A Note on the Regularization of Linear Inversion for Estimating Quasi-Static Fault Slip Distributions

Abstract:

During all the stages of the seismic cycle, earthquakes, aseismic slip, or even the onset of locking on the fault, may produce geodetically measurable deformation at the surface of the Earth. For instance, we can use space geodetic observations to measure crustal deformation associated to aseismic behavior of faults, which is essential to increase our level of understanding of the kinematics and physical processes controlling earthquake and tsunami occurrence. Estimating subsurface processes, such as distribution of fault slip, from surface observations at the Earth’s crust is an inherently ill-posed problem. Therefore, the adopted inverse methodology to obtain such estimates plays a key role in this learning process. There are two general end member approaches to estimate the distribution of slip on a fault that deals with the inherent instability of the inverse problem: An unregularized, computationally expensive, fully Bayesian approach and a much more expedient but biased optimization approach using some form of regularized least squares. We focus our efforts in the latter approach. On the regularized inversion, the chosen form of regularization will introduce a priori information on fault slip estimates that needs to be well understood to be able to reach rigorous interpretation of the inversion results. We discuss the effects that the a priori information implied by commonly used regularization schemes has on slip estimates of fault behavior. Also we discuss the importance of using a regularization scheme that accounts for the spatial variability of the constraints provided by the observations (typically onland), in order to improve the stability and resolution of the inferred slip distributions of fault behavior. We present study cases in the Japan Trench and Central Andean subduction megathrusts. We also discuss the impact that off-shore geodetic monitoring has on our ability to provide insights on the mechanical behavior of the shallower portions of subduction megathrusts.