Three-Dimensional Magnetotelluric Inversion: An Introductory Guide for Developers and Users

In the last few decades, the demand for three-dimensional (3-D) inversions for magnetotelluric data has significantly driven the progress of 3-D codes. There are currently a lot of new 3-D inversion and forward modeling codes. Some, such as the WSINV3DMT code of the author, are available to the academic community. The goal of this paper is to summarize all the important issues involving 3-D inversions. It aims to show how inversion works and how to use it properly. In this paper, I start by describing several good reasons for doing 3-D inversion instead of 2-D inversion. The main algorithms for 3-D inversion are reviewed along with some comparisons of their advantages and disadvantages. These algorithms are the classical Occam’s inversion, the data space Occam’s inversion, the Gauss–Newton method, the Gauss–Newton with the conjugate gradient method, the non-linear conjugate gradient method, and the quasi-Newton method. Other variants are based on these main algorithms. Forward modeling, sensitivity calculations, model covariance and its parallel implementation are all necessary components of inversions and are reviewed here. Rules of thumb for performing 3-D inversion are proposed for the benefit of the 3-D inversion novice. Problems regarding 3-D inversions are discussed along with suggested topics for future research for the developers of the next decades.     

Two-dimensional direct current (DC) resistivity inversion: Data space Occam's approach

A data space Occam's inversion algorithm for 2D DC resistivity data has been developed to seek the smoothest structure subject to an appropriate fit to the data. For traditional model space Gauss–Newton (GN) type inversion, the system of equations has the dimensions of M × M, where M is the number of model parameter, resulting in extensive computing time and memory storage. However, the system of equations can be mathematically transformed to the data space, resulting in a dramatic drop in its dimensions to N × N, where N is the number of data parameter, which is usually less than M. The transformation has helped to significantly reduce both computing time and memory storage. Numerical experiments with synthetic data and field data show that applying the data space technique to 2D DC resistivity data for various configurations is robust and accurate when compared with the results from the model space method and the commercial software RES2DINV.