**Contents**


## **Preface to "Statistics and Pattern Recognition Applied to the Spatio-Temporal Properties of Seismicity"**

In recent years, there have been significant advances in the understanding of seismicity scaling laws, the study of spatiotemporal correlations, and earthquake clustering, with direct implications for time-dependent seismic hazard assessment. New models based on seismicity patterns, considering their physical and statistical significance, have shed light on the preparation process before large earthquakes and the evolution of clustered seismicity in time and space. On the other hand, the increasing amount of seismic data available at both local and global scales, together with accurate assessments of the reliability of the catalogs, offers new opportunities for model verification.

This Special Issue brings together eight peer-reviewed articles. The articles represent a collection of innovative applications of earthquake forecasting, including the earthquake preparation process, seismic hazard assessment, statistical analysis of seismicity, synthetic catalogs, and cluster identification.

It is therefore invaluable to seismologists, statistical seismologists, research students, governmen<sup>t</sup> agencies, and academics.

We are especially grateful to all the authors as without them this Special Issue would not have become a reality. As gues<sup>t</sup> editors, we would like to thank the reviewers for their careful evaluation and valuable contributions. Special thanks go to Assistant Editors Carlos Sanchez and Jill Fang for their dedication to this project and their invaluable collaboration in setting up, promoting, and managing the Special Issue.

#### **Stefania Gentili, Rita Di Giovambattista, Robert Shcherbakov, and Filippos Vallianatos** *Editors*

### *Editorial* **Editorial of the Special Issue "Statistics and Pattern Recognition Applied to the Spatio-Temporal Properties of Seismicity"**

**Stefania Gentili 1,\*, Rita Di Giovambattista 2, Robert Shcherbakov 3,4 and Filippos Vallianatos 5**


#### **1. Summary of the Special Issue Contents**

Due to the significant increase in the availability of new data in recent years, as a result of the expansion of available seismic stations, laboratory experiments, and the availability of increasingly reliable synthetic catalogs, considerable progress has been made in understanding the spatiotemporal properties of earthquakes. The study of the preparatory phase of earthquakes and the analysis of past seismicity has led to the formulation of seismicity models for the forecasting of future earthquakes or to the development of seismic hazard maps. The results are tested and validated by increasingly accurate statistical methods. A relevant part of the development of many models is the correct identification of seismicity clusters and scaling laws of background seismicity. In this collection, we present eight innovative papers that address all the above topics.

The occurrence of strong earthquakes (mainshocks) is analyzed from different perspectives in this Special Issue.

Ref. [1] proposes analysis using a medium-term earthquake prediction method (EEPAS) applied to California and New Zealand and analyzes the trade-off between time and the area identified by precursor seismicity.

Ref. [2] aims to establish the mechanical stability of a fault system by analyzing modulations of seismic activity as a function of known perturbations, in order to assess how unstable the faults are for additional stress. The method is applied to Greek seismicity.

Ref. [3] proposes a pattern recognition approach to identify areas where strong earthquakes occur, for application in seismic hazard assessment studies. The method is applied to North and South America, Eurasia, and the Pacific Rim.

Three other papers are related to triggered and clustered seismicity analyses (foreshock and aftershock).

Ref. [4] presents the modeling of aftershock occurrence rates by comparing Omori-Utsu and ETAS laws, and estimates the probability of having the largest aftershock forecasted during a given future time interval using the extreme value theory and the Bayesian predictive framework. A retrospective forecasting of three sequences in Alaska is performed.

Ref. [5] describes a new cluster identification procedure, MAP-DBSCAN, and successfully compares its performance with that of other existing methods in the literature by using synthetic catalogs. The method is then applied to obtain a characterization of Greek seismicity.

Ref. [6] proposes the use of foreshock and aftershock data together with their mainshocks to improve an earthquake prediction technique based on spatially smoothed seismicity. The method is applied to a global catalog with two different magnitude thresholds, 5.5 and 6.5, showing improved performance.

**Citation:** Gentili, S.; Di Giovambattista, R.; Shcherbakov, R.; Vallianatos, F. Editorial of the Special Issue "Statistics and Pattern Recognition Applied to the Spatio-Temporal Properties of Seismicity". *Appl. Sci.* **2022**, *12*, 4504. https://doi.org/10.3390/ app12094504

Received: 15 April 2022 Accepted: 21 April 2022 Published: 29 April 2022

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The last two papers in the collection are closely related to the topic of the previous papers.

Ref. [7] shows an extended version of the maximum likelihood estimation method for estimating the parameters of the tapered Gutenberg–Richter distribution and their uncertainties, in the case of catalogs with a time-varying magnitude of completeness. The method is tested on synthetic catalogs and the global centroid moment tensor catalog.

Ref. [8] proposes an algorithm to simulate synthetic catalogs covering hundreds of thousands of years based on the ETAS model and seismogenic source data. The algorithm allows for obtaining a seismicity catalog, using the seismogenetic model of Italian seismicity derived from the DISS catalog, that reproduces sequences characterized by multiple mainshocks of similar magnitude, a typical aspect of northern and central Apennine seismicity.
