AGL831
Abstract
AGL831 Abstract A seismic survey was performed in Southeastern Idaho
from 1979-1980. The purpose of this geophysical study was to try to acquire
data over a seismically opaque layer, one which is overlain by soft, high
porosity volcanic tuffs and ash flows. A CDP line, Line 999 was processed
and analyzed in order to investigate the effects of the surficial volcanic
layer. Regional geology around the survey area was studied for interpreting
the seismic data. One cross-section of a 3D survey area, which is parallel
and close to Line 999, is shown and compared with 2D data. Several reasons
are given to explain why the 3D migrated data do not produce the best results.
An interpretation was made by relating the seismic data to well logs around
the survey area. Two different geological models are presented; both of
them are suitable models based on the available information.
AGL832
Abstract
Complex seismic trace attributes including the amplitude of the envelope,
instantaneous phase, instantaneous frequency, and apparent polarity are
computed and displayed from theoretical and scaled physical model data.
The models were chosen so the seismic data from them could demonstrate
the utility of attribute displays and their analysis when developing an
interpretation. Vertical and horizontal attribute sections are presented
which show their possible uses for delineating unconformities and fault
blocks and generating isochron contour maps. The instantaneous frequency
attribute is shown to be sensitive to waveform interferences and produces
characteristic patterns for pinch out models. The importance of source
wavelets, color codes and threshold parameters are demonstrated. Evaluation
of elastic wave equation modeling programs is carried out by comparing
complex trace attributes from synthetic and scaled physical model data.
Lithologies of exploration interest are modeled using an elastic modeling
program and their complex trace attributes are examined. Attribute displays
are shown to aid the analysis of waveshape variation with angle of incidence
in pre-stack common midpoint gathers. These variations might be able to
be used for predicting lithologies and porefill material.
AGL833
Abstract
Concurrency control is the activity of coordinating concurrent accesses
to a database in a multiuser database management system (DBMS). By preserving
database consistency, concurrency control ensures that all alterations
to the database are serializable (serializability is a situation in which
concurrent operations on a database result in a computationally equivalent
state of the database, compared with executing the operations in a serial
fashion). The concurrency control problem is very important in a distributed
DBMS (DDBMS) because: users may access data stored in many different computers
in a distributed system, and a concurrency control mechanism at one computer
cannot know about interaction at other computers. Concurrency control has
been actively investigated for the past several years. Many concurrency
control algorithms have been proposed for DDBMS and several have been,
or are being, implemented. It is difficult to compare the performances
of the many proposed algorithms. Naturally, each author proclaims his or
her approach as the best, but there is little compelling evidence to support
these claims. This thesis reviews the currently available algorithms concerning
the concurrency control in DDBMS and evaluates their performance through
simulation. The simulation software was developed to evaluate the performance
of the DDBMS with different concurrency control mechanisms based on the
timestamp technique. The results from the simulation are discussed and
the conclusions are presented.
AGL834
Abstract
The Fast Fourier Transform (FFT) is an efficient algorithm to compute
the discrete Fourier transform. The objective of this thesis is to analyze
a variety of problems which lead to inaccurate results in standard FFT
differentiation techniques. Methods which improve computational accuracy
are also reviewed. Two main approaches are followed in order to improve
the accuracy of the estimated derivative. The Fourier coefficients of the
function are estimated more accurately in the first approach. The second
approach is to improve the convergence of the Fourier series of the function.
The methods discussed are tested using FFT routines available on the FPS
100 array processor. The results indicate that the latter approach leads
to a higher accuracy.
AGL835
Abstract
This thesis describes a physical modeling study of seismic reflections
from thin beds. Three models representing common thin bed situations were
used in the study. In the first model, we studied the reflections from
a homogeneous thinning bed embedded in a low velocity material, to determine
amplitude and waveshape changes associated with changes in the bed thickness.
In the second model, we studied the reflections from a thin bed which is
composed of interlayering of high and low velocity materials of the same
thickness, to investigate how reflections from a series of strata differ
from reflection from a massive bed. In the third model, we extended the
second model to study the reflections when the layers composing the thin
bed are not of the same thickness, to verify the conclusion of numerical
modeling that reflection amplitude and waveshape are not sensitive to how
layers are distributed as long as the overall interval is thin. The results
from the first model mostly agree with theoretical predictions published
in the literature. In the second and third models the results show that
not only interference but also other factors are important in constructing
the reflection when the overall interval is thin. We also found that the
waveshape is affected by the distribution of the layers in the thin bed,
in contrast to the conclusion of numerical modeling published in the literature.
