimation of P-impedance perturbation only.
Multicomponent data are necessary to recover S-impedance
perturbation with this approach.

The adjoint of the viscous wave equation (ps 70K) (src 32K)
**Claerbout J.**

The scalar wave equation is a linear operator
whose output is any subset of the wavefield solution
and whose input is the source function.
Here we show how to compute the adjoint operator,
i.e., that whose input is the wavefield subset
and whose output is the sources.

Ellipsoids versus hyperboloids (ps 74K) (src 63K)
**Claerbout J.**

Many operators
can be coded in either ``push'' or ``pull'' forms,
namely, you can
loop over the space of outputs and find the inputs (pull),
or loop over the space of inputs and find the outputs (push).
The adjoint of a push operator is a pull operator
and vice versa.
Migration can be done with either hyperbolas or diffractors.
Inversions impose extra accuracy requirements
that may lead to forward modeling being a pull operator.
A DMO operator is a product of two operators,
either of which is a push or pull, leading to
four possible representations.

Approximate vs. exact adjoints in inversion (ps 92K) (src 77K)
**Crawley S.**

Gradient-based inversion methods employ adjoint operators
to find the gradient direction in the objective function.
Generally we assume that the exact adjoint is the
optimal choice.
In this paper I discuss
one type of approximate adjoint, called a pull
adjoint because of the way it discretizes the
output space.
For operators which sum and spray data along
curved trajectories,
such as Kirchoff and moveout operators,
pull adjoints more closely approximate an operator in
a continuous space.
This characteristic is important because we use these operators to
emulate the wave equation, which is a continuous
and unitary operator.
This paper presents a theoretical argument for the use
of pull adjoints in some inversions, and presents a
simple inversion example where the use of pull adjoints is of benefit.

Reproducible research documents using GNU make (ps 59K) (src 8K)
**Schwab M. and Schroeder J.**

The Stanford Exploration Project (SEP) publishes scores of
reproducible electronic research documents each
year. Traditionally, researchers at SEP have used the makefile
dialect `cake` to maintain their documents. Because of `cake`'s
limited distribution, we decided to replace it by
GNU `make`. GNU `make` is an alternative make dialect that is
widely used in software maintenance and is well documented.
To allow an author to cope with document maintenance as
opposed to software maintenance, Richard Stallman amended the
original GNU `make` source code: a new GNU `make` special
built-in target, `.SECONDARY`, enables the author to specify how
to deal with missing files when checking if a target is
up-to-date. Furthermore, the maintenance rules common to all
reproducible documents were rethought when we translated them
from `cake` to GNU `make`. The most significant change is the
introduction of three result lists that distinguish between
easily-reproducible, conditionally-reproducible, and
non-reproducible results. A declaration of the results'
reproducibility in the makefile simplified most of the crucial
reproducibility rules (such as `make burn`, which removes
all easily-reproducible results). We tested the new GNU `make` rules by translating Claerbout's three most recent textbooks.
SEP plans to publish all its future reproducible documents
using GNU `make`.

Interactive web pages with Java (ps 220K) (src 700K)
**Lenga K., Clapp R. G., and Claerbout J. F.**

Recently, Sun introduced Java, a new programming language with machine
independent object files.
Java, and the Java Browser, provides the next step in web browser technology by
bringing over
machine independent byte codes and interpreting them
on the local machine rather than the host machine.
This capability opens up a new realm of possibilities in information transfer
and interactive displays.
This summer SEP tested Java's capabilities by developing an interactive
web-based
demo
of wave propagation, a frame viewer (similar to SEP's old Animator), and
a cube viewer.

11/12/1997