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

Abstract

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.

Electrical conductivity of a locked fault: investigation of the Ganos segment of the North Anatolian Fault using three-dimensional magnetotellurics

“…Because 3D modeling schemes have progressed rapidly over the last two decades, the purpose of these analyses shifted to understanding the physical essence of data. The 3D modeling has a great advantage with respect to overcoming ambiguities that are caused by 2D modeling assumptions; it has been proven to be more effective and accurate, even for profile-based measurements (Ledo 2005;Siripunvaraporn et al 2005a;Patro and Egbert 2011;Siripunvaraporn 2012).…”

Application of evolutionary methods to 3D geoscience modelling

“…Note [15,14] for improvement. In contrast, most evolutionary approaches have a population size greater than one and a stochastic or hybrid improvement process [13,18,7].…”

“…Copyright 2012 ACM 978-1-4503-1177-9/12/07 ...$10.00. at depth, much of our geological knowledge is provisional and ambiguous [10,15]. Given this unavoidable uncertainty, there is a need to develop modelling techniques to help geologist explore the space of viable models.…”

“…Evolutionary search has been used in the derivation of simple 1D and 2D MT models [9,13,18,7] but, to date, there are no published applications to not 3D models. This omission is significant because 3D models not only provide much more detail than 2D models, they also reflect the complex threedimensional geometries of earth's subsurface structures [15]. The lack of evolutionary search applied to 3D models is, at least in part, due to the large size of 3D models which can consist of thousands to millions of real-valued parameters.…”

Integrating Electromagnetic Data with Other Geophysical Observations for Enhanced Imaging of the Earth: A Tutorial and Review

“…Given the importance of inversion not only in geophysics, a large number of different algorithms to achieve this task exist (Nocedal 2006). Good introductions to inverse methods in a geophysical context are given by Snieder and Trampert (1999), Tarantola (2004), Menke (2012), Mosegaard and Hansen (2016) and for the special cases of magnetotellurics (MT) and controlled-source electromagnetics (CSEM) in Avdeev (2005), Abubakar et al (2009), Siripunvaraporn (2012) and Rodi and Mackie (2012). Despite highly refined algorithms and intense research, the inversion of geophysical data is virtually always ill-posed, i.e.…”