We extended models two and three to model a concept of transgressive sands
onto an unconformity, which relates to the question as to whether seismic
reflections follow time or facies lines. The seismic sections show the
attitude of most reflections are those of time lines.
AGL836
Abstract
The physical seismic modeling system at the AGL has been utilized to
measure ultrasonic wave attenuation and dispersion in (1) homogeneous materials
(Plexiglas and silicone rubbers) used to construct geologic models and
(2) geologically more realistic two-phase materials (fluid-saturated sands
and fluid-solid suspensions). Such measurements are necessary to better
understand physical model data, and the data for two-phase media are helpful
in evaluating theories for wave propagation in heterogeneous media. A procedure
has been developed which successfully synthesizes the effect of a plane
wave by summing the responses to point sources arranged in a planar grid.
This data collection procedure provides a way to increase the signal/noise
ratio in a more physically meaningful and helpful way than other collection
schemes. It should also prove useful for studies in other areas. The P-wave
velocities for silicone rubber-sand (fluid-solid) mixtures are predicted
very well as a function of inclusion concentration by considering them
to be composed of spherical inclusions suspended in an ideal fluid matrix.
The spectral amplitude ratio and phase difference techniques yielded the
spatial attenuation coefficient and the phase velocity as functions of
frequency. The greatest attenuation and dispersion were observed for the
rubber-sand mixtures; relative motion between matrix and inclusions is
hypothesized as the principal attenuation mechanism. The fluid-saturated
sandpacks exhibited intermediate Qs and dispersion rates, while the silicone
rubbers were highly nonattenuative and nondispersive. For Plexiglas, attenuation
and dispersion were relatively high; this was the only material for which
Q appeared frequency-dependent. The envelope and instantaneous frequency
attributes are found to be more useful than other time-domain pulse characteristics,
especially in estimating Q and variation of pulse peak frequency. A complex
propagation operator was applied to pulses in the frequency domain. Waveforms
predicted for nondispersive, constant-Q propagation agree well with observed
waveforms for constant-Q media, but not so well for Plexiglas. An accurate
method of determining the peak-frequency Q has been developed which iteratively
models the effects of propagation with different trial Q values.
AGL837
Abstract
For a given geological model, the relationships (temporal, spatial
and causal) between the layers in the model, the raypaths and the seismic
wavefronts radiating from a point source can be preserved by means of a
linked tree data structure. Each node in the tree represents a seismic
hologram a collection of rays along the boundary of a geological layer,
defining the propagation of a particular seismic wavefront through that
layer. These structures used in combination with ray tracing algorithms
and interactive computer graphics open the possibility for many advanced
interactive, animated displays, including the ability to interactively
identify every event in the display as to its origin and history. The techniques
for building such data structures and for building the associated graphic
displays are described. An algorithm for reconstructing the seismic wavefronts
and arrival time curves using polynomial splines is developed. These procedures
are demonstrated for several geological models and the results compared
with data obtained from a physical modeling experiment.
AGL821
Abstract
A Fourier or pseudo-spectral forward modeling algorithm for solving
the 2-D acoustic wave equation is presented. Time derivatives which appear
in the wave equation are calculated by second order finite differencing,
whereas spatial derivatives are calculated by Fast Fourier Transforms (FFT).
The scheme requires fewer spatial grid points than finite difference methods
to achieve the same accuracy. This method is tested against known analytic
solutions and physical modeling results. The Exploding Reflector concept
(Loewenthal et al., 1976) is examined for the modeling of zero source-to-receiver
offset sections. The acoustic wave equation is compared with a one-way
wave equation which represents the upgoing wavefield only. The one-way
wave equation used is not derived through an expansion and, therefore,
can represent dips up to 90 degrees. There is apparently no simple counterpart
of this equation in the space domain and it can be conveniently implemented
only by a Fourier method. The inverse problem (migration) is investigated
using the complementary version of the one-way wave equation employed for
modeling. Also a novel alternative of carrying out the migration through
a reverse time extrapolation is examined. This method is tested using synthetic
data. A new two way non-reflecting wave equation is derived, which gives
highly reduced reflection coefficients at material boundaries. This new
equation is used in both zero source to receiver offset modeling and reverse
time depth migration. The examples show that this equation is capable of
simulating raypaths which bend beyond the horizontal due to refraction
associated with large velocity gradients. It should be useful for the modeling
or migration of primary reflections from the underside of complex structures
such as overhanging salt domes or steep thrust faults.
