Nonlinear, 2D uncertainty estimation in Magnetotelluric inversion using trans-dimensional Gaussian processes

Bayesian inversion of Magnetotelluric (MT) data produces crucial uncertainty information on inferred subsurface resistivity. Due to their high computational cost, however, Bayesian inverse methods have largely been restricted to 1D resistivity models. We successfully demonstrate a nonlinear 2D, trans-dimensional Bayesian inversion of MT data. We render this problem tractable from a sampling standpoint by using a stochastic interpolation algorithm known as a Gaussian process (GP) to achieve a parsimonious parameterisation of the model vis-a-vis the dense parameter grids used in numerical forward modelling codes. The Gaussian process links a transdimensional, parallel tempered Markov chain Monte Carlo sampler, which explores the parsimonious model space, to MARE2DEM, an adaptive finite element forward solver. MARE2DEM computes the model response using a dense parameter mesh with resistivity assigned via the Gaussian process model. We demonstrate the new trans-dimensional Gaussian process sampler by inverting both synthetic and field magnetotelluric data for 2D models of electrical resistivity, with the field data example converging within 10 days on 148 cores, a non-negligible but tractable computational cost. For the field data inversion, our algorithm achieves a parameter reduction of over 32x. Resistivity probability distributions computed from the ensemble of models produced by the inversion yield credible intervals and interquartile plots that quantitatively show the nonlinear 2D uncertainty in model structure. This uncertainty can then be propagated to other physical properties that impact resistivity including bulk composition, porosity and pore-fluid content, all of which can shed important light on prospective mineralisation as well as geodynamics.