The magnitude threshold and missing and pseudo links in Markov chains

Fidencio Alejandro Nava, Quiriat Jearim Gutiérrez
2022 · doi:10.21203/rs.3.rs-2282011/v1
preprint OA: closed CC-BY-4.0
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Abstract

A crisp step function is not an adequate threshold for studies of Markovian occurrence of large earthquakes, because it can lead to missing or pseudo links in an observed sequence that should be a Markov chain. A more realistic threshold is a fuzzy one where there is a magnitude band, located between those magnitudes that are too small for the earthquakes to be part of a Markovian process and those who are certainly large enough for the earthquakes to be part of it, where earthquakes may or may not be part of the process. This fuzzy threshold is described by a membership function that gives the probability of an earthquake with a given magnitude belonging to the process. We propose a counting strategy to evaluate the empirical transition probabilities when considering a fuzzy magnitude threshold, and justify it through Monte Carlo simulations. We also propose a membership function with probabilities in the transition band proportional to the seismic moment, and apply it to data from a seismic study of the Japan area. By comparing the results of three Markovianity measures for the observed data with those of Monte Carlo simulations, we find that a fuzzy threshold going from zero probability for magnitudes M≤6.9 to probability one for M≥7.2is the best model for the study area.

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License: CC-BY-4.0