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SEP -- TABLE OF CONTENTS
Multiple realizations using standard inversion techniques [pdf 444K]
Robert G. Clapp
When solving a missing data problem, geophysicists and geostatisticians have
very similar strategies.
Each use the known data to characterize the model's covariance. At SEP we
often characterize the covariance through Prediction Error Filters (PEFs)
(Claerbout, 1998). Geostatisticians build variograms from the known data
to represent the model's covariance (Issaks and Srivastava, 1989).
Iterative least-square inversion for amplitude balancing [pdf 296K]
Arnaud Berlioux and William S. Harlan
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.
Least-square inversion with inexact adjoints.
Method of conjugate directions: A tutorial [pdf 288K]
This tutorial describes the classic method of conjugate directions:
the generalization of the conjugate-gradient method in iterative
least-square inversion. I derive the algebraic equations of the
conjugate-direction method from general optimization principles. The
derivation explains the ``magic'' properties of conjugate gradients.
It also justifies the use of conjugate directions in cases when
these properties are distorted either by computational errors or by
inexact adjoint operators. The extra cost comes from storing a
larger number of previous search directions in the computer memory.
A simple program and two examples illustrate the method.
Asymptotic pseudounitary stacking operators [pdf 344K]
Stacking operators are widely used in seismic imaging and seismic data
processing. Examples include Kirchhoff datuming, migration, offset
continuation, DMO, and velocity transform. Two primary approaches
exist for inverting such operators. The first approach is iterative
least-squares optimization, which involves the construction of the adjoint
operator. The second approach is asymptotic inversion, where an approximate
inverse operator is constructed in the high-frequency asymptotics. Adjoint
and asymptotic inverse operators share the same kinematic properties, but
their amplitudes (weighting functions) are defined differently. This paper
describes a theory for reconciling the two approaches. I introduce a pair of
the asymptotic pseudo-unitary operators, which possess both the property
of being adjoint and the property of being asymptotically inverse. The
weighting function of the asymptotic pseudo-unitary stacking operators is
shown to be completely defined by the derivatives of the operator
kinematics. I exemplify the general theory by considering several particular
examples of stacking operators. Simple numerical experiments demonstrate a
noticeable gain in efficiency when the asymptotic pseudo-unitary operators are
applied for preconditioning iterative least-squares optimization.
Forward interpolation [pdf 780K]
As I will illustrate in later chapters, the crucial part of data
regularization problems is in the choice and implementation of the
regularization operator or the corresponding
preconditioning operator . The choice of the forward
modeling operator is less critical. In this chapter, I
discuss the nature of forward interpolation, which has been one of the
traditional subjects in computational mathematics. Wolberg (1990)
presents a detailed review of different conventional approaches. I
discuss a simple mathematical theory of interpolation from a regular
grid and derive the main formulas from a very general idea of function
Forward interpolation plays only a supplementary role in this
dissertation, but it has many primary applications, such as trace
resampling, NMO, Kirchhoff and Stolt migrations, log-stretch, and
radial transform, in seismic data processing and imaging. Two simple
examples appear at the end of this chapter.
Spitz makes a better assumption for the signal
PEF [pdf 128K]
Jon Claerbout and Sergey Fomel
In real-world extraction of signal from data we are not given the
needed signal prediction-error filter (PEF). Claerbout has taken ,
the PEF of the signal, to be that of the data, . Spitz
takes it to be . Where noises are highly predictable in
time or space, Spitz gets significantly better results.
Theoretically, a reason is that the essential character of a PEF is
contained where it is small.
Seismic reflection data interpolation with differential offset
and shot continuation [pdf 440K]
I propose a finite-difference offset continuation filter for
interpolating seismic reflection data. The filter is constructed
from the offset continuation differential equation and is applied on
frequency slices in the log-stretch frequency domain. Synthetic and
real data tests demonstrate that the proposed method succeeds in
structurally complex situations where more simplistic approaches
Applications of plane-wave destruction filters [pdf 776K]
Plane-wave destruction filters originate from a local plane-wave
model for characterizing seismic data. These filters can be thought
of as a - analog of - prediction-error filters and as an
alternative to - prediction-error filters. The filters are
constructed with the help of an implicit finite-difference scheme
for the local plane-wave equation. On several synthetic and
real-data examples, I demonstrate that finite-difference plane-wave
destruction filters perform well in applications such as fault
detection, data interpolation, and noise attenuation.
