Open AccessRemarks on the accelerated moment release model: problems of model formulation, simulation and estimation
Author(s) -
VereJones David,
Robinson Russell,
Yang Wenzheng
Publication year - 2001
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1046/j.1365-246x.2001.01348.x
Subject(s) - moment (physics) , identifiability , hierarchy , computer science , closeness , self organized criticality , statistical model , econometrics , mathematics , statistical physics , criticality , statistics , mathematical analysis , law , physics , classical mechanics , political science , nuclear physics
SUMMARY This report summarizes a variety of issues concerning the development of statistical 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 the model. We propose a hierarchy of simulation models, in which the increase in moment is apportioned in varying degrees between an increase in the average size of events and an increase in their frequency. To control the size distribution, we propose a version of the Gutenberg–Richter power law with exponential fall‐off, as suggested in recent papers by Kagan. The mean size is controlled by the location of the fall‐off, which in turn may be related to the closeness to criticality of the underlying seismic region. Other points touched on concern the logical structure of the model, in particular the identifiability of the parameter assumed to control the size of the main shock, and appropriate procedures to use for simulation and estimation. An appendix summarizes properties of the Kagan distribution. The simulations highlight the difficulty in identifying an AMR episode with only limited data.