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Inversion of three-dimensional direct current resistivity data Li, Yaoguo
Abstract
A direct current (d.c.) resistivity experiment investigates subsurface geo-electrical structures by measuring the electric field set up by introducing current into the earth. Information about geo-electrical structures is extracted by inverting the observed data to generate an image of the conductivity or to construct a conductivity model. The goal of this thesis is to develop efficient inversion techniques for the interpretation of three-dimensional (3d) d.c. resistivity data. The study assumes data consisting of pole-pole potentials measured over a regular grid on the surface for many current locations. The Born approximation is employed to linearize the inverse problem. The source of the electric field measured in the d.c. resistivity is the accumulated electric charges. Different aspects of the charge accumulation are reviewed, enlarged with new insights and presented in a unified notation. This provides the basis for understanding the fundamentals of d.c. resistivity experiments. Two algorithms are developed to image simple 2d conductivities. The first constructs a structural image by combining the charge density images obtained by inverting multiple sets of common current potentials. The second constructs a conductivity image directly. Processing and displaying the apparent conductivity, and constructing equivalent sources from secondary potentials are studied as the means of imaging. Assuming a multiplicative perturbation to a uniform half-space, the potential anomaly of pole-pole arrays is expressed as a depth integral of the logarithmic perturbation convolved with a kernel function in the horizontal directions. Applying the Fourier transform decomposes the data equation for a 3d problem into a set of id equations. A rapid approximate 3d inversion is developed based upon this decomposition by solving a sequence of id inversions in the wavenumber domain. The approximate 3d inversion is used to construct iterative inversion algorithms using the AIM (Approximate Inverse Mapping) formalism. The approximate inversion and an exact forward mapping are used to update the model successively so that the final result reproduces the observed data. The AIM inversion is applied to analyse a set of field data.
Item Metadata
Title |
Inversion of three-dimensional direct current resistivity data
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1992
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Description |
A direct current (d.c.) resistivity experiment investigates subsurface geo-electrical structures
by measuring the electric field set up by introducing current into the earth. Information about
geo-electrical structures is extracted by inverting the observed data to generate an image of the
conductivity or to construct a conductivity model. The goal of this thesis is to develop efficient
inversion techniques for the interpretation of three-dimensional (3d) d.c. resistivity data. The
study assumes data consisting of pole-pole potentials measured over a regular grid on the surface
for many current locations. The Born approximation is employed to linearize the inverse problem.
The source of the electric field measured in the d.c. resistivity is the accumulated electric
charges. Different aspects of the charge accumulation are reviewed, enlarged with new insights
and presented in a unified notation. This provides the basis for understanding the fundamentals
of d.c. resistivity experiments. Two algorithms are developed to image simple 2d conductivities.
The first constructs a structural image by combining the charge density images obtained by
inverting multiple sets of common current potentials. The second constructs a conductivity
image directly. Processing and displaying the apparent conductivity, and constructing equivalent
sources from secondary potentials are studied as the means of imaging. Assuming a multiplicative
perturbation to a uniform half-space, the potential anomaly of pole-pole arrays is expressed as a
depth integral of the logarithmic perturbation convolved with a kernel function in the horizontal
directions. Applying the Fourier transform decomposes the data equation for a 3d problem into a
set of id equations. A rapid approximate 3d inversion is developed based upon this decomposition
by solving a sequence of id inversions in the wavenumber domain. The approximate 3d inversion
is used to construct iterative inversion algorithms using the AIM (Approximate Inverse Mapping)
formalism. The approximate inversion and an exact forward mapping are used to update the
model successively so that the final result reproduces the observed data. The AIM inversion is
applied to analyse a set of field data.
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Extent |
7178648 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2008-12-18
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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 |
10.14288/1.0085637
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1992-11
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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.