Inverse B-spline interpolation [pdf 1.3M]
B-splines provide an accurate and efficient method for interpolating
regularly spaced data. In this paper, I study the applicability of
B-spline interpolation in the context of the inverse interpolation
method for regularizing irregular data. Numerical tests show that,
in comparison with lower-order linear interpolation, B-splines lead
to a faster iterative conversion in under-determined problems and a
more accurate result in over-determined problems. In addition, they
provide a constructive method for creating discrete regularization
operators from continuous differential equations.
Test case for PEF estimation with sparse data II [pdf 172K]
Morgan Brown, Jon Claerbout, and Sergey Fomel
The two-stage missing data interpolation approach of Claerbout (1998) (henceforth, the GEE
approach) has been applied
with great success (Fomel et al., 1997; Clapp et al., 1998; Crawley, 2000) in the past.
The main strength of the approach lies in the ability of the prediction error filter (PEF) to
Multiple suppression using prediction-error filter [pdf 240K]
I present an approach to multiple suppression, that is
based on the moveout between primary and multiple events in the CMP gather.
After normal moveout correction, primary events will be horizontal,
whereas multiple events will not be.
For each NMOed CMP gather, I reorder the
offset in random order. Ideally, this process has little influence on the
it destroys the shape of the multiples. In other words, after randomization
of the offset order, the multiples appear as random noise. This ``man-made''
random noise can be removed using prediction-error filter (PEF).
The randomization of the offset order can be regarded as a random process,
so we can apply it to the CMP gather many times and get many different
samples. All the samples can be arranged into a 3-D cube, which is further
divided into many small subcubes. A 3-D PEF can then be estimated from each
subcube and re-applied
to it to remove the multiple energy. After that, all the samples are averaged
back into one CMP gather, which is supposed to be free of multiple events.
In order to improve the efficiency of the
algorithm of estimating the PEF for each subcube, except for the first
subcube which starts with a zero-valued initial guess, all the subsequent
subcubes take the last estimated PEF as an initial guess.
Therefore, the iteration
count can be reduced to one step for all the subsequent subcubes with little
loss of accuracy.
Three examples demonstrate the performance of this new approach, especially in
removing the near-offset multiples.
Multidimensional recursive filter preconditioning
in geophysical estimation problems [pdf 1.3M]
Sergey Fomel and Jon Claerbout
Constraining ill-posed inverse problems often requires
regularized optimization. We consider two alternative approaches
to regularization. The first approach involves a column operator
and an extension of the data space. It requires a regularization
operator which enhances the undesirable features of the model.
The second approach constructs a row operator and expands the
model space. It employs a preconditioning operator, which
enforces a desirable behavior, such as smoothness, of the model.
In large-scale problems, when iterative optimization is incomplete,
the second method is preferable, because it often leads to
faster convergence. We propose a method for constructing
preconditioning operators by multidimensional recursive
filtering. The recursive filters are constructed by imposing
helical boundary conditions. Several examples with
synthetic and real data demonstrate an order of magnitude
efficiency gain achieved by applying the proposed technique to
data interpolation problems.
Exploring three-dimensional implicit wavefield extrapolation
with the helix transform [pdf 1.1M]
Sergey Fomel and Jon F. Claerbout
Implicit extrapolation is an efficient and unconditionally stable
method of wavefield continuation. Unfortunately, implicit wave
extrapolation in three dimensions requires an expensive solution of
a large system of linear equations. However, by mapping the
computational domain into one dimension via the helix transform, we
show that the matrix inversion problem can be recast in terms of an
efficient recursive filtering. Apart from the boundary conditions,
the solution is exact in the case of constant coefficients (that is,
a laterally homogeneous velocity.) We illustrate this fact with an
example of three-dimensional velocity continuation and discuss
possible ways of attacking the problem of lateral variations.
The Wilson-Burg method of spectral factorization
with application to helical filtering [pdf 840K]
Sergey Fomel, Paul Sava, James Rickett, and Jon F. Claerbout
Spectral factorization is a computational procedure for constructing
minimum-phase (stable inverse) filters required for recursive
inverse filtering. We present a novel method of spectral
factorization. The method iteratively constructs an
approximation of the minimum-phase filter with the given
autocorrelation by repeated forward and inverse filtering and
rearranging the terms. This procedure is especially efficient in
the multidimensional case, where the inverse recursive filtering
is enabled by the helix transform.
