Three-dimensional Inversion for Resistivity Method Based on Multiplicative Regularization

doi:10.19657/j.geoscience.1000-8527.2022.074

Abstract

Abstract:

To reduce the multiplicity of geophysical inversion solution, additive objective functions are usually used, i.e., the data term and regularization term. Inversion based on additive objective function has the problem of optimizing the regularization factor, which usually requires much inversion calculations. This study systematically analyzed and implemented the 3D resistivity inversion method, based on multiplicative objective function (i.e., multiplication of the data term and regularization term). The problem of optimizing regularization factor is absent in the inversion of multiplicative objective function. We used the unstructured finite element method for resolving the 3D forward problem, and the L-BFGS (Limited-memory Broyden-Flecher-Goldfarb-Shanno) method for 3D inversion. The feasibility and effectiveness of our approach is verified by using the synthetic data of the theoretical model. The results show that the inversion method (based on multiplicative objective function) can reliably recover the resistivity value, shape and position of anomalies.

Key words: resistivity method, regularization, multiplicative objective function, 3D inversion

CLC Number:

P631

XIE Haijun, TAN Handong, MA Fengqun. Three-dimensional Inversion for Resistivity Method Based on Multiplicative Regularization[J]. Geoscience, 2023, 37(01): 67-73.

Figures/Tables 9

Fig.1 Three-dimensional model of resistivity method

Fig.2 Schematic diagram of unstructured grid

Fig.3 Vector interaction relationship of 2D unstructured mesh model

Fig.4 Horizontal double prismatic model and surface-surface observation system

Fig.5 RMS misfit and model roughness inversion curves

Fig.6 Inversion results of the horizontal double prismatic model

Fig.7 Vertical double prismatic model and surface-surface, surface-borehole, borehole-surface and borehole-borehole observation system

Fig.8 RMS misfit and model roughness inversion curves

Fig.9 Inversion results of the vertical double prismatic model

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