The spatial‐temporal variations of b‐value in the Gutenberg‐Richter's relation are understood as stress meter and premonitory indicator of strong events. The characterization of the Gutenberg‐Richter's relation is complicated by the difficulty of identifying the completeness magnitude Mc, since its inaccurate estimate may lead to biased conclusions on b‐value. Therefore, many methods have been proposed to estimate b‐values and their changes, but no agreement has been reached on which is the most appropriate algorithm. Here a principled statistical framework is presented for discerning and quantifying variations in the Gutenberg‐Richter Law on empirical data. A new approach, called Normalized Distance (ND) test, is proposed, combining maximum‐likelihood estimates with a goodness‐of‐fit test and bootstrap resampling. The proposed method is evaluated on synthetic data and compared with the most used approaches. The main result is that the ND test provides better estimates of Mc and b‐value respect to all other methods. Finally, the same algorithms applied to the most recent Italian sequence provide contradictory results, indicating that detected b‐value fluctuations may be apparent.

中文翻译：

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用于确定地震目录完整性和b值的归一化距离测试

在古腾堡-里希特关系中，b值的时空变化被理解为压力表和强事件的预示指标。由于很难确定完整性量级Mc，因此对古腾堡-里希特关系的描述变得复杂，因为其不准确的估计值可能导致b值的结论有偏差。因此，提出了许多方法来估计b-值及其更改，但尚未就哪种算法最合适达成共识。这里提出了一个有原则的统计框架，用于识别和量化古腾堡-里希特定律关于经验数据的变化。提出了一种称为归一化距离（ND）测试的新方法，该方法将最大似然估计与拟合优度测试和自举重采样相结合。对提出的方法进行了综合数据评估，并与最常用的方法进行了比较。主要结果是，ND检验相对于所有其他方法提供了更好的Mc和b值估计。最后，应用于最新的意大利序列的相同算法提供了矛盾的结果，表明检测到的b值波动可能很明显。