Estimation of depth‐dependent fault slip from measured surface deformation with application to the 1906 San Francisco Earthquake

We estimate the depth distribution of slip in the 1906 San Francisco earthquake by applying new inversion methods to triangulation data collected near Point Arena, California. Modeling crustal deformation from antiplane slip in a half‐space, we define three regularizing functionals to produce minimum‐norm inverse problems. These functionals measure components of the coseismic change in elastic strain energy, stress magnitude, and stress variability and are all quadratic in slip. Orthogonality conditions define finite‐dimensional representations of slip estimates. Coefficients of basis functions in these representations are estimated by damped least squares with damping parameter and faulting depth chosen by cross validation. The best resulting estimates exhibit right lateral slip to depths of 15 to 20 km with about 6 m of surface slip. This is consistent with directly observed offsets of cultural landmarks at the surface and indicates deeper faulting than has been previously inferred for the 1906 earthquake.