AGL822
Abstract
A 3D acoustic wave equation modeling program was designed and implemented
on the CDC Cyber 205 vector processor. The program was designed to handle
a 256x256x128 spatial grid and approximately 3000 time steps within 40
hours of computing time. The Fourier method was selected as the computational
basis of the 3D modeling program. Some basic features of vector processors
are introduced such as pipelining, vector instructions . . .etc. A brief
overview of the Cyber 205 system and the algorithm used in solving the
wave equation are also discussed. The design of the 3D forward modeling
program has the following properties (1) Halfword (32-bit) storage and
computation. (2) Four- way concurrent I/O management (SLICE4). (3) Dynamic
startup computation involving only those spatial points at which wave activity
is present. The measured times and snapshots of the test models are presented.
Factors affecting the computing time and improvements of the 3D forward
modeling program are also discussed.
AGL823
Abstract
The Multi-channel Wavelet Extraction System (MWES) is a generalization
of the algorithm developed by Thomas (1976). It is a deterministic technique
which makes use of the velocity function and the offset distance to determine
the phase of the seismic wavelet. When the normal move-out correction is
known, the system appears to recover a consistent wavelet estimate. Several
rules of thumb are discussed for quantifying the input parameters necessary
for running the MWES in terms of the properties of the input data. These
rules of thumb are clarified by synthetic results. The MWES overcomes problems
related with real field data analysis such as additive noise introduced
into the traces and errors in stacking-velocity estimation. An application
of the System to real field data analysis demonstrates advantages of the
method with respect to the traditional algorithms for seismic deconvolution.
AGL824
Abstract
A generalization of the simplex algorithm for solving linear programming
problems is presented. In each iteration of the simplex algorithm the objective
function is improved by proceeding from one vertex to an adjacent vertex
along a one dimensional facet (an edge) of the convex polytope of feasible
solutions. We exhibit a k-dimensional analog of this where k>1 is chosen
so as to yield a steep descent. It is anticipated that the faster rate
of convergence to the optimal solution will more than offset the extra
work done to select a higher dimensional facet, resulting in a reduction
of overall computational effort. We have implemented this method by modifying
an existing program written in vector FORTRAN for CDC CYBER 203/205. The
original program used the simplex algorithm to solve transportation problems
which form an important special class of linear programming problems. We
discuss some details of this implementation and report some favorable numerical
results comparing the timings for the simplex method and our generalization
of the simplex method for some randomly generated transportation problems
involving upto 10,000 variables. Suggestions are given for future research.
AGL811
Abstract
Velocity analysis is an important step in seismic processing for final
proper interpretation. Three sets of computer programs have been designed
and tested for the analysis of velocity based on 3D seismic data. These
computer programs can be used with any set of 2D or 3D data provided the
source and receiver coordinates have been written in the header of each
trace. Program set A modifies Owusu&180;s (1981) velocity analysis
algorithm which is based on 3D migration. Program set B gives attributes
for a fixed velocity and variable arrival time. Each event has to be analyzed
separately. Program set C displays any selected event as a function of
offset from source to receiver. This allows one to analyze the distribution
of energy among offsets and hence to select weights for the offsets that
will improve resolution for the output from program set A or program set
B. Two physical models demonstrate the use of these computer programs.
The first model is a stack of 9 layers of RTV materials. A single multi-fold
CDP (Common Depth Point) line tests these programs for the 2D case. The
second model is a modified GULF model (SALGLF-5). Areal coverage data on
the second model tests these programs for the 3D case.
AGL812
Abstract
In recent years the acquisition, processing and interpretation of 3D
seismic data, for the purpose of locating gas and oil reservoirs, have
become practical. A typical seismic survey will sample a 25 square mile
area with about 2 million seismic recordings, each containing 4000 time
samples. The processing reconstructs these data by a 3D convolution into
a regular grid of data that represents the acoustic impedance distribution
in the earth for a volume of about 50 cubic miles. The interpretation requires
that this volume be searched and correlated with geologic information.
