Remarks on the accelerated moment release model: problems of model formulation, simulation and estimation

This report summarizes a variety of issues concerning the development of st atistical versions of the so-called 'accelerated moment release model' (AMR model). Until such statistical versions are developed, it is not possible to develop satisfactory procedures for simulating, fitting or forecasting t he model. We propose a hierarchy of simulation models, in which the increas e in moment is apportioned in varying degrees between an increase in the av erage size of events and an increase in their frequency. To control the siz e distribution, we propose a Version of the Gutenberg-Richter power law wit h exponential fall-off, as suggested in recent papers by Kagan. The mean si ze is controlled by the location of the fall-off, which in turn may be rela ted to the closeness to criticality of the underlying seismic region. Other points touched on concern the logical structure of the model, in particula r the identifiability of the parameter assumed to control the size of the m ain shock, and appropriate procedures to use for simulation and estimation. An appendix summarizes properties of the Kagan distribution. The simulatio ns highlight the difficulty in identifying an AMR episode with only limited data.