To exemplify a practical application of the proposed method, we
consider the problem of smooth two-dimensional data
regularization. Splines in tension are smooth interpolation
surfaces whose behavior in unconstrained regions is controlled
by the tension parameter. We show that such surfaces can be
efficiently constructed with recursive filter preconditioning
and introduce a family of corresponding two-dimensional
minimum-phase filters. The filters are created by spectral
factorization on a helix.
Spectral factorization revisited [pdf 168K]
Paul Sava and Sergey Fomel
In this paper, we review some of the iterative methods for the square
root, showing that all these methods belong to the same
family, for which we find a general formula. We then explain how those
iterative methods for real numbers can be extended to spectral
factorization of auto-correlations. The iteration based on
the Newton-Raphson method is optimal from the convergence stand point, though
it is not optimal as far as stability is concerned. Finally, we show
that other members of the iteration family are more stable, though
slightly more expensive and slower to converge.
Plane wave prediction in 3-D [pdf 772K]
The theory of plane-wave prediction in three dimensions is described
by Claerbout (1999,1993). Predicting a local plane wave with
T-X filters amounts to finding a pair of two-dimensional filters
for two orthogonal planes in the 3-D space. Each of the filters
predicts locally straight lines in the corresponding plane. The system
of two 2-D filters is sufficient for predicting all but purely
Solution steering with space-variant filters [pdf 388K]
Robert G. Clapp, Sergey Fomel, and Jon Claerbout
Most geophysical problem require some type of regularization.
Unfortunately most regularization schemes produce ``smeared'' results
that are often undesirable when applying other criteria (such as geologic
By forming regularization operators in terms of
recursive steering filters, built from a priori information sources,
we can efficiently guide the solution towards
a more appealing form. The steering
methodology proves effective in interpolating
low frequency functions, such as velocity,
but performs poorly when encountering multiple
dips and high frequency data. Preliminary results using steering filters for
regularization in tomography problems are encouraging.
Random lines in a plane [pdf 132K]
Locally, seismic data is a superposition of plane waves.
The statistical properties of such superpositions
are relevant to geophysical estimation
and they are not entirely obvious.
Clearly, a planar wave can be constructed from a planar
distribution of point sources.
Texture synthesis and prediction error filtering [pdf 476K]
The spectrum of a prediction-error filter (PEF) tends toward the inverse spectrum of the
data from which it is estimated.
I compute 2-D PEF's from known ``training images'' and use them to synthesize
similar-looking textures from random numbers via helix deconvolution.
Compared to a similar technique employing Fourier transforms, the PEF-based method is
generally more flexible, due to its ability to handle missing data, a fact which I
illustrate with an example.
Applying PEF-based texture synthesis to a stacked 2-D seismic section,
I note that the residual error in the PEF estimation forms the basis for ``coherency''
analysis by highlighting discontinuities in the data, and may also serve as a measure
of the quality of a given migration velocity model.
Last, I relate the notion of texture synthesis to missing data interpolation and show
Multi-dimensional Fourier transforms in the helical coordinate
system [pdf 632K]
James Rickett and Antoine Guitton
For every two-dimensional system with helical boundary
conditions, there is an isomorphic one-dimensional system.
Therefore, the one-dimensional FFT of a 2-D function wrapped on a
helix is equivalent to a 2-D FFT.
We show that the Fourier dual of helical boundary conditions is
helical boundary conditions but with axes transposed, and we
explicitly link the wavenumber vector, , in a
multi-dimensional system with the wavenumber of a helical 1-D FFT,
We illustrated the concepts with an example of multi-dimensional
Passive seismic imaging applied to synthetic data [pdf 180K]
James Rickett and Jon Claerbout
It can be shown that for a 1-D Earth model illuminated by random plane waves
from below, the cross-correlation of noise traces recorded at two points on the
surface is the same as what would be recorded if one location contained a
shot and the other a receiver. If this is true for real data, it could
provide a way of building `pseudo-reflection seismograms' from background
noise, which could then be processed and used for imaging.
This conjecture is tested on synthetic data from simple
1-D and point diffractor models,
and in all cases, the kinematics of observed events
appear to be correct.
