A Branching Poisson-Markov Model of Earthquake Occurrences

The Markov process is re-examined as a possible model for aftershock occurrences. In this model, ε the state variable is assumed to be the accumulated strain energy. The transition in the energy state is related directly to the magnitude of the aftershock. The known empirical relations on the decay of aftershock sequences and frequency-magnitude law, are incorporated in determining suitable functions for the rate [λ(ε)] and transition probabilities [T(X|ε)] of the Markov process. A computer simulation of the process using a random number generator verified that the empirical relations were properly duplicated with these functions. To model a complete earthquake catalog, including the main events and aftershocks, two processes are combined by assuming that: (1) independent earthquakes occur as a stationary Poisson process, and (2) they trigger aftershock sequences by channelling a fixed portion of their energy into the Markov process. A synthetic earthquake-aftershock catalogue is generated by simulating the branching Poisson-Markov process and is found to be fairly realistic.