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Robust Empirical Time–Frequency Relations for Seismic Spectral Amplitudes, Part 2: Model Uncertainty and Optimal Parameterization
Bulletin of the Seismological Society of America ( IF 3 ) Pub Date : 2021-02-01 , DOI: 10.1785/0120200180
Maryam Safarshahi 1 , Igor B. Morozov 1
Affiliation  

In a companion article, Safarshahi and Morozov (2020) argued that construction of distance‐ and frequency‐dependent models for seismic‐wave amplitudes should include four general elements: (1) a sufficiently detailed (parametric or nonparametric) model of frequency‐independent spreading, capturing all essential features of observations; (2) model parameters with well‐defined and nonoverlapping physical meanings; (3) joint inversion for multiple parameters, including the geometrical spreading, Q⁠, κ⁠, and source and receiver couplings; and (4) the use of additional dataset‐specific criteria of model quality, while fitting the logarithms of seismic amplitudes. Some of these elements are present in existing models, but, taken together, they are poorly understood and require an integrated approach. Such an approach was illustrated by detailed analysis of an S‐wave amplitude dataset from southern Iran. The resulting model is based on a frequency‐independent Q⁠, and matches the data closer than conventional models and across the entire epicentral‐distance range. Here, we complete the analysis of this model by evaluating the uncertainties and trade‐offs of its parameters. Two types of trade‐offs are differentiated: one caused by a (possibly) limited model parameterization and the second due to statistical data errors. Data bootstrapping shows that with adequate parameterization, attenuation properties Q⁠, κ⁠, and geometrical spreading parameters are resolved well and show moderate trade‐offs due to measurement errors. Using the principal component analysis of these trade‐offs, an optimal (trade‐off free) parameterization of seismic amplitudes is obtained. By contrast, when assuming theoretical values for certain model parameters and using multistep inversion procedures (as commonly done), parameter trade‐offs increase dramatically and become difficult to assess. In particular, the frequency‐dependent Q correlates with the distribution of the source and receiver‐site factors, and also with biases in the resulting median data residuals. In the new model, these trade‐offs are removed using an improved parameterization of geometrical spreading, constant Q⁠, and model quality constraints.

中文翻译:

地震频谱振幅的稳固经验时频关系,第2部分:模型不确定性和最佳参数化

Safarshahi和Morozov(2020)在一篇配套文章中指出,构造地震波振幅的距离和频率相关模型应包括四个基本要素:(1)足够详细的(参数或非参数)频率独立扩展模型捕获观测的所有基本特征;(2)具有明确定义和不重叠物理含义的模型参数;(3)对多个参数进行联合反演,包括几何扩展,Q⁠,κ⁠以及源和接收器耦合;(4)使用额外的特定于数据集的模型质量标准,同时拟合地震振幅的对数。这些元素中的某些元素存在于现有模型中,但加在一起,人们对它们的了解很少,因此需要采用集成方法。通过对伊朗南部的S波振幅数据集的详细分析说明了这种方法。结果模型基于与频率无关的Q⁠,并且比常规模型更接近数据且在整个震中距离范围内进行匹配。在这里,我们通过评估其参数的不确定性和权衡来完成对该模型的分析。权衡了两种类型:一种是(可能是)有限的模型参数化引起的,另一种是由于统计数据错误引起的。数据自举表明,通过适当的参数设置,衰减特性Q⁠,κ⁠和几何扩展参数得到了很好的解析,并且由于测量误差而显示出适度的取舍。使用这些折衷的主成分分析,获得了最佳的(无权衡)地震振幅参数。相反,当假设某些模型参数的理论值并使用多步反演程序(通常这样做)时,参数折衷会急剧增加,并且变得难以评估。尤其是,频率相关的Q与源和接收器站点因素的分布相关,并且与所得中值数据残差中的偏差相关。在新模型中,使用改进的几何扩展,常数Q⁠和模型质量约束的参数化消除了这些折衷。频率相关的Q与源和接收站因素的分布相关,并且与所得中值数据残差中的偏差相关。在新模型中,使用改进的几何扩展,常数Q⁠和模型质量约束的参数化消除了这些折衷。频率相关的Q与源和接收站因素的分布相关,并且与所得中值数据残差中的偏差相关。在新模型中,使用改进的几何扩展,常数Q⁠和模型质量约束的参数化消除了这些折衷。
更新日期:2021-01-31
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