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Implementations and applications of the sparse Radon transform Trad, Daniel
Abstract
The Radon transform (RT) has many desirable properties which make it particularly useful for multiple removal and interpolation of seismic reflections. However many practical difficulties arise as a consequence of poor sampling and limited aperture in the offset dimension. Furthermore the ever increasing volumes of seismic data make computing time a key issue in any practical implementation. The standard implementations of the Radon transform used in seismic processing fulfill very well the requirement of a fast transform but do not allow proper handling of problems associated with sampling and aperture. Many of these difficulties can be partially solved by using inverse theory to compute the transform subject to a sparseness constraint. The main thrust and contribution of this thesis lies in the exploration of the sparseness constraint and the design and implementation of the RT. Although this technique reduces sampling and aperture problems, it also considerably increases the computation time. Some of the possible solutions to decrease computation time discussed in this thesis are conjugate gradient methods, irregularly sampled model space and efficient operations with sparse matrices. Real data often have very complicated structure that makes sparseness criteria difficult to implement. Noise, non hyperbolic events and amplitude variation with offset conspire against sparseness. Therefore, the success of this method depends on the applied algorithms and on a delicate balance between sparseness and fit of data. Several real data examples of multiple removal and interpolation show the success of the proposed algorithms to achieve this balance. Another aspect of this thesis is the design of new applications for the Radon transform in seismic processing. Many new applications can be developed by designing new types of Radon operators. Some new applications implemented in this thesis are elliptical and hybrid linear-hyperbolic Radon transforms that should prove to be useful for slant-stack processing and ground roll removal respectively. As a final topic, this thesis presents an application of the RT to the enhancement of a prestack time migration method. Multiple attenuation, artifact filtering and automatic velocity model corrections result from the merging of the R T with equivalent offset migration.
Item Metadata
Title |
Implementations and applications of the sparse Radon transform
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2001
|
Description |
The Radon transform (RT) has many desirable properties which make it particularly useful
for multiple removal and interpolation of seismic reflections. However many practical
difficulties arise as a consequence of poor sampling and limited aperture in the offset
dimension. Furthermore the ever increasing volumes of seismic data make computing
time a key issue in any practical implementation.
The standard implementations of the Radon transform used in seismic processing
fulfill very well the requirement of a fast transform but do not allow proper handling
of problems associated with sampling and aperture. Many of these difficulties can be
partially solved by using inverse theory to compute the transform subject to a sparseness
constraint.
The main thrust and contribution of this thesis lies in the exploration of the sparseness
constraint and the design and implementation of the RT. Although this technique reduces
sampling and aperture problems, it also considerably increases the computation time.
Some of the possible solutions to decrease computation time discussed in this thesis are
conjugate gradient methods, irregularly sampled model space and efficient operations
with sparse matrices.
Real data often have very complicated structure that makes sparseness criteria difficult
to implement. Noise, non hyperbolic events and amplitude variation with offset
conspire against sparseness. Therefore, the success of this method depends on the applied
algorithms and on a delicate balance between sparseness and fit of data. Several real
data examples of multiple removal and interpolation show the success of the proposed
algorithms to achieve this balance.
Another aspect of this thesis is the design of new applications for the Radon transform
in seismic processing. Many new applications can be developed by designing new types
of Radon operators. Some new applications implemented in this thesis are elliptical and
hybrid linear-hyperbolic Radon transforms that should prove to be useful for slant-stack
processing and ground roll removal respectively.
As a final topic, this thesis presents an application of the RT to the enhancement
of a prestack time migration method. Multiple attenuation, artifact filtering and automatic
velocity model corrections result from the merging of the R T with equivalent offset
migration.
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Extent |
49287596 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-10-09
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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 |
10.14288/1.0052777
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2001-11
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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.