Joint inversion with petrophysical constraints using indicator functions and the extended alternating direction method of multipliers

Wang, Ke1; Yang, Dikun2,3

2023-02-01

10.1190/GEO2022-0167.1

GEOPHYSICS   Impact Factor & Quartile

0016-8033

1942-2156

Joint inversions often need to construct an objective function with multiple complex constraining terms, which usually in-crease the computational cost, take a long time to converge, and often are nondifferentiable. We have developed a joint in-version framework that implements petrophysical constraints by indicator functions and solves the optimization problem using the alternating direction method of multipliers (ADMM). An indicator function can describe arbitrary ranges and relation-ships of multiple physical property parameters by a feasible set. Objective functions involving multiple nondifferentiable terms are numerically not easy to solve, so we adopt an extended alternating direction method of multipliers (eADMM) that sep-arates the terms as independent subproblems and select the most straightforward and efficient solving technique for each of them. With the eADMM, every objective function term can generate its own model, and the models are forced to converge through equality constraints. Such a mechanism brings further efficiency from parallelization and the flexibility of allowing the final in-version model to not strictly obey the model constraints because of uncertainties in the data and petrophysical information. Our approach is tested on two synthetic examples of joint inversion of gravity and magnetic data. The first example contains two blocks having the same magnetic susceptibility but different densities. Our synthetic inversions verify that the combination of the indicator function and eADMM method effectively recov-ers exact boundaries and values. The second example uses the data synthesized from a realistic kimberlite exploration project. Our joint inversion can distinguish two kimberlite facies, image their position, and even delineate the boundary between the two facies with much improved accuracy. Based on the same model, the robustness of our method also has been tested with inexact and incorrect petrophysical information. The simplicity, flexibil-ity, effectiveness, and efficiency make our approach a good can-didate for a wide range of applications in joint inversion.

SCI

English

First ; Corresponding

Guangdong Provincial Key Labo- ratory of Geophysical High -resolution Imaging Technology[2022B1212010002] ; National Natural Science Foundation of China[42274102]

Geochemistry & Geophysics

Geochemistry & Geophysics

WOS:000944260800003

SOC EXPLORATION GEOPHYSICISTS - SEG

GEOSCIENCES

Web of Science

1.Southern Univ Sci & Technol, Dept Earth & Space Sci, Shenzhen, Peoples R China
2.Southern Univ Sci & Technol, Guangdong Prov Key Lab Geophys Highresolut Imaging, Shenzhen, Peoples R China
3.Southern Univ Sci & Technol, Dept Earth & Space Sci, Shenzhen, Peoples R China

Wang, Ke,Yang, Dikun. Joint inversion with petrophysical constraints using indicator functions and the extended alternating direction method of multipliers[J]. GEOPHYSICS,2023,88(1).

Wang, Ke,&Yang, Dikun.(2023).Joint inversion with petrophysical constraints using indicator functions and the extended alternating direction method of multipliers.GEOPHYSICS,88(1).

Wang, Ke,et al."Joint inversion with petrophysical constraints using indicator functions and the extended alternating direction method of multipliers".GEOPHYSICS 88.1(2023).