Directed graph representation of a Markov chain model to study global earthquake sequencing leads to a time series of state-to-state transition probabilities that includes the spatio-temporally linked recurrent events in the record-breaking sense.A state refers to a configuration comprised of zones with either the occurrence or non-occurrence of an earthquake in each zone in a pre-determined time interval.Since the time series is derived from non-linear and non-stationary earthquake sequencing, we use known analysis methods roneverhart.com to glean new information.
We apply decomposition procedures such as ensemble empirical mode decomposition (EEMD) to study the state-to-state fluctuations in each of the intrinsic mode functions.We subject the intrinsic mode functions, derived from the time series using the EEMD, to a detailed analysis to draw information content of the time series.Also, we investigate the influence of random noise on the data-driven state-to-state transition probabilities.
We consider a second aspect of earthquake sequencing that is closely tied to its time-correlative behaviour.Here, we extend the Fano factor and Allan factor analysis to the time series of state-to-state transition frequencies of a Markov chain.Our results support not only the usefulness of the intrinsic mode functions in understanding the time series but also the 3 piece horse wall art presence of power-law behaviour exemplified by the Fano factor and the Allan factor.