This thesis explores one way in which the volume can be searched and visualized,
which may aid the interpreter. The concept is based on steroscopic perception,
and was originally proposed for the interpretation of volume data for medical
applications. The illusion of looking at a 3D volume can be obtained by
fusing a stereoscopic pair of pictures. Each picture can be made by projecting
each data point of the volume into a plane from a point where the eye is
placed. The data values along any projection line can be summed to form
the picture, or only a segment along the line can be selected. By selective
projection, the volume can be searched and obscuring layers removed. This
thesis describes a VAX 11/780 computer program which generated stereoscopic
images from standard seismic data, and illustrates the concept of 3D perception
with synthetic and physical model data. The physical model simulated 5
stratigraphic traps in a marine environment, and the data simulated a survey
over the traps consisting of a 128 x 128 grid of seismic recordings. The
raw data were 3D migrated and the resulting volume was projected into stereoscopic
pairs of images. The data conversions required to display the images on
a RAMTEK graphic system are explained. The stereoscopic pictures show the
synthetic and physical models in their true spatial positions. A comparison
of the raw data and the 3D migrated data demonstrates the increase in lateral
resolution achieved by the 3D processing. Projection of the envelope function
of the seismic traces is shown to give improved depth perception compared
with projection of the positive amplitudes. The following lines of research
are suggested by this investigation: (1) to develop an interactive stereoscopic
display so that the data volume projected can be selected and enhanced
interactively, (2) to rewrite the algorithm for orthogonal projection,
or for vector processing computer, so that the computation time is reduced,
(3) to project contour plots of constant phase angle, (4) to investigate
the use of other seismic attributes of the data such as instantaneous frequency
or velocity and (5) to investigate enhancement techniques for visualizing
faults or for picking geologic horizons.
AGL813
Abstract
Traditional seismic imaging methods send pulse-like acoustic waveforms
into the subsurface and record the echoes. A large degree of data redundancy
is collected and wasted just to improve the output signal-to-noise ratio
to a limited amount. This study examines an alternative way in seismic
data acquisition, the sign-bit Vibroseis method. The objective is to evaluate
the method for 3D imaging applications; in particular, the holographic
method. Acoustical holography is identified as any image focusing scheme
that performs spatial correlations either implicitly or explicitly. One
particular implementation, the multifrequency acoustical holography, has
been suggested for seismic imaging. This method requires broadband yet
coherent input data, which is readily supplied by the Vibroseis sweep signals
and the associated temporal correlation procedure. The multifrequency holographic
method is compared with another similar approach, the lensless Fourier
transform holographic method. Also compared are other 3D wave equation
imaging algorithms, such as the Kirchhoff summation migration, the frequency
domain migration, the finite difference migration, the Fresnel imaging,
the Fraunhofer imaging and the wave vector diversity method. Fundamental
differences and similarities among these algorithms are compared on a theoretical
basis. The 3D Kirchhoff migration is also implemented in a more efficient
process, the two-step method. This approach approximates the 3D full-blown
integration by two 2D integrations. The resulting aberrations are tolerable.
Both the Vibroseis sweep and the sign-bit recording technique are recognized
as information encoding and compressing processes. The benefits of these
processes are to have less critical requirements for the input dynamic
range and higher utilization of the redundantly collected data. Data retrieval
of the sign-bit Vibroseis data is performed by either linear processes,
such as pilot-correlation and vertical stacking, or some nonlinear processes,
such as CDP stacking and migration. All nonlinear processes involve distortions
due to hard-limiting. Mathematical analyses are done to derive the relationship
between the input and output dynamic ranges. Distortions are pointed out.
Synthetic traces are generated to compare the results of sign-bit and 16-bit
recordings under the assumption of some simple noise models. Tank experiments
are performed to collect 3D reflection data from physical models, using
a pulse-like source and a Vibroseis simulating sweep source. The sign-bit
version of the Vibroseis- simulating data is correlated, migrated, and
compared with the 16-bit Vibroseis data and the pulse-echo data.
AGL814
Abstract
In this research, interpretations based on theoretical and physical
modeling data are given in the hope that they can be useful to the seismic
interpreter for discerning pitfalls in real data. Recognition of these
pitfalls could be an additional aid in the area of seismic interpretation.
As for the theoretical modeling, several interpretational pitfalls were
identified when a systematic analysis was carried out with respect to three
basic geological structures: basins, domes and partial reflectors. The
pitfalls identified include: apparent pinchouts and grabens which were
related to the profile line direction; extra reflection layers related
to the depth of the model and the areal size of the structure; cross-stratifications
related to the profile line direction and the areal size of the structure;
faults or extra events related to the processing flow; apparent ambient
noise related to structural dip change; etc. As for physical modeling,
both the lateral and vertical velocity variations in a 3-D environment
were evaluated and several pitfalls were identified. These pitfalls include:
a dim spot which was related to an overlying high-velocity lens; a bright
spot related to an overlying low velocity lens; an apparent velocity pullup
where actually a velocity pushdown should be observed; a low frequency
disturbed zone under the lens having a high velocity contrast; the thick
lens effect which distorted the appearance of the true structure; the wave
conversion within sharply curved 3-D structures which is yet an unsolved
problem of converted wave; ghost events which result from wavelet processing;
etc. Also in this research, three different velocity analysis algorithms
were developed and evaluated for areally gathered seismic data. The first
velocity algorithm was designed for data gathered by closely spaced conventional
CDP lines. An optimum stacking velocity along with the apparent dip were
obtained. The second velocity algorithm was designed for areal common-mid-point
data. A migration velocity along with strike and dip were obtained. The
third velocity algorithm was designed for multi-midpoint data such as would
be gathered in a crooked-line survey. An optimum stacking velocity as a
function of dip and strike and a final migration velocity were obtained.
