A Stochastic Two-node Stress Transfer Model Reproducing Omori's Law

Abstract

— We present an alternative to the epidemic type aftershock sequence (ETAS) model of Ogata (1988). The continuous time two-node network stress release/transfer Markov model is able to reproduce the (modified) Omori law for aftershock frequencies. One node (denoted by A) is loaded by external tectonic forces at a constant rate, with `events' (main shocks) occurring at random instances with risk given by a function of the `stress level' at the node. Each event is a random (negative) jump of the stress level, and adds (or removes) a random amount of stress to the second node (B), which experiences `events' in a similar way, but with another risk function (of the stress level at that node only). When that risk function satisfies certain simple conditions (it may, in particular, be exponential), the frequency of jumps (aftershocks) at node B, in the absence of any new events at node A, follows Omori's law \((\prpto (c + t)^{-1})\) for aftershock squenc es. When node B is allowed tectonic input, which may be negative, i.e., aseismic slip, the frequency of events takes on a decay form that parallels the constitutive law derived by Dieterich (1994), which fits very well to the modified Omori law. We illustrate the model by fitting it to aftershock data from California post-1973, and from the Valparaiso earthquake of March 3 1985.