The signal to noise ratio was found to increase as , where is
the length of the time series. The number of incident
plane waves does not directly affect the signal to noise ratio; however,
each plane wave contributes only its own slowness to the common
shot domain, so that if complete hyperbolas are to be imaged
then upcoming waves must be incident from all angles.
When is anti-aliasing needed in Kirchhoff migration? [pdf 700K]
Dimitri Bevc and David E. Lumley
We present criteria to determine when numerical integration
of seismic data will incur operator aliasing. Although there are
many ways to handle operator aliasing, they add expense to the
computational task. This is especially true in three dimensions.
A two-dimensional Kirchhoff migration example illustrates that
the image zone of interest may not always require anti-aliasing and
that considerable cost may be spared by not incorporating it.
Imaging complex structures with first-arrival traveltimes [pdf 680K]
I present a layer-stripping Kirchhoff migration algorithm which is
capable of obtaining accurate
images of complex structures by downward continuing
the data and imaging from a lower datum.
I use eikonal traveltimes in a Kirchhoff datuming algorithm for the
downward continuation. After downward continuation, I perform
The method alternates steps of datuming and imaging. Because traveltimes
are computed for each step, the adverse effects of caustics, headwaves, and
multiple arrivals do not develop.
In principal, this method only requires the same number of
traveltime calculations as a standard migration.
Tests on the Marmousi data set produce excellent results.
Evaluating the Stolt-stretch parameter [pdf 972K]
Sergey Fomel and Louis Vaillant
The Stolt migration extension to a variable velocity case describes
the velocity heterogeneity with a constant parameter, which is
related to the stretch transformation of the time axis. We exploit
a connection between modified dispersion relations and nonhyperbolic
traveltime approximations to derive an explicit expression for the
stretch parameter. This analytical expression allows one two achieve
the highest possible accuracy within the Stolt stretch
approximation. Using a real data example, we demonstrate an
application of the explicit Stolt stretch formula for an optimal
partitioning of the migration velocity in the method of cascaded
Antialiasing of Kirchhoff operators by reciprocal
parameterization [pdf 496K]
I propose a method for antialiasing Kirchhoff operators, which
switches between interpolation in time and interpolation in space
depending on the operator dips. The method is a generalization of
Hale's technique for dip moveout antialiasing. It is applicable to a
wide variety of integral operators and compares favorably with the
popular temporal filtering technique. Simple synthetic examples
demonstrate the performance and applicability of the proposed
Angle-gather time migration [pdf 440K]
Sergey Fomel and Marie Prucha
Angle-gather migration creates seismic images for different
reflection angles at the reflector. We formulate an angle-gather
time migration algorithm and study its properties. The algorithm
serves as an educational introduction to the angle gather concept.
It also looks attractive as a practical alternative to conventional
common-offset time migration both for velocity analysis and for
Wavefront construction using waverays [pdf 568K]
A method for computing first arrival traveltimes and amplitudes in
a general two-dimensional (2-D) velocity model is
presented. The method is the result of merging two
recently published ray tracing methods. The product is a
very robust algorithm that is able to produce broadband wave phenomena,
such as dispersion and wavelength dependent scattering.
Its ability to produce broadband wave phenomena, is achieved
by performing a wavelength-dependent smoothing of the velocity model
across wavefronts. In the limit of high frequency, the method
reduces to geometrical ray theory.
The method is able to illuminate areas of large geometrical
spreading where conventional ray tracing methods may give no
arrivals. The method is tested on synthetic complex
Traveltime computation with the linearized eikonal equation [pdf 192K]
Traveltime computation is an important part of seismic imaging
algorithms. Conventional implementations of Kirchhoff migration
require precomputing traveltime tables or include traveltime
calculation in the innermost computational loop . The cost of
traveltime computations is especially noticeable in the case of 3-D
prestack imaging where the input data size increases the level of
nesting in computational loops.
