Empirical models of geometrical‐, Q‐, t‐star, and kappa‐type attenuation of seismic waves and ground‐motion prediction equations (GMPEs) are viewed as cases of a common empirical standard model describing variation of wave amplitudes with time and frequency. Compared with existing parametric and nonparametric approaches, several new features are included in this model: (1) flexible empirical parameterization with possible nonmonotonous time or distance dependencies; (2) joint inversion for time or distance and frequency dependencies, source spectra, site responses, kappas, and Q⁠; (3) additional constraints removing spurious correlations of model parameters and data residuals with source–receiver distances and frequencies; (4) possible kappa terms for sources as well as for receivers; (5) orientation‐independent horizontal‐ and three‐component amplitudes; and (6) adaptive filtering to reduce noise effects. The approach is applied to local and regional S‐wave amplitudes in southeastern Iran. Comparisons with previous studies show that conventional attenuation models often contain method‐specific biases caused by limited parameterizations of frequency‐independent amplitude decays and assumptions about the models, such as smoothness of amplitude variations. Without such assumptions, the frequency‐independent spreading of S waves is much faster than inferred by conventional modeling. For example, transverse‐component amplitudes decrease with travel time t as about t−1.8 at distances closer than 90 km and as t−2.5 beyond 115 km. The rapid amplitude decay at larger distances could be caused by scattering within the near surface. From about 90 to 115 km distances, the amplitude increases by a factor of about 3, which could be due to reflections from the Moho and within the crust. With more accurate geometrical‐spreading and kappa models, the Q factor for the study area is frequency independent and exceeds 2000. The frequency‐independent and Q‐type attenuation for vertical‐component and multicomponent amplitudes is somewhat weaker than for the horizontal components. These observations appear to be general and likely apply to other areas.

中文翻译：

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地震频谱振幅的稳固经验时频关系，第1部分：在伊朗东南部地区S波中的应用

地震波的几何，Q，t星和kappa型衰减的经验模型以及地面运动预测方程（GMPE）被视为描述波幅随时间和频率变化的通用经验标准模型的情况。与现有的参数和非参数方法相比，该模型包含了几个新功能：（1）灵活的经验参数化，可能具有非单调的时间或距离依赖性；（2）对时间或距离和频率的依赖性，源光谱，站点响应，kappas和Q⁠进行联合反演；（3）附加约束消除了模型参数和数据残差与源-接收机距离和频率的虚假相关性；（4）来源和接收者可能使用的kappa术语；（5）与方向无关的水平和三分量振幅；（6）自适应滤波以减少噪声影响。该方法适用于伊朗东南部的局部和区域S波振幅。与先前研究的比较表明，传统的衰减模型通常包含特定于方法的偏差，这些偏差是由与频率无关的振幅衰减的有限参数化以及有关模型的假设（例如振幅变化的平滑度）引起的。如果没有这样的假设，S波的频率独立扩展比常规建模所推断的要快得多。例如，当行进时间t小于90 km时，横向分量振幅随行进时间t减小约t-1.8，而超过115 km则行进为t-2.5。较大距离处的快速幅度衰减可能是由于近表面内的散射引起的。从大约90到115 km的距离，振幅增加了大约3倍，这可能是由于莫霍面和地壳内部的反射所致。使用更精确的几何扩展和Kappa模型，研究区域的Q因子与频率无关，并且超过2000。垂直分量和多分量幅度的频率独立和Q型衰减比水平分量弱。这些观察似乎是一般性的，并且可能适用于其他领域。垂直分量和多分量幅度的频率独立和Q型衰减比水平分量弱。这些观察似乎是一般性的，并且可能适用于其他领域。垂直分量和多分量幅度的频率独立和Q型衰减比水平分量弱。这些观察似乎是一般性的，并且可能适用于其他领域。