Connection between Variations of the Probability Distribution of the Recurrence Time and Phases of the Seismic Activity
The probability distribution of the interevent time between two successive earthquakes has been the subject of numerous studies for its key role in seismic hazard assessment. In recent decades, many distributions have been considered, and there has been a long debate about the possible universality...
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MDPI AG
2023-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/10/1441 |
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| author | Elisa Varini Renata Rotondi |
| author_facet | Elisa Varini Renata Rotondi |
| author_sort | Elisa Varini |
| collection | DOAJ |
| description | The probability distribution of the interevent time between two successive earthquakes has been the subject of numerous studies for its key role in seismic hazard assessment. In recent decades, many distributions have been considered, and there has been a long debate about the possible universality of the shape of this distribution when the interevent times are properly rescaled. In this work, we aim to discover if there is a link between the different phases of a seismic cycle and the variations in the distribution that best fits the interevent times. To do this, we consider the seismic activity related to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>M</mi><mi>w</mi></msub></semantics></math></inline-formula> 6.1 L’Aquila earthquake that occurred on 6 April 2009 in central Italy by analyzing the sequence of events recorded from April 2005 to July 2009, and then the seismic activity linked to the sequence of the Amatrice-Norcia earthquakes of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>M</mi><mi>w</mi></msub></semantics></math></inline-formula> 6 and 6.5, respectively, and recorded in the period from January 2009 to June 2018. We take into account some of the most studied distributions in the literature: <i>q</i>-exponential, <i>q</i>-generalized gamma, gamma and exponential distributions and, according to the Bayesian paradigm, we compare the value of their posterior marginal likelihood in shifting time windows with a fixed number of data. The results suggest that the distribution providing the best performance changes over time and its variations may be associated with different phases of the seismic crisis. |
| first_indexed | 2024-03-10T21:16:39Z |
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| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T21:16:39Z |
| publishDate | 2023-10-01 |
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| series | Entropy |
| spelling | doaj.art-691f79c2ca314ed4a073bf530d23c2312023-11-19T16:24:57ZengMDPI AGEntropy1099-43002023-10-012510144110.3390/e25101441Connection between Variations of the Probability Distribution of the Recurrence Time and Phases of the Seismic ActivityElisa Varini0Renata Rotondi1National Research Council of Italy, Institute for Applied Mathematics and Information Technologies, Via Corti 12, 20133 Milan, ItalyNational Research Council of Italy, Institute for Applied Mathematics and Information Technologies, Via Corti 12, 20133 Milan, ItalyThe probability distribution of the interevent time between two successive earthquakes has been the subject of numerous studies for its key role in seismic hazard assessment. In recent decades, many distributions have been considered, and there has been a long debate about the possible universality of the shape of this distribution when the interevent times are properly rescaled. In this work, we aim to discover if there is a link between the different phases of a seismic cycle and the variations in the distribution that best fits the interevent times. To do this, we consider the seismic activity related to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>M</mi><mi>w</mi></msub></semantics></math></inline-formula> 6.1 L’Aquila earthquake that occurred on 6 April 2009 in central Italy by analyzing the sequence of events recorded from April 2005 to July 2009, and then the seismic activity linked to the sequence of the Amatrice-Norcia earthquakes of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>M</mi><mi>w</mi></msub></semantics></math></inline-formula> 6 and 6.5, respectively, and recorded in the period from January 2009 to June 2018. We take into account some of the most studied distributions in the literature: <i>q</i>-exponential, <i>q</i>-generalized gamma, gamma and exponential distributions and, according to the Bayesian paradigm, we compare the value of their posterior marginal likelihood in shifting time windows with a fixed number of data. The results suggest that the distribution providing the best performance changes over time and its variations may be associated with different phases of the seismic crisis.https://www.mdpi.com/1099-4300/25/10/1441interevent timeprobability distributionsprobabilistic forecastingseismic cyclestatistical seismologystatistical methods |
| spellingShingle | Elisa Varini Renata Rotondi Connection between Variations of the Probability Distribution of the Recurrence Time and Phases of the Seismic Activity Entropy interevent time probability distributions probabilistic forecasting seismic cycle statistical seismology statistical methods |
| title | Connection between Variations of the Probability Distribution of the Recurrence Time and Phases of the Seismic Activity |
| title_full | Connection between Variations of the Probability Distribution of the Recurrence Time and Phases of the Seismic Activity |
| title_fullStr | Connection between Variations of the Probability Distribution of the Recurrence Time and Phases of the Seismic Activity |
| title_full_unstemmed | Connection between Variations of the Probability Distribution of the Recurrence Time and Phases of the Seismic Activity |
| title_short | Connection between Variations of the Probability Distribution of the Recurrence Time and Phases of the Seismic Activity |
| title_sort | connection between variations of the probability distribution of the recurrence time and phases of the seismic activity |
| topic | interevent time probability distributions probabilistic forecasting seismic cycle statistical seismology statistical methods |
| url | https://www.mdpi.com/1099-4300/25/10/1441 |
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