Discrete cosine transform for parameter space reduction in Bayesian ERT inversion

Markov Chain Monte Carlo (MCMC) algorithms are employed for accurate uncertainty assessments in non-linear geophysical inverse problems. However, one of their main drawbacks is the considerable number of sampled models needed to attain stable posterior estimations, especially in high-dimensional parameter spaces. We use the Discrete Cosine Transform (DCT) to reparametrize a Bayesian Electrical Resistivity Tomography (ERT) inversion solved through an MCMC sampling. In this framework, the unknown parameters become the series of coefficients associated with the retained DCT base functions. We employ the Differential Evolution Markov Chain (DEMC) algorithm that guarantees a more accurate and rapid sampling of the posterior density than more standard MCMC algorithms (such as the random walk Metropolis). To draw essential conclusions about the reliability of the implemented algorithm, we focus on inversions of a synthetic subsurface block model. We assess the benefits provided by the DCT compression of the model space by comparing the outcomes of the implemented inversion approach with those provided by a DEMC algorithm running in the full, un-reduced model space. Although preliminary, our results are promising and prove that the implemented inversion approach guarantees rapid convergence toward the stationary regime, thereby preserving an accurate sampling of the posterior model.