Spatio-Temporal Complex Markov Chain (SCMC) Model Using Directed Graphs: Earthquake Sequencing

Abstract

We construct a directed graph to represent a Markov chain of global earthquake sequences and analyze the statistics of transition probabilities linked to earthquake zones. We use a simplified plate boundary template for earthquake zonation. We generalize this Markov chain of earthquake sequences by including the recurrent events in space and time for each event in the record-breaking sense. The record-breaking recurrent events provide the basis for redefining the weights for the state-to-state transition probabilities. We use a distance-dependent look-up array for each zone to assign the distance-dependent weights for the recurring events. We present here details of the method and the preliminary results on the structure and properties of the directed graphs corresponding to a Markov chain model without and with the inclusion of record-breaking events. The underlying directed graph provides the framework for earthquake sequencing. We examine the properties of the directed graph without and with the inclusion of recurrences. We consider the present method easily expandable for forecasting work as catalogues are routinely updated with seismic events and, also, widely applicable to a study of both the regional and global seismicity. We demonstrate the applicability of the directed graph approach to forecasting using some of the properties of graphs that represent the Markov chain.