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UBC Theses and Dissertations
Application of wavelet transforms to seismic data processing and inversion Li, Xin-Gong
Abstract
The goal of this thesis is to use wavelet transforms as tools to analyze simultaneously the time (or location) and frequency (or scale) variant characteristics of seismic data and then to apply these information to two important geophysical problems: noise filtering and traveltime inversion. In the noise filtering problem, the discrete non-orthogonal wavelet transform is used to analyze the time-variant characteristics of signal and noise. This information can be used to filter noise in the transformed domain. This approach is applied to ground roll attenuation for field seismic data according to the localized characteristics. Geophysical inverse problems are, in general, non-linear, underdetermined and ill-posed. An initial model and some prior information describing the model is needed to find the model perturbation that minimizes an objective function. Traditionally, the perturbation is assumed to be an independent Gaussian or a correlated but stationary process, an assumption which is not physically correct according to the analyses of well logs. Indeed, analysis of logs described in this thesis suggests that log data can be decomposed into (a) a fractal process, usually non-stationary, with wavelet coefficients which follow a power law, and (b) some non-fractal structures including a large scale trend and some spiky details. The inverse problem can be solved using the wavelet transform in two steps. First, I solve an overdetermined problem to invert the large scale trend, then, I solve for a model with fractal constraints. Another important application of the wavelet transform in inverse problems is to reduce the effects of the noise in the input data. Since the noise effect varies with scale, the regularization can be done accordingly. Wavelet transform constrained inversions are tested using 1-D and 2-D synthetic examples.
Item Metadata
Title |
Application of wavelet transforms to seismic data processing and inversion
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1997
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Description |
The goal of this thesis is to use wavelet transforms as tools to analyze simultaneously
the time (or location) and frequency (or scale) variant characteristics of seismic data and
then to apply these information to two important geophysical problems: noise filtering
and traveltime inversion.
In the noise filtering problem, the discrete non-orthogonal wavelet transform is used
to analyze the time-variant characteristics of signal and noise. This information can be
used to filter noise in the transformed domain. This approach is applied to ground roll
attenuation for field seismic data according to the localized characteristics.
Geophysical inverse problems are, in general, non-linear, underdetermined and ill-posed.
An initial model and some prior information describing the model is needed to
find the model perturbation that minimizes an objective function. Traditionally, the
perturbation is assumed to be an independent Gaussian or a correlated but stationary
process, an assumption which is not physically correct according to the analyses of well
logs. Indeed, analysis of logs described in this thesis suggests that log data can be
decomposed into (a) a fractal process, usually non-stationary, with wavelet coefficients
which follow a power law, and (b) some non-fractal structures including a large scale
trend and some spiky details. The inverse problem can be solved using the wavelet
transform in two steps. First, I solve an overdetermined problem to invert the large scale
trend, then, I solve for a model with fractal constraints.
Another important application of the wavelet transform in inverse problems is to
reduce the effects of the noise in the input data. Since the noise effect varies with scale,
the regularization can be done accordingly. Wavelet transform constrained inversions are
tested using 1-D and 2-D synthetic examples.
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Extent |
18242652 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-04-02
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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 |
10.14288/1.0088134
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1997-11
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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.