{"title":"Inference of the Gutenberg-Richter b-value: New insights and results","authors":"Eulogio Pardo-Igúzquiza , Peter A. Dowd","doi":"10.1016/j.tecto.2024.230486","DOIUrl":null,"url":null,"abstract":"<div><p>The size-frequency distribution of many geological and geophysical variables, in relation to fractures, faulting and seismicity, is well described by a statistical distribution of the power law type which is characterized by its exponent. For earthquake magnitudes, the exponent is the well-known <em>b</em>-parameter of the Gutenberg-Richter scaling law. In this paper we:</p><ul><li><span>•</span><span><p>provide a strict statistical derivation of the distribution law of earthquake magnitudes,</p></span></li><li><span>•</span><span><p>show that the maximum likelihood estimator of the <em>b</em>-parameter is unbiased,</p></span></li><li><span>•</span><span><p>demonstrate that the maximum likelihood estimator is invariant to the value chosen as the minimum magnitude threshold in so far as it is larger than the magnitude of completeness of the earthquake catalogue, and</p></span></li><li><span>•</span><span><p>provide a new estimator based on the minimization of the Kolmogorov-Smirnov statistic and provide a strategy for detecting and mapping the spatio-temporal variation of the <em>b</em>-parameter in seismic swarms.</p></span></li></ul><p>The findings are illustrated with simulated data and a case study with real data.</p></div>","PeriodicalId":22257,"journal":{"name":"Tectonophysics","volume":"890 ","pages":"Article 230486"},"PeriodicalIF":2.7000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0040195124002889/pdfft?md5=4a7c102349b09a342138fdb4e7bc30b6&pid=1-s2.0-S0040195124002889-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tectonophysics","FirstCategoryId":"89","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0040195124002889","RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"GEOCHEMISTRY & GEOPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
The size-frequency distribution of many geological and geophysical variables, in relation to fractures, faulting and seismicity, is well described by a statistical distribution of the power law type which is characterized by its exponent. For earthquake magnitudes, the exponent is the well-known b-parameter of the Gutenberg-Richter scaling law. In this paper we:
•
provide a strict statistical derivation of the distribution law of earthquake magnitudes,
•
show that the maximum likelihood estimator of the b-parameter is unbiased,
•
demonstrate that the maximum likelihood estimator is invariant to the value chosen as the minimum magnitude threshold in so far as it is larger than the magnitude of completeness of the earthquake catalogue, and
•
provide a new estimator based on the minimization of the Kolmogorov-Smirnov statistic and provide a strategy for detecting and mapping the spatio-temporal variation of the b-parameter in seismic swarms.
The findings are illustrated with simulated data and a case study with real data.
与断裂、断层和地震有关的许多地质和地球物理变量的大小-频率分布，都可以用幂律类型的统计分布来很好地描述。对于地震震级而言，指数就是著名的古腾堡-里克特缩放定律的 b 参数。在本文中，我们-提供地震震级分布规律的严格统计推导，证明 b 参数的最大似然估计值是无偏的，证明最大似然估计值与所选的最小震级临界值无关，只要该值大于地震目录的完整震级、提供一种基于科尔莫哥洛夫-斯米尔诺夫统计量最小化的新估计器，并提供一种检测和绘制地震群中 b 参数时空变化图的策略。研究结果通过模拟数据和真实数据案例研究进行了说明。
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