Spatial distribution of the b-value in Southern California based on Gauss process inference with a geologically defined prior

As a population parameter, reliable estimation of the b-value is intrinsically complicated, particularly when spatial variability is considered. We approach this issue by treating the spatial b-value distribution as a non-stationary Gauss process for the underlying earthquake-realizing Poisson process. For Gauss process inference the covariance—which describes here the spatial correlation of the b-value—must be specified a priori. We base the covariance on the local fault structure, i.e. the covariance is anisotropic: elongated along the dominant fault strike and shortened when normal to the fault trace. This adaptive feature captures the geological structure better than an isotropic covariance or similarly defined and commonly used running-window estimates of the b-value.We demonstrate the Bayesian inference of the Gauss process b-value estimation for southern California based on the SCEDC earthquake catalog and with the covariance calibrated with the USGS fault model.Our model provides a continuous b-value estimate which reflects the local fault structure to a very high degree. Therefore, we are able to associate the b-value with the local seismicity distribution and can link it to the major Californian faults and geothermal areas. This technique, in its general formulation, can be applied to other non-stationary seismicity parameters, e.g. Omori’s law.