A non-linear geodetic data inversion using ABIC for slip distribution on a fault with an unknown dip angle

We have developed a method of geodetic data inversion for slip distribution on a fault with an unknown dip angle. A common strategy for obtaining slip distribution in previous studies is to first determine the fault geometry by minimizing the square misfit under the assumption of a uniform slip on a rectangular fault, and then apply the usual linear inversion technique to estimate a slip distribution on the determined fault. It is not guaranteed, however, that the fault determined under the assumption of a uniform slip gives the best fault geometry for a spatially variable slip distribution. The inverse problem is non-linear for cases with unknown fault geometries, but the non-linearity of the problems is actually weak, when we can assume the fault surface to be a flat plane. In particular, when a clear trace of coseismic faults is observed on the Earth's surface, only the dip angle is an unknown parameter to determine the fault geometry. Then, we regarded the dip angle as an hyperparameter that prescribed the structure of parametric models, and obtained the best estimate of the dip angle using Akaike's Bayesian Information Criterion (ABIC). With the best estimate of the dip angle, we can obtain the slip distribution on the fault based on the maximum-likelihood principle. We applied the method to the InSAR data of the 1995 Dinar, Turkey earthquake and obtained a much lower dip angle than the previous analyses.