Geodetic data inversion using a Bayesian information criterion for spatial distribution of fault slip

SUMMARY We developed a new inversion method to reconstruct static images of seismic sources from geodetic data, using Akaike’s Bayesian Information Criterion (ABIC). Coseismic surface displacements are generally related with a slip distribution on a fault surface by linear integral equations. Parametric expansion of the fault slip distribution by a finite number of known basis functions yields a set of observation equations expressed in a simple vector form. Incorporating prior constraints on the smoothness of slip distribution with the observation equations, we construct a Bayesian model with unknown hyperparameters. The optimal values of the hyperparameters, which control the structure of the Bayesian model, are objectively determined from observed data by using ABIC. Once the values of hyperparameters are determined, we can use the maximum likelihood method to find the optimal distribution of fault slip. We examined the validity of this method through a numerical experiment using theoretical data with random noise. We analysed geodetic data associated with the 1946 Nankaido earthquake (Ms = 8.2) by using this method. The result shows that the fault slip distribution of this earthquake has two main peaks of 4 and 6 m, located off Kii Peninsula and Muroto Promontory. These two high-slip areas are clearly separated by a low-slip zone extending along Kii Strait. Such a slip distribution corresponds with the fact that the rupture process of this earthquake in the western part is notably different from that in the eastern part.