An EPIC Tikhonov Regularization: Application to Quasi‐Static Fault Slip Inversion. Issue 7 (28th June 2021) - Ortega‐Culaciati, F.; Simons, M.; Ruiz, J.; Rivera, L.; Díaz‐Salazar, N.
Abstract: 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 (Mw 9.0) Tohoku‐Oki, Japan, earthquake, obtaining robust slip estimates that are similar to those inferred using a unregularized fully Bayesian approach. Plain Language Summary: Inferring the distribution of relative motion across earthquake faults in Earth's subsurface using observations of motion at the surface is an essential component of improving our knowledge of the physics of earthquakes and tsunamis. However, surface observations only provide limited resolution and thus the estimation problem is non‐unique and may be unstable in the presence of noise. Therefore, prior information or regularization is commonly used to control the solutions. We analyze the influence that different regularization schemes have on inferred images of fault motion. In addition, we propose a novel Equal Posterior Information Condition (EPIC) ‐based Tikhonov regularization, that selects a spatially variable strength of regularization to obtain images with spatially uniform precision. In synthetic tests, this new approach shows an improvement of the quality, interpretability and stability of fault motion estimates in the presence of different noise realizations. We investigate the quality of the EPIC‐based regularization on simulated earthquake scenarios and demonstrate the methodology by inferring images of fault slip for the March 11, 2011, (Mw 9.0) great Tohoku‐Oki, Japan, earthquake. Key Points: Common approaches to spatial regularization are susceptible to unstable biases in estimates of subsurface fault slip We introduce a novel spatially variable regularization scheme called Equal Posterior Information Condition (EPIC) Tikhonov Use of EPIC Tikhonov results in robust estimates of fault slip, in terms of stability, bias, and ease of uncertainty analysis