The Adaptive Regularized Inversion Algorithm (ARIA) for Magnetotelluric Data

Abstract

In this paper, a new inversion method, Adaptive Regularized Inversion Algorithm (ARIA), is presented to overcome the difficulty of the determination for the regularized factor. Firstly, a new data variance disposing method, data variance normalization method, is put forward. This method uses a new way to calculate the influence matrix of data variance in inversion. Thus, the data variance only influences data fitting, and has no influence on the weight between data object function and the model constraint object function. So the influencing factors of the determination of the regularized factor are reduced. Secondly, the definition of the roughness kernel matrix is presented in the course of constructing model constraint object function, and a concise equation of it is derived. Thus the construction of the model object function becomes very simple and direct. Thirdly, two adaptive methods of the regularized factor are put forward based on the relations of data object function, the model constraint object function, and the regularized factor. Finally, ARIA is used to solve an magnetotelluric (MT) one‐dimensional inversion problem by the constraint of the flattest model. Several examples are illustrated to exemplify the effect of ARIA.

Evidence of crustal ‘channel flow’ in the eastern margin of Tibetan Plateau from MT measurements

“…Several methods, including NLCG, are used to inverse the data [41][42][43][44] . Because the profile is perpendicular to the structure strike, the curves of apparent resistivity and phase are rotated to the orientation of the profile and direction perpendicular to the profile, respectively (i.e.…”

Lp-Norm Inversion of Gravity Data Using Adaptive Differential Evolution

“…In which, d obs max and d obs min denote the maximum and minimum data among the observed data, respectively. In Equation ( 21), the normalization process is carried out, and the purpose is to weaken the influence of the observation data error on the misfit function [45]. Φ m (m) is regularization term of Lp (1 ≤ p < ∞), and expressed as:…”

A MPI + OpenMP + CUDA Hybrid Parallel Scheme for MT Occam Inversion

“…The major causes are: 1) the jacobian matrix of the explicit calculation consuming too much CPU time; 2) too dense finite element grid subdivision will lead to huge coefficient matrix, make the amount of calculation increased rapidly; 3) using adaptive algorithm to calculate the Lagrange multiplier will lead to the increase of the iteration, making the overall increase of the calculation. After the algorithm been put forward, many geophysical workers home and abroad have targeted made some improvements to it, obtained certain achievements on its time performance [7][8][9][10].…”