Uncertainty quantification for regularized inversion of electromagnetic geophysical data—Part I: motivation and theory

SUMMARY We present a method for computing meaningful uncertainty quantification (UQ) regularized inversion of electromagnetic (EM) geophysical data that combines the machineries and Bayesian sampling with ‘randomize-then-optimize’ (RTO) approach. The RTO procedure is to perturb canonical objective function in such way minimizers perturbations closely follow posterior distribution. In practice, this means we can compute UQ by running standard inversion/optimization algorithms parallel for-loop only minor modification existing codes. Our work split into two parts. Part I, review extend methodology estimate regularization penalty weight on fly, not unlike Occam inversion. call resulting algorithm RTO-TKO explain it samples from biased distribution which numerically demonstrate be nearby return accepting small bias, advantage over asymptotically unbiased samplers significantly accelerates convergence leverages computational parallelism, makes highly scalable 2-D 3-D EM problems. II, showcase versatility efficiency apply variety inversions 1-D 2-D, carefully comparing results established estimates using other methods. further investigate scalability 3-D, discuss influence prior assumptions model parametrizations UQ.