Stochastic interpretation of magnetotelluric data, comparison of methods

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.