These velocity algorithms offered a new processing flow which was applied
on the crooked-line data using the output parameters derived from the third
velocity algorithm. A satisfactory depth reconstruction was obtained and
it proved that the processing flow and velocity algorithm were correct.
AGL815
Abstract
The problem of determining the proper subsurface velocity model has
been an area of active concern since the inception of acoustic remote sensing
methods. The co-problem of determination of structural parameters, strike
and dip, has also generated a great deal of research. The relatively recent
development of computerized acoustic imaging techniques has placed an even
greater emphasis on the need for accurate models of the subsurface velocity
structure. Once one has recognized the complementary nature of the velocity
analysis and optimal migration problems, which will be demonstrated, a
number of physically obvious solutions become apparent. Through the use
of general techniques of image formation, two algorithms that yield both
optimum velocity for migration, and strike and dip parameters will be presented.
The formation and evaluation of acoustic images is of prime importance
to the methods employed. The particular images of interest are the source
image for field gathers and the common reflection point for common midpoint
gathers. Through the utilization of approximate forms of the Rayleigh-Sommerfeld
Diffraction formula, acoustic images for these types of recordings are
focused for a range of parameters (velocity, dip, and strike), the image
of highest intensity corresponding to the best bit set of trial parameters.
These procedures are undertaken in the space-temporal frequency domain.
Results from analyses on theoretical and physical model data are used to
demonstrate the effectiveness of the techniques. These are presented as
a series of parameter spectra for each of the search variables; velocity,
strike, and dip. The accuracy and reliability of the results, as expected,
were seen to depend on the range of offset and number of traces in the
aperture, the size of the aperture with respect to image depth, and the
grid density of the analysis parameters. The successful extraction of the
actual model parameters involved in the tests performed has demonstrated
the effectiveness of the methods employed.
AGL816
Abstract
Many of the existing seismic velocity estimation techniques use common
depth point (CDP) data, and are based on a horizontally layered media assumption.
These techniques have a degraded performance in areas of complex geology.
The primary causes of such a degradation are the effects of structure,
diffraction effects, and 3-D sideswipe energy that gets superimposed on
the CDP data. The geometrical effects on the velocity needed to stack CDP
data over a curved reflector were studied using a mathematical surface
of second degree in x and y. The velocities were found to vary as a function
of the profile direction, as a function of the depth of the reflector,
and as a function of the principal radii of curvature. To overcome the
geometrical effects, a 3-D stacking velocity for an arbitrary 3-D areal
coverage was defined based on the first of two-step approximation to 3-D
migration. The method of velocity analysis eliminates many of the difficulties
associated with a 3-D subsurface. This is so because it basically extracts
a true 2-D profile (without sideswipe) from 3-D multi-fold data and computes
the corresponding stacking velocity. The velocity estimate obtained is
still dependent on the dip and curvature of the reflector in the plane
of the profile, although the cross-dip and cross-curvature effects have
been eliminated. The analysis was demonstrated using physical model data
obtained in a 3-D tank experiment. To overcome the still persistent effects,
an algorithm based on a complete 3-D migration, without any approximations,
was developed. In the conventional use of migration for velocity analysis,
each input trace of N samples, is migrated for each of M constant velocity
functions requiring about N x M moveout calculations. The algorithm used
here, transforms the input traces into a logarithmic space and scans for
constructive interference at a number of depth locations along the proposed
axis of a well. From the formulation, a constant shift is calculated for
a particular trace, for each depth scanned. This reduces the number of
calculations to about N. The algorithm was tested on a number of computer
generated 3-D model data and also on a 3-D physical model data. It was
found that by having the data cover an area that includes the normal incidence
point of a reflector, a velocity estimate was obtained which was independent
of structure. The method also worked where random noise was superimposed
on the data with a signal-to-noise ratio of about 1:300. It also worked
when the transformed data was converted to sign bit only.
