Colloquium (DSAS) - Dr. Mariano Rodrigo

Speaker: Dr. Mariano Rodrigo (University of Wollongong, New South Wales, Australia)

The Omori law has been widely applied in practice for describing the occurrence rate decay of aftershock activity over time. This talk will consist of two parts. The first part of the talk will give an alternative to maximum likelihood estimation (MLE) by proposing an integration-based method (IBM) to estimate the parameters in the Omori law. IBM takes advantage of stable characteristics of integrated occurrence rates and facilitates the robust estimation of the parameters by deriving explicit analytical formulas, thus avoiding nonlinear numerical optimisation. The proposed method is applied to real aftershock data from Japan and is demonstrated to work effectively as MLE.

The second part of the talk is work in progress. A stochastic differential equation (SDE) extension of the Omori law is proposed to incorporate the inherent observed stochasticity. Using ideas from the Stratonovich calculus, the nonlinear Ito SDE will be shown to be analytically tractable. Numerical simulations will also be provided.

This is joint work with K. Goda, Department of Earth Sciences, Western University. The talk will assume only a basic knowledge of ordinary differential equations (and some familiarity with stochastic differential

equations).