Ultra Efficient Methods of Seismic Wave Modeling for Waveform Tomography

波形层析成像是成像地球内部的最高分辨率方法之一。波形层析成像在实际资料中的应用需要对三维地震波场进行大量的计算。为了在有限的计算机资源下迭代计算合成地震记录，需要一种快速而准确的建模方法。为此，我们发展了以下有效的地震波形数值模拟方法：1.地震波在二维切片中通过具有横向非均质性的全球地球模型传播的准球方法：球坐标的弹性动力学方程不是在传统的球域中求解，而是用有限差分方法在“准球域”中求解。该方法可以正确地模拟三维几何扩展效应，计算时间和内存与二维方法相当，并且可以处理包括源在内的垂直轴上的非对称结构。轴对称建模：它还可以在与2-D建模相当的计算资源内正确地模拟3-D中的几何扩散效果。然而，在以往的轴对称模拟工作中，震源被限制在轴对称震源，如爆炸震源。在这项研究中，我们提出了一种利用FDM.3实现任意矩张量点源到轴对称建模的方法。用于模拟垂直非均匀“粘弹性”介质的地震平面波的高效有限差分算法：它可以模拟频率相关的滞弹性(Q)效应。该格式使用一维网格，与相应的2D或3D计算相比，大大减少了计算时间和内存需求。

Waveform tomography is one of the highest resolution methods for imaging the Earth's interior. Application of the waveform tomography to real data requires huge number of computations of 3D seismic wavefields. For such iterative calculations of synthetic seismograms with limited computer resources, a fast and accurate modeling method is needed. For this purpose, we developed the following efficient numerical methods for modeling seismic waveforms :1. Quasi-spherical approach for seismic wave propagation in a 2D slice through a global earth model with lateral heterogeneity : The elastodynamic equation for spherical coordinates is not solved in the conventional spherical domain but instead in a "quasi-spherical domain" using the finite-difference method (FDM). This approach can correctly model 3D geometrical spreading effects with computational times and memories comparable to 2D methods, and can treat asymmetric structure about the vertical axis including the source.2. Axisymmetric modeling : It can also correctly model geometrical spreading effects in 3-D within computational resources comparable to 2-D modeling. However, in the previous works with the axisymmetric modeling, seismic sources were restricted to axisymmetric sources such as an explosive source. In this study, we proposed an implementation of an arbitrary moment tensor point source to axisymmetric modeling using the FDM.3. Efficient FDM algorithm for modeling seismic plane waves for vertically heterogeneous "viscoelastic" media : It can model frequency-dependent anelastic (Q) effects. The scheme uses a 1D grid, which causes a significant reduction in computation time and memory requirement compared to the corresponding 2D or 3D computations.