An EPIC Tikhonov Regularization: Application to Quasi-Static Fault Slip Inversion

Imaging subsurface fault slip from surface observations is essential to improving our understanding of the physics of earthquakes and tsunamis. As the estimation of subsurface fault slip is inherently ill-posed, common inversion methods usually require a regularization term to counteract instabilities. Such regularization introduces biases in inferred slip estimates. Here, we discuss the effects that prior information, implied by a given regularization scheme, can have on fault slip estimates. We propose a novel Equal Posterior Information Condition (EPIC)-based Tikhonov regularization that generalizes the concept of prior information. The EPIC determines variances of prior information based on a chosen form of the structure of the posterior covariance matrix. In the context of subduction zone earthquakes, use of the EPIC counterbalances the spatial heterogeneity of observational constraints on fault slip, improving stability, quality and interpretability of fault slip estimates. We investigate the efficiency of the EPIC in the context of various synthetic fault slip distributions. We also demonstrate the methodology by inferring co-seismic slip from geodetic data for the 2011 (M-w 9.0) Tohoku-Oki, Japan, earthquake, obtaining robust slip estimates that are similar to those inferred using a unregularized fully Bayesian approach.