Estimation of the Tapered Gutenberg-Richter Distribution Parameters for Catalogs with Variable Completeness: An Application to the Atlantic Ridge Seismicity
The use of the tapered Gutenberg-Richter distribution in earthquake source models is rapidly increasing, allowing overcoming the definition of a hard threshold for the maximum magnitude. Here, we expand the classical maximum likelihood estimation method for estimating the parameters of the tapered G...
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| Format: | Article |
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MDPI AG
2021-12-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/24/12166 |
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| author | Matteo Taroni Jacopo Selva Jiancang Zhuang |
| author_facet | Matteo Taroni Jacopo Selva Jiancang Zhuang |
| author_sort | Matteo Taroni |
| collection | DOAJ |
| description | The use of the tapered Gutenberg-Richter distribution in earthquake source models is rapidly increasing, allowing overcoming the definition of a hard threshold for the maximum magnitude. Here, we expand the classical maximum likelihood estimation method for estimating the parameters of the tapered Gutenberg-Richter distribution, allowing the use of a variable through-time magnitude of completeness. Adopting a well-established technique based on asymptotic theory, we also estimate the uncertainties relative to the parameters. Differently from other estimation methods for catalogs with a variable completeness, available for example for the classical truncated Gutenberg-Richter distribution, our approach does not need the assumption on the distribution of the number of events (usually the Poisson distribution). We test the methodology checking the consistency of parameter estimations with synthetic catalogs generated with multiple completeness levels. Then, we analyze the Atlantic ridge seismicity, using the global centroid moment tensor catalog, finding that our method allows better constraining distribution parameters, allowing the use more data than estimations based on a single completeness level. This leads to a sharp decrease in the uncertainties associated with the parameter estimation, when compared with existing methods based on a single time-independent magnitude of completeness. This also allows analyzing subsets of events, to deepen data analysis. For example, separating normal and strike-slip events, we found that they have significantly different but well-constrained corner magnitudes. Instead, without distinguishing for focal mechanism and considering all the events in the catalog, we obtain an intermediate value that is relatively less constrained from data, with an open confidence region. |
| first_indexed | 2024-03-10T04:36:22Z |
| format | Article |
| id | doaj.art-171a8cddff38453c927d8839922ef0ed |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T04:36:22Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
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| series | Applied Sciences |
| spelling | doaj.art-171a8cddff38453c927d8839922ef0ed2023-11-23T03:44:12ZengMDPI AGApplied Sciences2076-34172021-12-0111241216610.3390/app112412166Estimation of the Tapered Gutenberg-Richter Distribution Parameters for Catalogs with Variable Completeness: An Application to the Atlantic Ridge SeismicityMatteo Taroni0Jacopo Selva1Jiancang Zhuang2Istituto Nazionale di Geofisica e Vulcanologia (INGV), 00143 Roma, ItalyIstituto Nazionale di Geofisica e Vulcanologia (INGV), 40100 Bologna, ItalyThe Institute of Statistical Mathematics, Tokyo 190-0014, JapanThe use of the tapered Gutenberg-Richter distribution in earthquake source models is rapidly increasing, allowing overcoming the definition of a hard threshold for the maximum magnitude. Here, we expand the classical maximum likelihood estimation method for estimating the parameters of the tapered Gutenberg-Richter distribution, allowing the use of a variable through-time magnitude of completeness. Adopting a well-established technique based on asymptotic theory, we also estimate the uncertainties relative to the parameters. Differently from other estimation methods for catalogs with a variable completeness, available for example for the classical truncated Gutenberg-Richter distribution, our approach does not need the assumption on the distribution of the number of events (usually the Poisson distribution). We test the methodology checking the consistency of parameter estimations with synthetic catalogs generated with multiple completeness levels. Then, we analyze the Atlantic ridge seismicity, using the global centroid moment tensor catalog, finding that our method allows better constraining distribution parameters, allowing the use more data than estimations based on a single completeness level. This leads to a sharp decrease in the uncertainties associated with the parameter estimation, when compared with existing methods based on a single time-independent magnitude of completeness. This also allows analyzing subsets of events, to deepen data analysis. For example, separating normal and strike-slip events, we found that they have significantly different but well-constrained corner magnitudes. Instead, without distinguishing for focal mechanism and considering all the events in the catalog, we obtain an intermediate value that is relatively less constrained from data, with an open confidence region.https://www.mdpi.com/2076-3417/11/24/12166statistical methodsstatistical seismologymagnitude-frequency distributioncorner magnitudetapered Paretotapered Gutenberg-Richter |
| spellingShingle | Matteo Taroni Jacopo Selva Jiancang Zhuang Estimation of the Tapered Gutenberg-Richter Distribution Parameters for Catalogs with Variable Completeness: An Application to the Atlantic Ridge Seismicity Applied Sciences statistical methods statistical seismology magnitude-frequency distribution corner magnitude tapered Pareto tapered Gutenberg-Richter |
| title | Estimation of the Tapered Gutenberg-Richter Distribution Parameters for Catalogs with Variable Completeness: An Application to the Atlantic Ridge Seismicity |
| title_full | Estimation of the Tapered Gutenberg-Richter Distribution Parameters for Catalogs with Variable Completeness: An Application to the Atlantic Ridge Seismicity |
| title_fullStr | Estimation of the Tapered Gutenberg-Richter Distribution Parameters for Catalogs with Variable Completeness: An Application to the Atlantic Ridge Seismicity |
| title_full_unstemmed | Estimation of the Tapered Gutenberg-Richter Distribution Parameters for Catalogs with Variable Completeness: An Application to the Atlantic Ridge Seismicity |
| title_short | Estimation of the Tapered Gutenberg-Richter Distribution Parameters for Catalogs with Variable Completeness: An Application to the Atlantic Ridge Seismicity |
| title_sort | estimation of the tapered gutenberg richter distribution parameters for catalogs with variable completeness an application to the atlantic ridge seismicity |
| topic | statistical methods statistical seismology magnitude-frequency distribution corner magnitude tapered Pareto tapered Gutenberg-Richter |
| url | https://www.mdpi.com/2076-3417/11/24/12166 |
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