Seismic activity analysis of five major earthquake source segments in the Sumatra megathrust zone

The Sumatra megathrust zone has five major earthquake sources, namely the Aceh-Andaman, Nias-Simeulue, Mentawai-Siberut, Mentawai-Pagai, and Enggano segments. This paper provides seismic activity analysis in these five segments via an unobserved process study of tectonic plate movements, which is conducted in two cases: each of the five segments independently (Case 1), and a pair of two adjacent segments (Case 2). To do this, two specific types of Hidden Markov Models (HMMs), i.e., Poisson-HMMs and Copula-HMMs, dealing with unobserved process issues, are applied. In practice, the data used is the annual frequency of mainshock earthquakes with a magnitude of >4.6 that occurred from 1971 to 2018. This data is obtained by working out the declustering process and estimating the magnitude of completeness from a particular earthquake catalogue. Due to the incompleteness of the data sets, the parameters of the two HMMs are estimated using the Expectation-Maximization algorithm. Results show that for Case 1, the model that fits the data for each of the five segments is the 3-state Poisson-HMM. The three states, in this instance, stand for the rates of seismic activity that correspond to the dynamic level of tectonic plate movements. Furthermore, in Case 2, the selected model for the Aceh-Andaman with Nias-Simeulue is the 2-state Gumbel Copula-HMM. Meanwhile, for the three groups remaining, namely Nias-Simeulue with Mentawai-Siberut, Mentawai-Siberut with Mentawai-Pagai, and Mentawai-Pagai with Enggano, the appropriate models are Gaussian, Gumbel, and Frank Copulas, respectively. In this case, the number of states represents the seismic activity association of two adjacent segments that corresponds to the association level of two adjacent tectonic plate dynamics.