A statistical evaluation of a ‘stress‐forecast’ earthquake
A statistical evaluation of a ‘stress‐forecast’ earthquake
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DOI：
10.1111/j.1365-246x.2004.02186.x
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发表时间：
2004-04
影响因子：
2.8
通讯作者：
T. Seher;I. Main
中科院分区：
文献类型：
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作者：
T. Seher;I. Main
具有不同自由度的竞争统计模型的拟合优度不能仅仅通过残差平方和来评估，因为更复杂的模型自然会有更低的残差。大型数据集假设检验的标准方法是使用客观贝叶斯信息准则（BIC），该准则适当地惩罚具有大量自由参数的模型。我们将此方法应用于冰岛西南部地震剪切波分裂资料的时间延迟分析。同样的数据集以前被用来估计应力修正微裂纹达到断裂临界状态的时间。该方法无法预测地震发生的位置，但时间和震级与该地区实际发生的5级地震一致。预测基于17个自由度的多线模型（5条直线，每条直线有一个起点和终点，加上方差，其中4个终点由主震的发生固定），信噪比接近一致。BIC用于与泊松、多线、正弦或多项式（截断泰勒展开）假设的竞争曲线拟合相比较，评估这一预测。对于正弦模型，随机发生的零假设只能被正式拒绝，这意味着周期为134.6天的周期性重复。我们考虑的所有其他模型都有较低的BIC。我们还分析了用高斯统计方法预测断裂临界的数据集的选定部分。预测主震震级的95%置信区间在3.9至6.7级之间。相同置信限所表示的时间范围从实际事件发生前42天开始计算；无法找到一个清晰的端点。预测震级与等待时间之间的关系与从模式不确定性范围内的背景Gutenberg - Richter频率-震级关系推断的结果没有显著差异。因此，根据这些数据，不可能正式拒绝5级地震是正常背景地震活动的一部分的假设。
SUMMARY The goodness of fit for competing statistical models with different numbers of degrees of freedom cannot be assessed solely by the residual sum of squares, because more complex models will naturally have lower residuals. A standard approach to hypothesis testing for large data sets is to use the objective Bayesian information criterion (BIC), which penalizes models with larger numbers of free parameters appropriately. We apply this method to the analysis of time delays from data on seismic shear-wave splitting in SW Iceland. The same data set has previously been used to estimate the time at which stress-modified micro-cracking reaches an inferred state of fracture criticality. The method does not forecast the location of the event, however, the time and magnitude were consistent with the actual occurrence of an M = 5 earthquake in the region. The forecast was based on a multi-line model with 17 degrees of freedom (five straight lines, each with a start and end point, plus the variance, with four endpoints being fixed by the occurrence of a main shock), and a signal-to-noise ratio near unity. The BIC is used to assess this forecast in comparison with competing curve fits for Poisson, multiline, sinusoidal, or polynomial (truncated Taylor expansion) hypotheses. The null hypothesis of random occurrence can only be rejected formally for the sinusoidal model, implying cyclical recurrence with a period of 134.6 days. All other models we consider have a lower BIC. We also analyse the selected portion of the data set used to make the forecast of fracture criticality using Gaussian statistics. The 95 per cent confidence intervals on the predicted main shock magnitude range between magnitudes of 3.9 and 6.7. The time range indicated by the same confidence limits starts 42 days before the actual event; a clear end cannot be located. The relation between predicted magnitude and waiting time is not significantly different from that inferred from the background Gutenberg‐Richter frequency‐magnitude relation within the model uncertainties. Thus, it is not possible, based on the data, to formally reject the hypothesis that the magnitude 5 event was part of the normal background seismicity.