Huygens wavefront tracing: A robust alternative to conventional
ray tracing [pdf 840K]
Paul Sava and Sergey Fomel
We present a method of ray tracing that is based on a system of
differential equations equivalent to the eikonal equation, but formulated
in the ray coordinate system. We use a first-order discretization scheme
that is interpreted very simply in terms of the Huygens' principle. The
method has proved to be a robust alternative to conventional ray tracing,
while being faster and having a better ability to penetrate the shadow
A variational formulation of the fast marching eikonal solver [pdf 540K]
I exploit the theoretical link between the eikonal equation and
Fermat's principle to derive a variational interpretation of the
recently developed method for fast traveltime computations. This
method, known as fast marching, possesses remarkable computational
properties. Based originally on the eikonal equation, it can be
derived equally well from Fermat's principle. The new variational
formulation has two important applications: First, the method can be
extended naturally for traveltime computation on unstructured
(triangulated) grids. Second, it can be generalized to handle other
Hamilton-type equations through their correspondence with
A second-order fast marching eikonal solver [pdf 444K]
James Rickett and Sergey Fomel
The fast marching method (Sethian, 1996) is widely used for solving the
eikonal equation in Cartesian coordinates.
The method's principal advantages are: stability,
computational efficiency, and algorithmic simplicity.
Within geophysics, fast marching traveltime
calculations (Popovici and Sethian, 1997) may be used
for 3-D depth migration or velocity analysis.
The time and space formulation of azimuth moveout [pdf 808K]
Sergey Fomel and Biondo L. Biondi
Azimuth moveout (AMO) transforms 3-D prestack seismic data from one
common azimuth and offset to different azimuths and offsets.
AMO in the time-space domain is represented by a three-dimensional
integral operator. The operator components are the summation path,
the weighting function, and the aperture. To determine the summation path and
the weighting function, we derive the AMO operator by cascading dip
moveout (DMO) and inverse DMO for different azimuths in the time-space
domain. To evaluate the aperture, we apply a geometric approach,
defining AMO as the result of cascading prestack migration (inversion)
and modeling. The aperture limitations provide a consistent
description of AMO for small azimuth rotations (including zero) and justify the
economic efficiency of the method.
Theory of differential offset continuation [pdf 364K]
I introduce a partial differential equation to describe the
process of prestack reflection data transformation in the offset,
midpoint, and time coordinates. The equation is proved theoretically
to provide correct kinematics and amplitudes on the transformed
constant-offset sections. Solving an initial-value problem with the
proposed equation leads to integral and frequency-domain offset
continuation operators, which reduce to the known forms of dip
moveout operators in the case of continuation to zero offset.
Amplitude preservation for offset continuation:
Confirmation for Kirchhoff data [pdf 132K]
Sergey Fomel and Norman Bleistein
Offset continuation (OC) is the operator that transforms common-offset
seismic reflection data from one offset to another. Earlier
papers by the first author presented a partial differential
equation in midpoint and offset to achieve this transformation.
The equation was derived from the kinematics of the continuation
process with no reference to amplitudes. We present here a proof
that the solution of the OC partial differential equation does
propagate amplitude properly at all offsets, at least to the same
order of accuracy as the Kirchhoff approximation. That is, the
OC equation provides a solution with the correct traveltime and
correct leading-order amplitude. ``Correct amplitude'' in this
case means that the transformed amplitude exhibits the right
geometrical spreading and reflection-surface-curvature effects
for the new offset. The reflection coefficient of the original
offset is preserved in this transformation. This result is more
general than the earlier results in that it does not rely on the
two-and-one-half dimensional assumption.
Effective AMO implementation in the log-stretch,
frequency-wavenumber domain [pdf 204K]
Ioan Vlad and Biondo Biondi
Azimuth moveout (AMO), introduced by Biondi et al. (1998), is used
as part of the styling goal (in conjunction with a derivative as a
roughener) in Biondi and Vlad (2001). This paper describes the
implementation of AMO for the above-stated purpose, with a historical
background, proof, and discussion of pitfalls and practical steps.
Earthquake stacks at constant offset [pdf 452K]
Jon F. Claerbout
I show Shearer's earthquake stacks
over all source-receiver locations at constant offset
and compare them to exploration seismic data.
This electronic document simply reads the stacks and plots them.
A prospect for super resolution
Wouldn't it be great if I could take signals of
10-30 Hz bandwidth
from 100 different offsets and construct a zero-offset trace with 5-100 Hz
This would not violate Shannon's sampling theorem
which theoretically allows us to have a transform
from 100 signals of 20 Hz bandwidth to one signal
at 2000 Hz bandwidth.
The double-elliptic approximation in the group and phase domains [pdf 184K]
Joe Dellinger and Francis Muir
Elliptical anisotropy has found wide use as a simple approximation
to transverse isotropy because of a unique symmetry property
(an elliptical dispersion relation corresponds to an elliptical
impulse response) and a simple relationship to standard geophysical
techniques (hyperbolic moveout corresponds to elliptical wavefronts;
NMO measures horizontal velocity, and time-to-depth conversion
depends on vertical velocity).
