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Aperture compensated radon and fourier transforms Sacchi, Mauricio Dino
Abstract
In seismic data analysis, recorded data often are transformed to various domains to discriminate against coherent and incoherent noise. For instance, by mapping a shot record from time-space domain to frequency-wavenumber domain, coherent linear noise can be attenuated. Similarly, by mapping a common-midpoint gather from time-space to time-velocity domain (velocity stacks) multiples are separated from primaries based on moveout discrimination. In these procedures the correct identification of seismic events with similar moveout can be severely affected by the aperture of the array and the discrete sampling of the wavefield. Economic and/or logistic reasons usually dictate the cable length and spatial sampling of the seismic experiment. This thesis examines how the resolution (the ability to distinguish close events) of slant stack and parabolic stack operators deteriorates under limited aperture. An algorithm is developed to increase the resolution of the aforementioned operators. This procedure constructs an operator that collapses each seismic signal in the transform domain, thus diminishing truncation artifacts. The overall procedure is equivalent to the simulation of a longer array of receivers. Slant stacks and the parabolic stacks are linear operations used to map the seismic data into another domain, the transform domain (r — p or r — q). In this thesis an inverse problem is posed. This is accomplished by considering the data as the result of a linear operation onto the transform domain. This approach permits one to incorporate prior information into the problem which is utilized to attenuate truncation artifacts. The prior information is incorporated into the inverse problem by means of the Bayesian formalism. The observational errors and the prior information are combined through Bayes' rule using the likelihood function and a long tailed distribution, respectively. The posteriori probability is then used to induce the objective function of the problem. Finally, minimizing the objective function leads to the solution of the inverse problem. The advantage of incorporating a long tailed distribution to model the transform domain is that the solution is constrained to be sparse which is a desired feature for highly resolved models. The method is also used to design an artifacts-reduced 2-D discrete Fourier transform. A by-product of the method is a high resolution periodogram. This periodogram coincides with the periodogram that would have been computed with a longer array of receivers if the data consist of a limited superposition of linear events.
Item Metadata
Title |
Aperture compensated radon and fourier transforms
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1996
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Description |
In seismic data analysis, recorded data often are transformed to various domains to
discriminate against coherent and incoherent noise. For instance, by mapping a shot
record from time-space domain to frequency-wavenumber domain, coherent linear noise
can be attenuated. Similarly, by mapping a common-midpoint gather from time-space to
time-velocity domain (velocity stacks) multiples are separated from primaries based on
moveout discrimination. In these procedures the correct identification of seismic events
with similar moveout can be severely affected by the aperture of the array and the discrete
sampling of the wavefield.
Economic and/or logistic reasons usually dictate the cable length and spatial sampling
of the seismic experiment. This thesis examines how the resolution (the ability to distinguish
close events) of slant stack and parabolic stack operators deteriorates under limited
aperture. An algorithm is developed to increase the resolution of the aforementioned operators.
This procedure constructs an operator that collapses each seismic signal in
the transform domain, thus diminishing truncation artifacts. The overall procedure is
equivalent to the simulation of a longer array of receivers.
Slant stacks and the parabolic stacks are linear operations used to map the seismic
data into another domain, the transform domain (r — p or r — q). In this thesis an inverse
problem is posed. This is accomplished by considering the data as the result of a linear
operation onto the transform domain. This approach permits one to incorporate prior
information into the problem which is utilized to attenuate truncation artifacts.
The prior information is incorporated into the inverse problem by means of the
Bayesian formalism. The observational errors and the prior information are combined through Bayes' rule using the likelihood function and a long tailed distribution, respectively.
The posteriori probability is then used to induce the objective function of the
problem. Finally, minimizing the objective function leads to the solution of the inverse
problem. The advantage of incorporating a long tailed distribution to model the transform
domain is that the solution is constrained to be sparse which is a desired feature
for highly resolved models.
The method is also used to design an artifacts-reduced 2-D discrete Fourier transform.
A by-product of the method is a high resolution periodogram. This periodogram coincides
with the periodogram that would have been computed with a longer array of receivers if
the data consist of a limited superposition of linear events.
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Extent |
19268727 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-02-18
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0052951
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1996-05
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.