Brief Communication: Earthquake sequencing: analysis of time series constructed from the Markov chain model

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 recordbreaking 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 nonstationary 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.

Time clustering of wave storms in the Mediterranean Sea

“…When the underlying process is characterized by clustering, the AF of a specific sequence of events is larger than 1 and shows a power-law behaviour at the timescales that exhibit departure from a Poisson distribution. The simplicity of the AF analysis made it popular in the study of time sequences of a number of physical processes such as earthquakes (Telesca et al, 2002;Cavers and Vasudevan, 2015), lightning (Telesca et al, 2008), rainfall (Telesca et al, 2007;García-Marín et al, 2008) or fires (Telesca and Pereira, 2010). However, the AF can also be larger than 1 for non-homogeneous Poisson processes, as shown in Serinaldi and Kilsby (2013).…”

Ekonometri̇ Öğrenci̇leri̇ni̇n Sayisal Derslerdeki̇ Akademi̇k Performansi: Markov Modeli̇ İle Bi̇r Hesaplama

“…Yazarlar, dört tanesi belirli geçiş dönemlerine ait (1995-1998, 1998-2001, 2001-2004, 2004-2007) bir adımlı matrisler ve bir tanesi bütün çalışma periyodunu kapsayan (durağan model,1995-2007) olmak üzere toplam beş geçiş matrisini analiz etmiştir. Cavers ve Vasudevan (2015); rekor kıran anlamda uzaysal zamana bağlı tekrarlayan olayları içeren geçiş olasılıklarının bir zaman serisini veren global deprem sıralamasını çalışmak için grafik gösterimini yönlendirmiştir. Bu çalışmada bir durum, her bölgede daha önceden belirlenmiş bir zaman aralığında bir depremin meydana geldiği veya gelmediği bölgelerden oluşan bir konfigürasyonu ifade etmektedir.…”

Tax declaration rates via audits: a prediction using Markov model

“…An estimated percentage of realization of investment program for 2011 and results are interpreted with Markov analysis. Cavers and Vasudevan (2015) 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 recordbreaking 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.…”