Stochastic interpretation of magnetotelluric data, comparison of methods

Abstract

Global optimization and stochastic approaches to the interpretation of measured data have recently gained particular
attraction as tools for directed search for and/or verification of characteristic structural details and quantitative
parameters of the deep structure, which is a task often arising when interpreting geoelectrical induction
data in seismoactive and volcanic areas. We present a comparison of three common global optimization and stochastic
approaches to the solution of a magnetotelluric inverse problem for thick layer structures, specifically the
controlled random search algorithm, the stochastic sampling by the Monte Carlo method with Markov chains
and its newly suggested approximate, but largely accelerated, version, the neighbourhood algorithm. We test the
algorithms on a notoriously difficult synthetic 5-layer structure with two conductors situated at different depths,
as well as on the experimental COPROD1 data set standardly used to benchmark 1D magnetotelluric inversion
codes. The controlled random search algorithm is a fast and reliable global minimization procedure if a relatively
small number of parameters is involved and a search for a single target minimum is the main objective of the
inversion. By repeated runs with different starting test model pools, a sufficiently exhaustive mapping of the parameter
space can be accomplished. The Markov chain Monte Carlo gives the most complete information for the
parameter estimation and their uncertainty assessment by providing samples from the posterior probability distribution
of the model parameters conditioned on the experimental data. Though computationally intensive, this
method shows good performance provided the model parameters are sufficiently decorrelated. For layered models
with mixed resistivities and layer thicknesses, where strong correlations occur and even different model classes
may conform to the target function, the method often converges poorly and even very long chains do not guarantee
fair distributions of the model parameters according to their probability densities. The neighbourhood resampling
procedure attempts to accelerate the Monte Carlo simulation by approximating the computationally expensive
true target function by a simpler, piecewise constant interpolant on a Voronoi mesh constructed over a
set of pre-generated models. The method performs relatively fast but seems to suggest systematically larger uncertainties
for the model parameters. The results of the stochastic simulations are compared with the standard
linearized solutions both for thick layer models and for smooth Occam solutions.