3-D resistivity forward modeling and inversion using conjugate gradients
Name
Zhang-1995-3-D resistivity.pdf
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1.63 MB
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Adobe PDF
Checksum (MD5)
04c74bfe973d34b7de72a1392491b6cc
Author(s)
Zhang, Jie
Mackie, Randall L.
Madden, Theodore R.
Date Issued
September 1995
Journal
Geophysics
Publisher
Society of Exploration Geophysicists
Citation
Zhang, Jie, Randall L. Mackie, and Theodore R. Madden. “3-D Resistivity Forward Modeling and Inversion Using Conjugate Gradients.” GEOPHYSICS 60.5 (1995): 1313–1325. © 1995 Society of Exploration Geophysicists
Version
Final published version
Abstract
We have developed rapid 3-D dc resistivity forward modeling and inversion algorithms that use conjugate gradient relaxation techniques. In the forward network modeling calculation, an incomplete Cholesky decomposition for preconditioning and sparse matrix routines combine to produce a fast and efficient algorithm (approximately 2 minutes CPU time on a Sun SPARC‐station 2 for 50 × 50 × 20 blocks). The side and bottom boundary conditions are scaled impedance conditions that take into account the local current flow at the boundaries as a result of any configuration of current sources. For the inversion, conjugate gradient relaxation is used to solve the maximum likelihood inverse equations. Since conjugate gradient techniques only require the results of the sensitivity matrix [tilde under A] or its transpose [tilde under A][superscript T] multiplying a vector, we are able to bypass the actual computation of the sensitivity matrix and the inversion of [tilde under A][superscript T] [tilde under A], thus greatly decreasing the time needed to do 3-D inversions. We demonstrate 3-D resistivity tomographic imaging using pole‐pole resistivity data collected during an experiment for a leakage monitoring system near evaporation ponds at the Mojave Generating Station in Laughlin, Nevada.
MIT Department
Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1190/1.1443868
