Bayesian Assessment of the Maximum Possible Earthquake Magnitude m max

This work is focused on the Bayesian assessment of the regional maximum possible earthquake magnitude mmax. The problem in the application of current statistical procedures for mmax is that seismic event catalogues are often too short to provide a reliable assessment of mmax . The remedy is to incorporate any relevant information about mmax in the computation processes. The roots of such information could be in geophysics, geology, tectonics, rheological behaviour of deformation in lithospheric zones, the worldwide database of mmax, and the seismicity of similar regions. Regarding anthropogenic seismicity induced by large water reservoirs, mining or fracking, the relevant information is available in the observations deriving from explorations of neighbouring mines and fields. The second problem in the application of the current Bayesian formalism for m estimation is that one of the components of the posterior max distribution is the sample likelihood function for which the range of observations (earthquake magnitudes) depends on the unknown mmax. This dependence violates the regularity property. The resulting likelihood function, therefore, reaches its maximum at the maximum observed earthquake magnitude mmaxobs, and not at the required maximum possible magnitude mmax. As the sample likelihood function is a key component of the posterior distribution, the posterior estimate of m^max, is biased. Here, a brief discussion is presented on the currently used Bayesian procedure for mmax and several alternative approaches are suggested.