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What is Equivalent in an ``Equivalent Medium? (ps 41K) (src 3K)
Nichols D. and Karrenbach M.
The static behaviour of a medium consisting of infinite horizontal
layers can be described by an equivalent homogeneous
medium (Schoenberg and Muir, 1989). In this article we give a simplified
notation for the calculation of the equivalent medium and discuss the
question of how an equivalent medium should be defined.
If stress is applied on the top boundary of a stack of layers and the
homogeneous equivalent medium, both media
show identical changes in elastic deformation energy within the medium and
the same exterior displacements and average forces on the boundaries.
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A general theory for equivalent media (ps 50K) (src 6K)
Karrenbach M.
Conservation of deformation energy, volume and mass lead to a general
formulation for finding the static homogeneous equivalent of an
arbitrary heterogeneous anisotropic medium.
The homogeneous equivalent has identical integral properties and
on a large scale, shows the same average behavior in displacements
and stresses. The medium is not restricted to a special geometry.
Modeling vector fields in regions with irregular boundaries (ps 117K) (src 273K)
Muir F., Dellinger J., Etgen J., and Nichols D.
Geologists often see the Earth as homogeneous blocks separated by
smooth curved boundaries. In contrast, computer modeling algorithms
based on finite-difference schemes need to have the elastic constants
of the Earth specified at the points of a regular grid. A common way
of gridding a geological model is to lay the computer model grid down
and use whatever elastic constants lie beneath each grid point. This
naive method may result in artifacts; for example, a gently sloping
interface will be modeled as a coarse staircase, which generates
unwanted diffractions at the stair edges.
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Cross-hole seismology at SEP (ps 34K) (src 2K)
Muir F.
Although surface-to-surface geometry is still pre-eminent in seismic
exploration, the increasing use of the seismic method in oil field
exploitation applications such as reservoir delineation has led to the
development of new downhole tools, and with these tools the need for
new data processing techniques. To this end, the SEP conducted a weekly
seminar/workshop throughout the Summer Quarter on cross-hole data
processing.
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Rotation and wavelet estimation using crosshole data (ps 326K) (src 581K)Biondi:
Cole S. and Karrenbach M.
A first task in processing our three-component crosshole dataset is to separate
P and S wavetypes. Given the arrival direction of incident energy,
one can rotate and combine the three components to produce P, SV, and
SH wave sections.
We developed an automatic scheme to perform this separation. A window
of data is
rotated over all possible arrival directions and the direction
that maximizes the power of a given wave type is chosen. The
entire trace is then rotated according to this direction to produce
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Deconvolution of cross-hole data (ps 28K) (src 1K)
Vanyan L.
One of the works of the cross-hole SEP subseminar during the
summer quarter, 1990 was processing 3-component
data obtained using an experimental borehole vibrosource.
In (Cole and Karrenbach,1990) the ``rotation" of the data
is described. Technically the rotation is transformation
of the coordinate system and respectively the components of the data;
new axes were chosen the following way: 1) along the direction source-receiver,
2) normal to the first axis in the vertical plane, 3) perpendicular to
the vertical plane.
The purpose of such processing is separating the waves with
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Traveltime inversion of a cross-well dataset for elliptically anisotropic media (ps 75K) (src 39K)
Filho C. A. C.
Using the paraxial elliptical approximation for the
dispersion relation around a horizontal axis, I applied a
homogeneous and a layered traveltime inversion scheme
to a common-receiver, multi-component, cross-well dataset.
Each wave-type was inverted independently for the two
parameters that describe the elastic model for media with
elliptical anisotropy.
The layered inversion scheme decomposes the model
into a set of symmetric and anti-symmetric square functions.
Results of the homogeneous inversion for the P and SV waves
show a considerable degree of elliptical anisotropy. Even with
the absence of SH information we were able to obtain four of
the five transverse isotropic elastic parameters. Although
the insufficient coverage of this specific dataset compromises
the uniqueness of the solution, the first iterations
of the layered scheme represent at least one resolution-step ahead of
the homogeneous results.
A modified anisotropic system (ps 32K) (src 1K)
Muir F.
Some years back, Muir & Dellinger (1985), in an attempt to simplify
the processing of multi-component seismic data, introduced a system of
equations that unified ray and wave theory in an approximate manner.
This allowed, for example, time/offset relations to be converted to
dispersion relations which could then form the basis for anisotropic
imaging schemes.
This paper removes one drawback from that scheme-the use of an
anelliptic factor that had no counterpart in normal experience-and
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Extending a CMP gather by optimization in velocity space (ps 100K) (src 134K)
Claerbout J. F.
A test of linear inversion theory yields weak and unconvincing
extrapolations of a CMP gather.
An ambient noise dataset from a producing field (ps 539K) (src 932K)
Cole S. and Vanyan L.
We have recently begun looking at an interesting dataset
where ambient seismic noise was recorded using a 480 channel
array of buried geophones in a producing field.
Pumps provide strong, broadband
coherent energy. Using techniques that we have applied to
other ambient noise datasets, we hope to locate sources
of noise on the surface and at depth, and infer some details
about the subsurface.
A Generalized Phase-Shift Method (ps 58K) (src 5K)
Ji J.
A basic part of seismic migration is downward continuation of surface data into
the subsurface. Gazdag (1978) introduced the phase-shift method which yields
complete accuracy for laterally uniform structures. Kosloff and Kessler (1987)
showed how the phase-shift method can be generalized for an arbitrary
velocity structure in the space-frequency domain. The generalized phase-shift
method by Kosloff and Kessler is instructive to understand how
the phase-shift method works and can be implemented in both space-frequency
domain and wavenumber-frequency domain.