AGL817
Abstract
Three-dimensional (3D) migration applied to 3D seismic data provides
a reliable image of the subsurface and excludes misleading effects of sidewipe
events which occur when complicated 3D subsurface structures are explored
by conventional 2D methods. Several types of 3D migration methods have
been developed at the Allied Geophysical Laboratories at the University
of Houston. This thesis aims at investigating another way to migrate 3D
seismic data. Integration of the input data over diffraction surfaces is
done in two steps, first by integration at constant time and then over
a range of time. The values of the input data on the surfaces are obtained
from the input samples by trigonometric interpolation. For constant velocity
laterally the contribution of each input time slice to each output time
slice is obtained by convolution with a space invariant 2D operator constructed
from the interpolation weights. The convolution is implemented by multiplication
in the Fourier domain. Results for synthetic and scaled physical model
data are compared with results using well-establishing 3D migration programs.
It is concluded that a tapered weighting function over the diffraction
surface is necessary to avoid false events caused by a sharp truncation
of the integration. The Fortran program for a VAX 11/780 is included.
AGL818
Abstract
In the past, the Kirchhoff method has been used both in a forward mode
to generate synthetic seismic sections and in a backward mode to migrate
field data. This work addresses the practical implementation of either
mode through a unified treatment of Kirchhoff´s integral solution
of the acoustic wave equation. Laboratory- collected data have played an
important part in this analysis since solutions for practical forward modeling
and migration problems require extensive numerical calculations and these
must be verified. These data have confirmed several theoretical considerations
which show how problems in one mode of the Kirchhoff method are solved
with the other mode. For example, downward continuation of surface-recorded
wavefields for migration depends heavily on several features of the integration
aperture, such as aperture size and shape, sampling, and weight functions,
and these are readily related to forward modeling techniques. Migration
noises in the form of ghosts and halos are easily evaluated with forward
modeling, and hence, modeling results serve as a basis for their removal.
Theoretical considerations for forward modeling lead to a set of design
criteria for migration. On the other hand, a problem inherent in forward
modeling is the proper selection of Green´s functions, and these
are easily evaluated through migration techniques using image positions
of sources and receivers. Horizontal resolution in migration is related
to the Rayleigh criterion of optics, and at the same time it is related
to scattering of small thin right-circular cylinders in forward modeling.
Theoretical and physical model studies have been conducted for several
new field acquisition and migration display schemes with results that have
been confirmed with laboratory measurements.
AGL819
Abstract
One of the least investigated and most tedious and error-prone tasks
associated with computer graphics is producing a description of a complex
object in a form suitable for manipulation by a graphics system. The information
required for this description is generally of two types: (1) 3-D coordinates
of certain points, and (2) some organization of these points into sets
describing portions of the surface, usually as polygonal faces. This is
accomplished in two distinct stages, one for each of the two types of information,
or by alternating between the two. Several means of automating the first
stage, the collection of coordinates, have been suggested. This discussion
centers on the second stage, that of generating polygonal descriptions
of the surface. Several existing object description methods are described
and their benefits and limitations discussed. A very general algorithm,
assuming only knowledge of the point co-ordinates is presented. This algorithm
can be modified to use any one of a large class of cost functions in choosing
from among the many topologically legitimate surfaces possible. This algorithm
is analyzed for its worst case execution speed using standard techniques.
A discussion of how to evaluate the quality of the approximations generated
by this algorithm (or any other for the same purpose) is pursued, resulting
in a metric and two algorithms useful in computing it. One algorithm computes
the intersection (and symmetric difference) of two polyhedra. The other
algorithm computes the volume of an arbitrary polyhedron (or set of polyhedra).
Finally, several extensions to the main algorithm are presented. The theme
of these extensions is the incorporation of additional knowledge which
may be available.
AGL8110
Abstract
The forward modeling technique developed by Trorey in 1970 can be cast
in the form of a matrix equation that linearly relates subsurface reflection
coefficients to CDP (Common Depth Point) data. The proposed inversion attempts
to solve these matrix equations for the unknown reflection coefficients.
The complete inversion procedure can be described in five steps: I) divide
the subsurface into a rectangular grid and then guess an initial model
by assigning reflection coefficients at the grid points; II) calculate
the weighting of each grid element with respect to each CDP position; III)
forward construct the seismogram based on the initial model; IV) subtract
this calculated result from the corresponding observed data, resulting
in the so called error vector; V) solve a system of equations by minimizing
the error vector in a least-squares sense while subject to the constraints
that the distance of the result from the true model is fixed. The result
can be improved iteratively by repeating the procedure from III to V. In
the processing, a 2-D operation block is chosen which, depending on the
complexity of the subsurface, should have the proper size. This size must
be large enough to cover the necessary diffraction and small enough to
be computationally efficient. The whole seismic section is covered by these
blocks with some overlapping on the edges. The most time consuming step
in the processing is to calculate the inverse operator for the chosen operation
block. This inverse operator changes slowly in both vertical and horizontal
direction for a regular subsurface; thus, the processing time can be reduced
when a matrix factorization technique is used. The proposed inversion algorithm
has been tested with a set of synthetic traces, physical tank data, and
field data. Of particular note in this paper is that a forward construction
and backward reconstruction pair are explicitly presented.
