A Bayesian Method for Incorporating Self‐Similarity Into Earthquake Slip Inversions

Distributions of coseismic slip help illuminate many properties of earthquakes, including fault geometry, stress changes, frictional properties, and potential future hazard. Slip inversions take observations and calculate slip at depth, but there are a number of commonly adopted assumptions such as minimizing the second spatial derivative of slip (the Laplacian) that have little physical basis and potentially bias the result. In light of growing evidence that fault slip shows fractal properties, we suggest that this information should be incorporated into slip inversions as a form of regularization, instead of Laplacian smoothing. We have developed a Bayesian approach to efficiently solve for slip incorporating von Karman regularization. In synthetic tests, our approach retrieves fractal slip better than Laplacian regularization, as expected, but even performs comparably, or better, when the input slip is not fractal. We apply this to the 2014 Mw 6.0 Napa Valley earthquake on a two‐segment fault using Interferometric Synthetic Aperture Radar (InSAR) and Global Positioning System (GPS) data. We find the von Karman and Laplacian inversions give similar slip magnitude but in different locations, and the von Karman solution has much tighter confidence bounds on slip than the Laplacian solution. Differences in earthquake slip due to the regularization technique could have important implications for the interpretation and modeling of stress changes on the causative and neighboring faults. We therefore recommend that choice of regularization method should be routinely made explicit and justified and that von Karman regularization is a better default than Laplacian.