The Modeling of Earthquake Occurrence

Abstract

Recent developments in nonlinear science give impetus to an attack on the problems of developing physical models for seismicity. The irreversibility of earthquake events is simple enough testimony to support the proposal that the problems of earthquake occurrence are imbedded in the broader range of problems of nonlinear science. The nonlinearity is more profound than this: the deformation of the earth in the time and space between earthquake rupture events is a complex process, with strong accelerated deformation prior to ultimate fracture; the earthquake events themselves are rapidly running changes of state taking place on a much shorter time scale than that of the interludes; and the occurrence of each earthquake influences the times and locations of the others. The simulation targets of modeling endeavors are the rich phenomenology of statistical and case history seismicity which I have described in the preceding chapter; in most cases, we have information about the events themselves but relatively little information about the deformation in the intervals between the earthquakes. This is unfortunate for the purposes of mathematics, since it would seem, at least superficially, that one should focus on the state of stress as a continuous variable, rather than on the episodes of rapidly running changes of state that are the earthquake events themselves. A start on a theoretical study of the state of deformation as a stochastic process has been made by Knopoff^[1] and Lomnitz-Adler[^2], but few concrete results in this direction are available to date.