We derive a theoretical parameter for three seismic scattering regimes where seismic wavelengths are either much shorter, similar, or much longer than the correlation length of small‐scale Earth heterogeneities. We focus our analysis on the power spectral density (PSD) of the von Karman autocorrelation function (ACF), used to characterize the spatial heterogeneity of small‐scale variations of elastic rock parameters that cause elastic seismic‐wave scattering. Our analysis is based on the assumption that the PSD of the medium heterogeneities at the corresponding wavenumber is related to the wavefield scattering. Our theoretical findings are verified by numerical simulations. The seismic scattering effects in our simulations are assessed by examining attenuation of peak ground acceleration. We discover (1) that seismic scattering is proportional to the standard deviation of velocity variations in all three regimes, (2) that scattering is inversely proportional to the correlation length for the regime where seismic wavelengths are shorter than correlation length, but directly proportional to the correlation length in the other two regimes, and (3) that scattering effects are weak due to heterogeneities characterized by a gentle decay of the von Karman ACF for regimes where seismic wavelengths are similar or much longer than the correlation length.

中文翻译：

---

通过单参数表征3D非均质地球中的地震散射

我们推导了三种地震散射制度的理论参数，在这些制度中，地震波长比小规模地球异质性的相关长度短，相似或长得多。我们将分析重点放在冯·卡曼自相关函数（ACF）的功率谱密度（PSD）上，该功率谱密度用于表征引起弹性地震波散射的弹性岩石参数小尺度变化的空间异质性。我们的分析基于这样一个假设，即在相应波数下的介质异质性的PSD与波场散射有关。我们的理论发现通过数值模拟得到了验证。通过检查峰值地面加速度的衰减来评估我们模拟中的地震散射效应。