3-D Resistivity Inversion by the Least-Square QR Factorization Method Under Improved Smoothness Constraint

We make a deep study of 3‐D resistivity inversion, and propose a practical algorithm of 3‐D inversion. Using the finite difference method to solve the 3‐D forward problem. We have properly improved the elements of roughness matrix in order to form the roughness matrix in different cases, setting up...

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Bibliographic Details
Published in:Chinese journal of geophysics 2005-03, Vol.48 (2), p.486-492
Main Authors: WAN, Xin‐Lin, XI, Dao‐Ying, GAO, Er‐Gen, SHEN, Zhao‐Wu
Format: Article
Language:English
Subjects:
3-D inversion
LSQR algorithm
Partial derivative matrix
Smoothness constraint
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Summary:We make a deep study of 3‐D resistivity inversion, and propose a practical algorithm of 3‐D inversion. Using the finite difference method to solve the 3‐D forward problem. We have properly improved the elements of roughness matrix in order to form the roughness matrix in different cases, setting up the inversion equation under the condition that the total roughness of the model is minimum. We use the least‐squares QR factorization (LSQR) algorithm, which is fast and stable, to solve inversion equations. The LSQR algorithm only requires the result of the derivative matrix and its transpose multiplying vectors. Therefore we avoid direct and complicated computations of the derivative matrix. This approach reduces the need for computer memory, and speeds the inversion calculation. Two different calculation examples show that this approach is very efficacious for solving large scale 3‐D resistivity inversion.
ISSN:0898-9591
2326-0440
DOI:10.1002/cjg2.678