Simple statistics for complex Earthquake time distributions

Abstract

Abstract. Here we investigated a statistical feature of earthquake time distributions in the southern California earthquake catalog. As a main data analysis tool, we used a simple statistical approach based on the calculation of integral deviation times (IDT) from the time distribution of regular markers. The research objective is to define whether and when the process of earthquake time distribution approaches to randomness. Effectiveness of the IDT calculation method was tested on the set of simulated color noise data sets with the different extent of regularity, as well as for Poisson process data sets. Standard methods of complex data analysis have also been used, such as power spectrum regression, Lempel and Ziv complexity, and recurrence quantification analysis, as well as multiscale entropy calculations. After testing the IDT calculation method for simulated model data sets, we have analyzed the variation in the extent of regularity in the southern California earthquake catalog. Analysis was carried out for different periods and at different magnitude thresholds. It was found that the extent of the order in earthquake time distributions is fluctuating over the catalog. Particularly, we show that in most cases, the process of earthquake time distributions is less random in periods of strong earthquake occurrence compared to periods with relatively decreased local seismic activity. Also, we noticed that the strongest earthquakes occur in periods when IDT values increase.

Mahalanobis distance-based recognition of changes in the dynamics of a seismic process

“…In other words, we aimed to assess the changes that occurred in the seismic process over the period covered by the SC catalogue . It is well known that the correctness of a multivariate assessment and classification of a system is strongly dependent on correct feature extraction (McLachlan, 1992(McLachlan, , 1999. In other words, the data sets used should be specifically focused on the targeted features of the process under investigation.…”

“…The MD (Mahalanobis, 1930;McLachlan, 1992McLachlan, , 1999) is a widely accepted method of measuring the separation of two groups of vectors (e.g. one group A, consisting of N A vectors a i = (a ix , a iy , a iz ), and another group B, with N B vectors b i ).…”

“…According to present knowledge, and in complete accordance with the concept of intermittent criticality, it is accepted that the extent of regularity (order) of the seismic process may vary in all its domains (temporal, spatial, and energetic) (Goltz, 1998;Abe and Suzuki, 2004;Chelidze and Matcharashvili, 2007;Iliopoulos et al, 2012;Matcharashvili et al, 2000Matcharashvili et al, , 2002Matcharashvili et al, , 2018. At the same time, despite the large number of recent publications demonstrating the diversity of these changes in the dynamics of the seismic process, interest in this issue continues to grow.…”

“…This approach was based on a widely accepted practice (see e.g. Bak et al, 2002;Christensen et al, 2002;Corral, 2004;Davidsen and Goltz, 2004;Matcharashvili et al, 2018) in which all events are assumed to be on the same footing and the catalogue is considered as a whole. In other words, we did not pay attention to the details of tectonic features, the locations of the earthquakes, or their classification as mainshock or aftershock (Bak et al, 2002;Christensen et al, 2002;Corral, 2004).…”

“…The practical and scientific reasons for this interest are well known and easily explainable. However, despite this strong interest and the enormous research efforts that have already been applied, many important aspects of the complex seismic process characterised by space and time clustering are still not clear (Bowman and Sammis, 2004;Godano and Tramelli, 2016;Kossobokov and Nekrasova, 2017;Matcharashvili et al, 2018;Pasten et al, 2018).…”