  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.