AGL801
Abstract
The seismic response of several coal depositional environments are
examined by two sets of physical models. First, meandering-stream models
provide tools for channel location by seismic methods, and they also document
interpretational pitfalls. Undisturbed coal is discerned from channel eroded
coal by: (1) the presence of 2-D and 3-D foci; (2) velocity induced pull-up
or sag of the reflectors underlying the channels; and (3) amplitude analysis.
However, the 2-D and 3-D foci are absent when an interface is placed between
the channel walls and their respective centers of curvature. Also, if the
velocity of the channel-fill is higher than the coal´s, the velocity
pull-up displays a diffraction-like appearance, due to the channel´s
refractive properties. Second, progradational delta coal models emphasize
the effects of small, thin coal bodies upon the seismic response of an
underlying, thick coal seam. Velocity pull-up, strong diffraction events
and dim-spots from each overlying coal prevents mapping of the thick coal
seam. 2-D studies on transitional coal-to-sand contacts and vertically-thinning
beds highlight the subtle characteristics of certain coal depositional
environments, by demonstrating that not only does a thinning coal bed have
an amplitude tuning at (lambda)/4, but it also has a characteristic frequency
response. The interrelationship of amplitude and frequency provides both
an estimate of thickness and a clue as to the style of the coal´s
vertical contact. The 2-D studies are extended to 3-D, to provide an estimate
of total coal volume from reflection data. The thin-bed frequency and amplitude
behavior is the same for spatial discs which are a fraction of a Fresnel
disc. The measurable waveform for thin beds results from interference of
reflections from the top and base, while for small bodies, it results from
interference of the reflection and coherent edge diffraction. The tuned
waveform, for both cases, is 90 degrees out of phase with the input wavelet.
For coal bodies which are both thin and small, the amplitude still tunes
at the characteristic fraction of a wavelength; however, the wavelength
is defined by the spatially-altered frequency, not the input frequency.
For this case, the tuned waveform is 180 degrees out of phase with the
input wavelet.
AGL802
Abstract
A simple 2-D model for the acoustic impedance structure of the earth
is proposed to model and migrate seismic data using a hybrid Kirchhoff-Trorey
approach. The new technique is based upon the summation of fields from
linear diffraction sources over space and time to obtain the total acoustic
field (analogous to Kirchhoff integral theory). The time response of the
linear diffraction sources has been derived by Trorey (1970). Accurate
seismic responses of known acoustic impedance models of the earth can be
simulated using this new theory. The inverse procedure (or migration) while
conceptually simple to consider in the context of the 2-D earth model,
is not a stable algorithm due to numerical error propagation problems.
A discussion of the sources of these numerical errors is presented.
AGL803
Abstract
The sedimentary section in the southwestern abyssal Gulf of Mexico
(7 to 10 km thick) is divided into 8 major depositional sequences. The
sequence boundaries represent widespread unconformities or major changes
in regional depositional conditions. These depositional sequences provide
a framework for reconstructing the depositional history of the area. The
pre-middle Cretaceous sedimentary section consists of detrital clastic
sediments of varied provenance, deposited after the formation of the Gulf
(probably early Mesozoic). However, the post-middle Cretaceous sediments
were deposited in deep marine environments and essentially consists of
a combination of pelagic and hemipelagic deposits and turbidites derived
from the continental terraces to the west along eastern Mexico. The area
experienced several major transgressions and regressions as evidenced by
the presence of well-developed relict submarine channels and growth of
submarine fan complexes. The youngest depositional sequence (Pleistocene)
displays dune-like features with wavelength of 2-4 km and thickness of
10-50 m.
AGL791
Abstract
This thesis deals with the research work related to a consortium project
on 3-D Seismic Data Acquisition, Processing, and Interpretation using a
physical model. The research work encompassed three major areas. The first
was the study of the candidate materials for the model construction. A
number of materials were tested for their physical and ultrasonic characteristics.
