Turn your regularized inversion code into a Bayesian sampler: Efficient uncertainty quantification for resistivity models estimated from electromagnetic geophysical data

Quantifying uncertainty on inverted resistivity models is becoming more and more crucial to making robust interpretations based on these models. Workhorse methods for inverting EM geophysical data rely on regularization, yet up until now no satisfactory method has existed to estimate uncertainty for regularized models. Here we present a method for uncertainty quantification on regularized models called RTO-TKOa stochastic optimization algorithm that uses the randomize-then-optimize strategy to turn gradient-based inversion codes into Bayesian samplers. In this context, the data misfit and model regularization terms in the objective function are associated with a likelihood and prior distribution, respectively, defining a Bayesian posterior from which samples can be drawn by repeatedly minimizing a perturbed objective function. RTO-TKO has many attractive qualities: it requires minimal tuning, uses well understood gradient-based inversion codes, allows the data to select the regularization strength parameter, and is independent of the choice of parameter grid. Most of all, however, it is highly efficient computationallyit requires relatively few samples to obtain a solid estimate of model uncertainty and is fully parallel, enabling it to take full advantage of high performance computing. We will briefly discuss the theory behind RTO-TKO, demonstrate its desirable features on 1D DC resistivity, MT, and CSEM inversions, then showcase its efficiency on 2D MT inversions.