Richter b-value maps from local moments of seismicity

Abstract: We develop a technique to estimate spatially varying seismicity patterns. It is based on a Gaussian approximation of the underlying Poisson Process. A link function is used to estimate local moments of the seismicity from observed catalogues. These are modeled by a nonstationary Gaussian field. We construct a prior based on the local distribution of seismic faults. This allows us to incorporate geological information into the Bayesian inversion of the observed seismicity. In this paper we limit ourselve to the $b$-value field for which we compute the posterior expectations as well as the uncertainties. The technique however may be applied to other seismically relevant parameters like Omori $c$ and $p$-values.