The second area was the ultrasonic characteristics. The second areas was
the ultrasonic characterization of various avail-able transducers and the
plotting of their pulse-mode beam patterns. These transducers were used
as sources to generate sound signals and/or as receivers to collect the
returned signals from the model surface. The data so obtained could be
utilized, when processed, for the interpretation of the geological structure,
or for making a hologram of the geological structure. The third area was
the design of an ultrasonic receiver which would meet all or most of a
set of desired characteristics in order to obtain the seismic data from
the model. A waveguide type ultrasonic receiver was designed and constructed
to meet these objectives. The waveguide receiver was characterized and
its sensitivity was compared with other available receivers.
AGL792
Abstract
Wave-Vector Diversity is a new technique of imaging pioneered by Dr.
N.H. Farhat. This involves a Fourier Optics approach to imaging, where
the frequency sweep and the relative orientations of the sources and receivers
produce diversity in the wave vector. This is also a new analytical approach
to imaging. The super resolving features found in mammals such as bottle
nosed dolphins, whales and bats, have been the prime motivation in the
development of the theory. The theory which had been developed for a general
case with a continuous frequency sweep, has been extended in this thesis,
to a special case of ZSRO (zero-source-receiver-offset) imaging with a
broad band pulse. It has been shown that for the use of FFT (Fast Fourier
Transform) in reconstruction, the interpolation could be done in the temporal
frequency spectra of traces instead of spatial or spatial frequency domains.
The advantages of this type of interpolation have been discussed. Other
special features and limitations of this new technique of imaging are also
discussed towards the end of this thesis. Synthetic data analysis has been
done for the case of ZSRO imaging with WVD (Wave-Vector Diversity) and
the results are explained. Suggestions for future work are made.
AGL761
Abstract
The extraction of elastic parameters from seismic reflected data with
the state-of-the-art indicates little success. The specific method tried
was the inversion of the seismic reflection amplitude curve with respect
to offset angle to yield the elastic parameters on either side of a plane
reflection boundary. By numerically evaluating the partial derivatives
of the reflection coefficient equation with respect to the elastic parameters,
almost all the problems found could be explained. In fact, many of the
conclusions by earlier investigators of the reflection coefficient curve
such as Koefoed (1955) can also be easily explained by the partial derivatives.
The inversion of the reflection coefficient curve for P-waves, when the
acoustic impedance ratio is known, is not unique for incidence angles below
the critical. This is because the two Poisson´s ratios approximately
cancel each other´s effect on the reflection coefficient. However,
when reflection amplitudes above and below the critical angle are inverted,
then a unique solution of the problem is possible, but is highly sensitive
to error. Once again, the acoustic impedance ratio is known. For SH-waves,
the inversion of the reflection coefficient curve was unique, for the cases
studied. A SH-error analysis indicates the inversion is more stable when
the acoustic impedance ratio is known. Among the different propagation
factors affecting the amplitude curve, and consequently the inversion problem,
the most important factor is usually the geophone array.
AGL762
Abstract
In the stochastic deconvolution process, the assumption of a random
reflectivity function can be replaced by the NMO curve and a CDP gather
record. With this information, the seismic wavelet can be compressed. This
compression method operates in a manner opposite to the NMO correction
stretch. Shaping filters are interactively computed either in the time
domain or in the frequency domain which subsequently compress the seismic
wavelet. Based on the principles of the wavelet compression technique,
the seismic wavelet can be extracted without making any assumption about
the shape of the seismic wavelet. From an initial estimate of the seismic
wavelet, the method computes interactively new estimations in order to
minimize the energy error between the predicted seismic trace at various
offsets and the field traces at the same offsets. The NMO-curve provides
the information to predict the far traces from the near traces. Stability
problems limit the process to wide band source signatures.
Wavelet Extraction Parameters of Homomorphic Deconvolution
Abstract
Homomorphic extraction of the seismic wavelet has been reported in the literature where the assumption that the wavelet cepstrum
and reflectivity function cepstrum are separable by linear filtering has been made. This assumption however restricts the application of the technique to simple relectivity models. Thus it is desirable to design homomorphic wavelet extraction techniques that are not based on this assumption; this
has been done by using two statistical methods.
The first method uses the cepstrum of the seismic trace autocorrelation
to estimate the cepstrum of the minimum-delay wavelet equivalent. If the reflectivity function is minimum-delay then mixed-delay wavelets can also be estimated
.
The second method involves teh cepstral averaging of seismic trace windows. It is shown
that this procedure cancels the cepstrum of the reflectivity function and recovers the wavelet cepstrum. Both methods were tested with synthetic seismic traces.