S U M M A R Y Small-scale heterogeneities in the Earth’s mantle, the origin of which is likely compositional anomalies, can provide critical clues on the evolution of mantle convection. Seismological investigation of such small-scale heterogeneities can be facilitated by forward modelling of elastic wave scattering at high frequencies, but doing so with conventional 3-D numerical methods has been computationally prohibitive. We develop an efficient approach for computing high-frequency synthetic wavefields originating from small-scale mantle heterogeneities. Our approach delivers the exact elastodynamic wavefield and does not restrict the geometry or physical properties of the local heterogeneity and the background medium. It combines the technique of wavefield injection and a numerical method called AxiSEM3D. Wavefield injection can decompose the total wavefield into an incident and a scattered part. Both these two parts naturally have low azimuthal complexity and can thus be solved efficiently using AxiSEM3D under two different coordinate systems. With modern high-performance computing (on an order of magnitude of 105 CPU-hr), we have achieved a 1 Hz dominant frequency for global-scale problems with strong deep Earth scattering. Compared with previous global injection approaches, ours allows for a 3-D background medium and yields the exact solution without ignoring any higher-order scattering by the background medium. Technically, we develop a traction-free scheme for realizing wavefield injection in a spectral element method, which brings in several flexibilities and simplifies the implementation by avoiding stress or traction computation on the injection boundary. For a spherical heterogeneity in the mid-lower mantle, we compare the 3-D full-wave solution with two approximate ones obtained, respectively, by the perturbation theory and in-plane (axisymmetric) modelling. As a comprehensive application, we study S-wave scattering by a 3-D ultra-low velocity zone, incorporating 3-D crustal structures on the receiver side as part of the background model.

中文翻译：

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地幔中小尺度异质性对弹性波的 3-D 散射

总结地球地幔中的小尺度异质性，其起源可能是成分异常，可以为地幔对流演化提供关键线索。通过对高频弹性波散射进行正向建模，可以促进对这种小规模非均质性的地震学调查，但使用传统的 3-D 数值方法进行计算在计算上令人望而却步。我们开发了一种有效的方法来计算源自小尺度地幔异质性的高频合成波场。我们的方法提供了精确的弹性动力学波场，并且不限制局部异质性和背景介质的几何或物理特性。它结合了波场注入技术和称为 AxiSEM3D 的数值方法。波场注入可以将整个波场分解为入射部分和散射部分。这两个部分自然具有较低的方位角复杂度，因此可以在两个不同的坐标系下使用 AxiSEM3D 有效地求解。通过现代高性能计算（大约 105 CPU-hr 的数量级），我们已经实现了 1 Hz 的主频，以解决具有强烈地球深部散射的全球规模问题。与之前的全局注入方法相比，我们的方法允许使用 3-D 背景介质并在不忽略背景介质的任何高阶散射的情况下产生精确解。在技​​术上，我们开发了一种无牵引方案，用于在光谱元方法中实现波场注入，这带来了一些灵活性并通过避免注射边界上的应力或牵引力计算来简化实施。对于中下地幔中的球形不均匀性，我们将 3-D 全波解与分别通过微扰理论和面内（轴对称）建模获得的两个近似解进行比较。作为一项综合应用，我们研究了 3-D 超低速区的 S 波散射，将接收器侧的 3-D 地壳结构作为背景模型的一部分。