1Producing Omori’s law from stochastic stress transfer and release

We present an alternative to the ETAS model. The continuous time two-node network stress release/transfer Markov model has one node (denoted by A) loaded by external tectonic forces at a constant rate, with `events ' (mainshocks) occurring at random instances with risk given by a function of the `stress level' at the node. Each event adds (or removes) a proportional 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 for aftershock sequences. 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). This fits very well to the modified Omori law, with a wide possible variation in the p-value. We illustrate the model by fitting it to aftershock data from the Valparaiso earthquake of March 3 1985, and showing how it can be used in place of conventional `stacking ’ procedures to determine regional p-values. 3Variation in Aftershock Decay The modified Omori aftershock formula is n(t) = K(c+t)-p where 0.9 < p < 1.8, differing from sequence to sequence. Stochastic seismicity models have to cater for this variation in p, e.g., the ETAS model (Ogata, 1988). We construct an alternative model which also allows for more general background sequence behaviour