A reversible-jump Markov chain Monte Carlo algorithm for 1D inversion of magnetotelluric data

Eric Mandolesi,Xenia Ogaya,Joan Campanyà,Nicola Piana Agostinetti

doi:10.1016/j.cageo.2018.01.011

Abstract

This paper presents a new computer code developed to solve the 1D magnetotelluric (MT) inverse problem using a Bayesian trans-dimensional Markov chain Monte Carlo algorithm. MT data are sensitive to the depth-distribution of rock electric conductivity (or its reciprocal, resistivity). The solution provided is a probability distribution - the so-called posterior probability distribution (PPD) for the conductivity at depth, together with the PPD of the interface depths. The PPD is sampled via a reversible-jump Markov Chain Monte Carlo (rjMcMC) algorithm, using a modified Metropolis-Hastings (MH) rule to accept or discard candidate models along the chains. As the optimal parameterization for the inversion process is generally unknown a trans-dimensional approach is used to allow the dataset itself to indicate the most probable number of parameters needed to sample the PPD. The algorithm is tested against two simulated datasets and a set of MT data acquired in the Clare Basin (County Clare, Ireland). For the simulated datasets the correct number of conductive layers at depth and the associated electrical conductivity values is retrieved, together with reasonable estimates of the uncertainties on the investigated parameters. Results from the inversion of field measurements are compared with results obtained using a deterministic method and with well-log data from a nearby borehole. The PPD is in good agreement with the well-log data, showing as a main structure a high conductive layer associated with the Clare Shale formation.In this study, we demonstrate that our new code go beyond algorithms developend using a linear inversion scheme, as it can be used: (1) to by-pass the subjective choices in the 1D parameterizations, i.e. the number of horizontal layers in the 1D parameterization, and (2) to estimate realistic uncertainties on the retrieved parameters. The algorithm is implemented using a simple MPI approach, where independent chains run on isolated CPU, to take full advantage of parallel computer architectures. In case of a large number of data, a master/slave appoach can be used, where the master CPU samples the parameter space and the slave CPUs compute forward solutions.

Highlights

Magnetotellurics is an electromagnetic (EM) passive method that infers the electrical conductivity of the subsurface structures by measuring orthogonal components of electric and magnetic fields on the Earth surface and relies on accurate data and a robust inversion algorithm
The algorithm presented in this study is composed of two main codes: a reversible-jump Markov Chain Monte Carlo (rjMcMC) sampler for extracting model according to the posterior probability distribution (PPD), and a MT 1D forward solver, for computing synthetic MT responses
We tested our routines against two synthetic simulations, using synthetic models previously adopted in literature, and field data recorded in Western Ireland

Summary

Introduction

Magnetotellurics is an electromagnetic (EM) passive method that infers the electrical conductivity of the subsurface structures by measuring orthogonal components of electric and magnetic fields on the Earth surface and relies on accurate data and a robust inversion algorithm. Most of the recent MT inversion works explore threedimensional (3D) models, obtained by partitioning the subsurface in large regions of constant electrical conductivity and solving the inverse problem via a linearization of the forward MT equation [e.g. The one-dimensional (1D) MT inverse problem has been solved following a broad range of different approaches, both linearized and stochastic [e.g. Linearized approaches provides weak solutions, whilst popular stochastic approaches (e.g. Genetic Algorithms) rely on appropriate parameters (i.e. number of layers in partition, model space dimension, number of iterations) chosen ad-hoc, often not justified by the data.

Methods

Results

Conclusion