Abstract
Abstract. 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 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 presence of power-law behaviour exemplified by the Fano factor and the Allan factor.
Highlights
We examine the criteria used for the selection of the added noise and the ensemble number for the ensemble empirical mode decomposition (EEMD)
We describe the EEMD procedure used and the analysis of the results that accrue from this procedure
In our adaptation of the sum of edge weights for the stateto-state transition frequencies as a new representation of a point-process embedded in the modified Markov chain here, the arguments of Thurner et al (1997), Telesca (2005) and Telesca et al (2001, 2009, 2011) would apply. This means that the Fano factor (FF) of the modified Markov chain sequence would follow a power law with the power-law exponent, α, satisfying 0 < α < 1. Extending this to FFsstf and AFsstf, as is shown in Fig. 6c and d, we find that the power law exponent calculated, corresponding to the least-squares fit of the data is greater than zero (0.27 and 0.30 respectively)
Summary
Earthquake sequencing has been the subject of detailed research (Nava et al, 2005; Ünal and Çelebioğlu, 2011; Ünal et al, 2014; Telesca et al, 2001, 2009, 2011; Telesca and Lovallo, 2008; Cavers and Vasudevan, 2013, 2015; Vasudevan and Cavers, 2012, 2013) both in the regional and global sense in recent years. Nava et al (2005) have introduced the Markov chain model to study the earthquake sequencing in a seismogenically active region where the region is partitioned into zones. As described by Cavers and Vasudevan (2015), a Markov chain with the inclusion of spatiotemporal complexity of recurring events is derived by summing the weights of the recurrence arcs corresponding to occurrences from state i to state j in consecutive time intervals. Vasudevan: Earthquake sequencing: analysis from the Markov chain to time series without the additional information such as the catalogue and the record-breaking statistics of recurrences. Since it is obtained from the non-linear, non-stationary global earthquake sequence, we consider it non-linear and nonstationary as well, and can be subjected to analysis methods. It is not shown here, the approach applies to earthquake catalogues from localized seismogenic zones
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