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Migration, tomography, seismic inversion theory, and how they relate to each other (ps 75K) (src 11K)
Kneib G.
The Kirchhoff integral can only be used to propagate wavefields forward.
Backward propagation is based on the Porter-Bojarski integral.
Both integrals simplify if data is registered on a plane.
Transmission and reflection data should be combined to increase
spatial resolution. Angles and
frequencies should vary as much as possible to cover the largest area possible of the k-space.
Migration is identical to diffraction tomography for varying frequencies
if the weak scatterer assumption is valid in a constant background velocity
medium. Holography is backpropagation and imaging of a monofrequent wavefield.
Linear and non-linear inversions improve the migration and tomography results
because they consider the data as imperfect.
Finite-difference calculation of Residual-migration operators (ps 251K) (src 713K)
Zhang L.
Using a kinematic approach, I derive two sets of partial differential equations
whose solutions define the kinematics of residual-migration operators.
These operators
can transform
an image migrated with one velocity model to an image migrated
with another velocity model.
Under the assumption of knowing the partial derivatives of traveltimes
with respect to the coordinates of velocity models on a regular grid,
these two sets of partial differential equations can
then be solved with standard finite-difference techniques.
This algorithm can efficiently calculate the residual-migration operators for
common shot gathers or constant offset sections migrated with general velocity
models.
Examples with residual profile migration prove that the
accuracy of the algorithm is sufficient for seismic applications.
Correlation-picking deconvolution (ps 173K) (src 210K)
Filho C. A. C.
A scaled correlation between the residuals and the wavelet is
used as the basis of a new deconvolution approach, which
resolves first the strongest events and then, as the number of
iteration increases, the weaker events of the reflectivity
sequence. An important property of this method
is that the retrieved series has the same
frequency content as the original sequence. The results
obtained with the application of this algorithm to real
data are equivalent to a sharper version of the results
of predictive deconvolution.
Automatic dip-picking by non-linear optimization (ps 201K) (src 803K)
Zhang L. and Claerbout J.
We have developed a new automatic dip-picking
method that is superior to the dip-scan method in
several aspects. In our method, we estimate the dip of an event through
the relative time-shift between neighboring traces.
The optimal time-shift is defined to be the minimizer of a non-quadratic
objective function that measures the discrepancies between the neighboring
traces after these traces are shifted relative to one another. To eliminate aliasing effects,
data-dependent weighting functions are included in the objective
function. This non-linear optimization problem is solved by searching.
Once a preliminary solution is obtained, the objective
function is approximately reduced to a quadratic form and the residual
time-shift is then estimated by solving a linear equation.
In the end, the time-shift is converted into the dip.
Examples with synthetic and field data show that the combination of the
linear and non-linear optimizations enables our algorithm to have the
properties of antialiasing, high resolution and high accuracy.
The applications of the algorithm include event-picking, moveout corrections,
local dip-filtering and missing data interpolation.
Active documents and reproducible results (ps.gz 15K) (pdf 37K)
Claerbout J.
A revolution in education and technology transfer will follow from the marriage of word processing and software command scripts.
In this marriage, here being called an active document (a-doc), an author attaches to every figure caption a pushbutton or a name tag
usable to recalculate the figure from from all its data, parameters, and programs. An a-doc provides a concrete definition of
reproducibility in computational oriented research. Given suitable interactive software, an active document is easily converted
into an interactive document (i-doc). I have two textbooks undergoing conversion to i-books.
Why Active documents need cake (ps.gz 8K) (pdf 22K)
Claerbout J. and Nichols D.
An active document (a-doc) is software that reproduces a document
including its plots. When plot files are absent the a-doc software should regenerate them. One reason to author active documents with
the freely-available utility cake instead of the UNIX utility make is because cake handles an environment where
intermediate files are missing.
Progress towards the interactive book (ps 400K) (src 550K)
Karrenbach M. and Nichols D.
We have been able to use recent advances in workstation technology and
software to make progress towards Jon's goal of an ``interactive book''.
By using
the ``xtex'' previewer we can preview
documents written in the typesetting language TEX.
Furthermore by using special TEX commands we can add ``hot spots'' to the previewed document, when the user clicks on these areas a sequence of commands is executed on the workstation. This ability makes the document interactive, the text can describe an idea and then clicking on a button will start a program that shows the idea in action. Clicking on the button can also regenerate a figure within the text, either the same figure or a version made with new parameters.
Xvpanel: interactive programs in one line or less (ps 48K) (src 8K)
Cole S.
In SEP-65, I described an interactive data processing environment
that I developed called IPE. Briefly, IPE allows you to use existing
batch programs in a pseudo-interactive manner, complete with buttons
and sliders that can be used to change parameter values.
No programming is required;
all that is needed is an ASCII description of the parameters for each
program.
While IPE is fine for many purposes, in other cases it is overkill.
This became clear during the development of interactive documents at
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X3D (extensible 3-D visualization) update (ps 86K) (src 273K)
Ottolini R.
The X3D graphics system has been upgraded to XView user interface
with the additional graphics functionality of illuminated surfaces
and transformable raster images.
A geometrical approach to seismic processing: the method of discontinuities (ps 191K) (src 46K)
Goldin S.
What do we expect from a theory? Efficiency, prediction, and
explanation. Certainly the first aim seems to be the most
important. Many specialists apply a theory mainly with the
purpose to construct effective algorithms.
But I believe the prediction and explanation by no means are
less important. Though we do use computers, we ourselves are
not computers at all. And an investigator who possesses
algorithms but does not understand why and how it works cannot
estimate proper results of processing and realize all
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