Mathematical Theory of Seismic Activity and Its Specific Cases: Gutenberg–Richter Law, Omori Law, Roll-Off Effect, and Negative Binomial Distribution
We discuss a model of seismic activity that is based on the concept of energy in a cluster of sources of seismic activity. We show that specific cases of the studied model lead to the Gutenberg–Richter relationship and the Omori law. These laws are valid for earthquakes that happen in a single clust...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/27/2/130 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849718777572229120 |
|---|---|
| author | Roumen Borisov Nikolay K. Vitanov |
| author_facet | Roumen Borisov Nikolay K. Vitanov |
| author_sort | Roumen Borisov |
| collection | DOAJ |
| description | We discuss a model of seismic activity that is based on the concept of energy in a cluster of sources of seismic activity. We show that specific cases of the studied model lead to the Gutenberg–Richter relationship and the Omori law. These laws are valid for earthquakes that happen in a single cluster of sources of seismic activity. Further, we discuss the distribution of earthquakes for several clusters containing sources of seismic activity. This distribution contains, as a specific case, a version of the negative binomial distribution. We show that at least a part of the roll-off effect connected to the parameter <i>b</i> of the Gutenberg– Richter law occurs because one records earthquakes that happen in more than one cluster of sources of seismic activity. |
| format | Article |
| id | doaj-art-54502d72d00549fbab2ed009e6cab2ed |
| institution | DOAJ |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-54502d72d00549fbab2ed009e6cab2ed2025-08-20T03:12:18ZengMDPI AGEntropy1099-43002025-01-0127213010.3390/e27020130Mathematical Theory of Seismic Activity and Its Specific Cases: Gutenberg–Richter Law, Omori Law, Roll-Off Effect, and Negative Binomial DistributionRoumen Borisov0Nikolay K. Vitanov1Institute of Mechanics, Bulgarian Academy of Sciences, Academician Georgi Bonchev Street, Block 4, 1113 Sofia, BulgariaInstitute of Mechanics, Bulgarian Academy of Sciences, Academician Georgi Bonchev Street, Block 4, 1113 Sofia, BulgariaWe discuss a model of seismic activity that is based on the concept of energy in a cluster of sources of seismic activity. We show that specific cases of the studied model lead to the Gutenberg–Richter relationship and the Omori law. These laws are valid for earthquakes that happen in a single cluster of sources of seismic activity. Further, we discuss the distribution of earthquakes for several clusters containing sources of seismic activity. This distribution contains, as a specific case, a version of the negative binomial distribution. We show that at least a part of the roll-off effect connected to the parameter <i>b</i> of the Gutenberg– Richter law occurs because one records earthquakes that happen in more than one cluster of sources of seismic activity.https://www.mdpi.com/1099-4300/27/2/130seismic activityearthquakesenergy-based modelGutenberg–Richter lawOmori lawnegative binomial distribution |
| spellingShingle | Roumen Borisov Nikolay K. Vitanov Mathematical Theory of Seismic Activity and Its Specific Cases: Gutenberg–Richter Law, Omori Law, Roll-Off Effect, and Negative Binomial Distribution Entropy seismic activity earthquakes energy-based model Gutenberg–Richter law Omori law negative binomial distribution |
| title | Mathematical Theory of Seismic Activity and Its Specific Cases: Gutenberg–Richter Law, Omori Law, Roll-Off Effect, and Negative Binomial Distribution |
| title_full | Mathematical Theory of Seismic Activity and Its Specific Cases: Gutenberg–Richter Law, Omori Law, Roll-Off Effect, and Negative Binomial Distribution |
| title_fullStr | Mathematical Theory of Seismic Activity and Its Specific Cases: Gutenberg–Richter Law, Omori Law, Roll-Off Effect, and Negative Binomial Distribution |
| title_full_unstemmed | Mathematical Theory of Seismic Activity and Its Specific Cases: Gutenberg–Richter Law, Omori Law, Roll-Off Effect, and Negative Binomial Distribution |
| title_short | Mathematical Theory of Seismic Activity and Its Specific Cases: Gutenberg–Richter Law, Omori Law, Roll-Off Effect, and Negative Binomial Distribution |
| title_sort | mathematical theory of seismic activity and its specific cases gutenberg richter law omori law roll off effect and negative binomial distribution |
| topic | seismic activity earthquakes energy-based model Gutenberg–Richter law Omori law negative binomial distribution |
| url | https://www.mdpi.com/1099-4300/27/2/130 |
| work_keys_str_mv | AT roumenborisov mathematicaltheoryofseismicactivityanditsspecificcasesgutenbergrichterlawomorilawrolloffeffectandnegativebinomialdistribution AT nikolaykvitanov mathematicaltheoryofseismicactivityanditsspecificcasesgutenbergrichterlawomorilawrolloffeffectandnegativebinomialdistribution |