TY - JOUR

T1 - Improving the use of the randomized singular value decomposition for the inversion of gravity and magnetic data

AU - Vatankhah, Saeed

AU - Liu, Shuang

AU - Renaut, Rosemary Anne

AU - Hu, Xiangyun

AU - Baniamerian, Jamaledin

N1 - Funding Information:
The authors would like to thank M. Pilkington for providing data from the Wuskwatim Lake area. We also are very appreciative of the suggestions made by the associate editor Y. Li, reviewer V. C. F. Barbosa, and two anonymous reviewers. Their comments assisted significantly with the presentation of the contributions of the paper. This study was financially supported by the National Key R&D Program of China (grant nos. 2016YFC0600109 and 2017YFC0602405) and the China Postdoctoral Science Foundation (grant no. 2019M660191). R. Renaut acknowledges the support of NSF grant DMS 1913136: Approximate Singular Value Expansions and Solutions of Ill-Posed Problems.
Publisher Copyright:
© 2020 Society of Exploration Geophysicists.

PY - 2020/9/1

Y1 - 2020/9/1

N2 - The focusing inversion of gravity and magnetic potential-field data using the randomized singular value decomposition (RSVD) method is considered. This approach facilitates tackling the computational challenge that arises in the solution of the inversion problem that uses the standard and accurate approximation of the integral equation kernel. We have developed a comprehensive comparison of the developed methodology for the inversion of magnetic and gravity data. The results verify that there is an important difference between the application of the methodology for gravity and magnetic inversion problems. Specifically, RSVD is dependent on the generation of a rank q approximation to the underlying model matrix, and the results demonstrate that q needs to be larger, for equivalent problem sizes, for the magnetic problem compared to the gravity problem. Without a relatively large q, the dominant singular values of the magnetic model matrix are not well approximated. We determine that this is due to the spectral properties of the matrix. The comparison also shows us how the use of the power iteration embedded within the randomized algorithm improves the quality of the resulting dominant subspace approximation, especially in magnetic inversion, yielding acceptable approximations for smaller choices of q. Further, we evaluate how the differences in spectral properties of the magnetic and gravity input matrices also affect the values that are automatically estimated for the regularization parameter. The algorithm is applied and verified for the inversion of magnetic data obtained over a portion of the Wuskwatim Lake region in Manitoba, Canada.

AB - The focusing inversion of gravity and magnetic potential-field data using the randomized singular value decomposition (RSVD) method is considered. This approach facilitates tackling the computational challenge that arises in the solution of the inversion problem that uses the standard and accurate approximation of the integral equation kernel. We have developed a comprehensive comparison of the developed methodology for the inversion of magnetic and gravity data. The results verify that there is an important difference between the application of the methodology for gravity and magnetic inversion problems. Specifically, RSVD is dependent on the generation of a rank q approximation to the underlying model matrix, and the results demonstrate that q needs to be larger, for equivalent problem sizes, for the magnetic problem compared to the gravity problem. Without a relatively large q, the dominant singular values of the magnetic model matrix are not well approximated. We determine that this is due to the spectral properties of the matrix. The comparison also shows us how the use of the power iteration embedded within the randomized algorithm improves the quality of the resulting dominant subspace approximation, especially in magnetic inversion, yielding acceptable approximations for smaller choices of q. Further, we evaluate how the differences in spectral properties of the magnetic and gravity input matrices also affect the values that are automatically estimated for the regularization parameter. The algorithm is applied and verified for the inversion of magnetic data obtained over a portion of the Wuskwatim Lake region in Manitoba, Canada.

KW - 3D

KW - algorithm

KW - gravity

KW - inversion

KW - magnetics

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U2 - 10.1190/geo2019-0603.1

DO - 10.1190/geo2019-0603.1

M3 - Article

AN - SCOPUS:85094904804

VL - 85

SP - G93-G107

JO - Geophysics

JF - Geophysics

SN - 0016-8033

IS - 5

ER -