3-D resistivity forward modeling and inversion using conjugate gradients

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 effic...

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Main Authors: Zhang, Jie, Mackie, Randall L., Madden, Theodore R.
Other Authors: Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences
Format: Article
Language:en_US
Published: Society of Exploration Geophysicists 2017
Online Access:http://hdl.handle.net/1721.1/108498
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author Zhang, Jie
Mackie, Randall L.
Madden, Theodore R.
author2 Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences
author_facet Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences
Zhang, Jie
Mackie, Randall L.
Madden, Theodore R.
author_sort Zhang, Jie
collection MIT
description 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.
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spelling mit-1721.1/1084982022-10-02T03:36:04Z 3-D resistivity forward modeling and inversion using conjugate gradients Zhang, Jie Mackie, Randall L. Madden, Theodore R. Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Zhang, Jie Mackie, Randall L. Madden, Theodore R. 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. United States. Environmental Protection Agency (grant #CR-821516) 2017-04-28T17:45:04Z 2017-04-28T17:45:04Z 1995-09 1994-12 Article http://purl.org/eprint/type/JournalArticle 0016-8033 1942-2156 http://hdl.handle.net/1721.1/108498 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 en_US http://dx.doi.org/10.1190/1.1443868 Geophysics 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. application/pdf Society of Exploration Geophysicists Society of Exploration Geophysicists
spellingShingle Zhang, Jie
Mackie, Randall L.
Madden, Theodore R.
3-D resistivity forward modeling and inversion using conjugate gradients
title 3-D resistivity forward modeling and inversion using conjugate gradients
title_full 3-D resistivity forward modeling and inversion using conjugate gradients
title_fullStr 3-D resistivity forward modeling and inversion using conjugate gradients
title_full_unstemmed 3-D resistivity forward modeling and inversion using conjugate gradients
title_short 3-D resistivity forward modeling and inversion using conjugate gradients
title_sort 3 d resistivity forward modeling and inversion using conjugate gradients
url http://hdl.handle.net/1721.1/108498
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