3-D Seismic Imaging (ps 255K) **Biondi B.**

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The History of the Mitchell Building Skylight (ps 3904K) (src 33635K)
**Levin S. A.**

During recent earthquake reinforcement of the Ruth Wattis Mitchell
Earth Sciences Building, funds were successfully raised
to install a skylight in the th}}$"> floor. The skylight
was completed in January of 1998 and dedicated during
the Stanford Exploration Project's th}}$"> year reunion
on July th}}$">, 1998. Here is the story.

Double porosity modeling in elastic wave propagation for reservoir characterization (ps 618K) (src 171K)
**Berryman J. G. and Wang H. F.**

To account for large-volume low-permeability storage porosity and
low-volume high-permeability fracture/crack porosity in oil and gas
reservoirs, phenomenological equations for elastic wave propagation in
a double porosity medium have been formulated and the coefficients
in these linear equations identified. The generalization from single
porosity to double porosity modeling increases the number of independent
inertial coefficients from three to six, the number of independent drag
coefficients from three to six, and the number of independent stress-strain
coefficients from three to six for an isotropic applied stress and
assumed isotropy of the medium. The analysis leading to physical
interpretations of the inertial and drag coefficients is relatively
straightforward, whereas that for the stress-strain coefficients
is more tedious. In a quasistatic analysis of stress-strain,
the physical interpretations are based upon considerations of
extremes in both spatial and temporal scales. The limit of very short
times is the one most relevant for wave propagation, and in this case
both matrix porosity and fractures are expected to behave in an undrained
fashion, although our analysis makes no assumptions in this regard.
For the very long times more relevant for reservoir drawdown, the
double porosity medium behaves as an equivalent single porosity medium.
At the macroscopic spatial level, the pertinent parameters (such as the
total compressibility) may be determined by appropriate field tests.
At the mesoscopic scale pertinent parameters of the rock matrix can
be determined directly through laboratory measurements on core, and
the compressiblity can be measured for a single fracture. We show
explicitly how to generalize the quasistatic results to incorporate
wave propagation effects and how effects that are usually attributed
to squirt flow under partially saturated conditions can be explained
alternatively in terms of the double-porosity model. The result
is therefore a theory that generalizes, but is completely consistent
with, Biot's theory of poroelasticity and is valid for analysis
of elastic wave data from highly fractured reservoirs.

The azimuth moveout operator for anisotropic media (ps 671K) (src 26K)
**Alkhalifah T.**

The azimuth moveout (AMO) operator in homogeneous,
moderate to strong, anisotropic media, like in isotropic media,
has an overall skew saddle shape. Yet, the AMO
operator in anisotropic media is complicated;
it includes, among other things, triplications at low angles. Even,
in weaker anisotropies, with anisotropy parameter
=0.1 ( anisotropy), the AMO operator differs from the isotropic one,
though does not include
triplications. The structure of the operator
in VTI media (positive ) is
stretched compared to operators in the isotropic media, with the amount
of stretch dependent on the
strength of anisotropy. If the medium is both
*v*(*z*) and anisotropic, a likely combination in practical problems,
the shape of the operator again differs from that
for isotropic media. Yet, the difference
in the AMO operator for the homogeneous case and the *v*(*z*) one is small even for anisotropic
media. Simply stated, anisotropy impacts AMO more than typical smooth vertical velocity variations.

An acoustic wave equation for orthorhombic anisotropy (ps 527K) (src 54K)
**Alkhalifah T.**

Using a dispersion relation derived under the acoustic medium
assumption for *P*-waves in orthorhombic anisotropic media, I obtain an acoustic wave equation
valid under the same assumption. Although this assumption is physically impossible for anisotropic media, it
results in wave equations that are kinematically and dynamically accurate for elastic media.
The orthorhombic
acoustic wave equation, unlike the transversely isotropic (TI) one, is a six-order equation with
three sets of complex conjugate solutions. Only one set of these solutions are perturbations
of the familiar acoustic wavefield solution
in isotropic media for in-coming and out-going *P*-waves, and thus, are of interest here. The other two sets of solutions
are simplify the result of this artificially derived
sixth order equation, and thus, represent unwanted artifacts. Like in the TI case, these artifacts
can be eliminated by placing the source in an isotropic layer, where such artifacts do not exist.

8/21/1998