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

Abstract

SUMMAR YThis 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, ®tting 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 identi®ability 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 dif®culty in identifying an AMR episode with only limited data.

Probabilistic Analysis of Tsunami Hazards*

“…Other parameters that are typically taken to be constant are fault plane geometry, shear modulus, and a constant scaling relationship between seismic moment and the length and width dimensions of rupture. The Monte Carlo simulation is based on selecting a random sample of earthquake magnitudes from the modified G-R distribution of Kagan and Jackson (2000) (see also Vere-Jones et al, 2001). For a lower-magnitude cutoff (M t ) that represents catalog completeness and an upper-magnitude corner (M c ) that fixes the tail of the distribution, the cumulative distribution is given by…”

Estimation of the upper cutoff parameter for the tapered Pareto distribution

“…In addition, di erent parametric forms for the tapered upper moment of the Pareto distribution have been proposed ( 18], 25], 26]). The tapered Pareto distribution of Vere-Jones et al 30] is preferred largely because of its simplicity and paucity of free parameters; available data from catalogs of seismic moments do not seem to warrant more than two or three degrees of freedom (see Table 2 of 26]).…”

Description of earthquake aftershock sequences using prototype point patterns

“…Several different measures of earthquake magnitude exist, and several variants of the G-R law have been proposed, e.g. Kagan (1994), Main (1996), Jackson and Kagan (1999), Kagan (1999), Utsu (1999), Vere-Jones et al (2001), Kagan and Schoenberg (2001).…”