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Three dimensional magnetotelluric inversion using L BFGS

Lu Libin, Wang Kunpeng, Tan Handong, Li Qingkun

Acta Geophysica

2020

Vol. 68, no. 4

1049--1066

The gradient-based optimization methods are preferable for the large-scale three-dimensional (3D) magnetotelluric (MT) inverse problem. Compared with the popular nonlinear conjugate gradient (NLCG) method, however, the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) method is less adopted. This paper aims to implement a L-BFGS-based inversion algorithm for the 3D MT problem. And we develop our code on top of the ModEM package, which is highly extensible and popular among the MT community. To accelerate the convergence speed, the preconditioning technique by the afne linear transformation of the original model parameters is used. Two modifcations of the conventional L-BFGS algorithm are also made to get a comparable convergence rate with the NLCG method. The impacts of the preconditioner parameters, the regularization parameters, the starting model, etc., on the inversion are evaluated by synthetic examples for both L-BFGS and NLCG methods. And the real MT Kayabe dataset is also inverted by the inversion algorithms. The synthetic tests show that through our L-BFGS inversion algorithm the similar resistivity models can be obtained with that from the NLCG method. For the real data inversion, the L-BFGS method performs more efciently and reasonable results could be obtained by less iterations of the inversion process than the NLCG method. Thus, we suggest the common usage of the L-BFGS method for the 3D MT inverse problem.

Nonmonotone line searches for optimization algorithms

Sachs E. W., Sachs S. M.

Control and Cybernetics

2011

Vol. 40, no 4

1059-1075

In this paper we develop a general convergence theory for nonmonotone line searches in optimization algorithms. The advantage of this theory is that it is applicable to various step size rules that have been published in the past decades. This gives more insight into the structure of these step size rules and points to several relaxations of the hypotheses. Furthermore, it can be used in the framework of discretized infinite-dimensional optimization problems like optimal control problems and ties the discretized problems to the original problem formulation.