Implementations and applications of the sparse Radon transform
department or school: Science, Faculty of
department or school: Earth, Ocean and Atmospheric Sciences, Department of
data provider: DSpace
degree campus: UBCV
creator: Trad, Daniel
issued: 2009-10-09T18:51:33Z
issued: 2001
related degree: Doctor of Philosophy - PhD
degree grantor: University of British Columbia
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 u…
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/13822
extent: 49287596 bytes
format: application/pdf
note: IMPLEMENTATIONS AND APPLICATIONS OF T H E SPARSE RADON TRANSFORM By Daniel Trad Geofisico, Universidad Nacional de San Juan, Argentina, 1994 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S Department of E A R T H A N D O C E A N S C I E N C E S We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F BRITISH C O L U M B I A September 2001 © Daniel Trad, 2001 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Earth and Ocean Sciences The University of British Columbia 6339 Stores Road Vancouver, Canada V 6 T 1Z4 Date: October a * 2.001 A b s t r a c t The Radon transform (RT) has many desirable properties which make it particularly use-ful 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 contri…
has type: Thesis/Dissertation
date issued: 2001-11
is shown at: 10.14288/1.0052777
language: eng
degree discipline: Oceanography
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
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.
scholar level: Graduate
type: Text
identifier URI: http://hdl.handle.net/2429/13822