However, elliptical anisotropy is only useful as an approximation
in certain restricted cases, such as when the underlying true anisotropy
does not depart too far from ellipticity
Velocity continuation and the anatomy of
residual prestack time migration [pdf 340K]
Velocity continuation is an imaginary continuous process of
seismic image transformation in the post-migration domain. It generalizes
the concepts of residual and cascaded migrations. Understanding the laws
of velocity continuation is crucially important for a successful application
of time migration velocity analysis. These laws predict the changes
in the geometry and intensity of reflection events on migrated images with
the change of the migration velocity. In this paper, I derive kinematic
and dynamic laws for the case of prestack residual migration from simple
geometric principles. The main theoretical result is a decomposition
of prestack velocity continuation into three different components
corresponding to residual normal moveout, residual dip moveout, and residual
zero-offset migration. I analyze the contribution and properties of each of
the three components separately. This theory forms the basis for
constructing efficient finite-difference and spectral algorithms for
time migration velocity analysis.
Velocity continuation by spectral methods [pdf 520K]
I apply Fourier and Chebyshev spectral methods to derive accurate
and efficient algorithms for velocity continuation. As expected,
the accuracy of the spectral methods is noticeably superior to that
of the finite-difference approach. Both methods apply a
transformation of the time axis to squared time. The Chebyshev
method is slightly less efficient than the Fourier method, but has
less problems with the time transformation and also handles
accurately the non-periodic boundary conditions.
Time migration velocity analysis by velocity continuation [pdf 992K]
Time migration velocity analysis can be performed by velocity
continuation, an incremental process that transforms
migrated seismic sections according to changes in the migration velocity.
Velocity continuation enhances residual normal moveout correction by
properly taking into account both vertical and lateral movements of
events on seismic images. Finite-difference and spectral algorithms
provide efficient practical implementations for velocity continuation.
Synthetic and field data examples demonstrate the performance of the method
and confirm theoretical expectations.
Traveltime sensitivity kernels: Banana-doughnuts or just
plain bananas? [pdf 132K]
Estimating an accurate velocity function is one of the most critical
steps in building an accurate seismic depth image of the subsurface.
In areas with significant structural complexity, one-dimensional
updating schemes become unstable, and more robust algorithms are
Reflection tomography both in the premigrated (Bishop et al., 1985) and
postmigrated domains (Stork, 1992; Kosloff et al., 1996) bring the powerful
Modeling 3-D anisotropic fractal media [pdf 592K]
This paper presents stochastic descriptions of anisotropic fractal media.
Second order statistics are used to represent the continuous random field as a
stationary zero-mean process completely specified by its two-point covariance
In analogy to the two-dimensional Goff and
Jordan model for seafloor morphology, I present the von Karman functions as
a generalization to media with exponential correlation functions.
I also compute a two-state
model by mapping the random field from continuous realizations to a binary
field. The method can find application in modeling impedances from fractal
media and in fluid flow problems.
AVO & Elasticity
Seismic AVO analysis of methane hydrate structures [pdf 300K]
Christine Ecker and David E. Lumley
Marine seismic data from the Blake Outer Ridge offshore Florida show strong
``bottom simulating reflections'' (BSR) associated with methane hydrate
occurence in deep marine sediments. We use a detailed amplitude versus
offset (AVO) analysis of these data to explore the validity of models which
might explain the origin of the bottom simulating reflector. After careful
preprocessing steps, we determine a BSR model which can successfully reproduce
the observed AVO responses. The P- and S-velocity behavior predicted by the
forward modeling is further investigated by estimating the P- and S-impedance
contrasts at all subsurface positions. Our results indicate that the Blake Outer
Ridge BSR is compatible with a model of methane hydrate in sediment, overlaying
a layer of free methane gas-saturated sediment. The hydrate-bearing
sediments seem to be characterized by a high P-wave velocity of
approximately 2.5 km/s, an anomalously low S-wave velocity of
approximately 0.5 km/s, and a thickness of around 190 meters.
The underlaying gas-saturated sediments have a P-wave velocity of 1.6 km/s, an
S-wave velocity of 1.1 km/s, and a thickness of approximately 250 meters.
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