Modelling seismic wave propagation in a two-dimensional cylindrical whole-earth model using the pseudospectral method
Modelling seismic wave propagation in a two-dimensional cylindrical whole-earth model using the pseudospectral method
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DOI：
10.1046/j.1365-246x.2001.01413.x
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发表时间：
2001-06
影响因子：
2.8
通讯作者：
Yanbin Wang;H. Takenaka;T. Furumura
中科院分区：
文献类型：
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作者：
Yanbin Wang;H. Takenaka;T. Furumura
总结我们提出了一种方法，用于模拟地震波传播的整个地球模型，通过求解弹性动力学方程在2-D柱坐标（r，h）使用傅立叶伪谱方法（PSM）。在求解全地球模型的二维圆柱弹性动力学方程时，在地球的中心（r=0）处出现一个奇异点。为了避免奇异性，我们开发了一个计划，使用在径向方向上的场变量的扩展，与该计算的波场在中心是避免的，所以可以计算通过中心的波传播。计算中使用的时间间隔由模型中心周围的最小横向网格间距确定。在圆柱坐标系中，最小横向网格间距通常很小，以至于计算太耗时，即使在超级计算机上也无法实际执行。我们采用了多域方案，以增加最小的横向网格间距，并避免过采样的物理域周围的地球中心。本文还提出了一种波数域的平滑方法，它使我们能够使用足够大的时间间隔，在桌面工作站上进行全地球模型的计算。将本方法计算的波形与直接求解法（DSM）计算的波形进行了比较，结果表明本方法具有较高的精度。这种方法显着减少了计算机内存和计算时间，使人们有可能研究的小波长的非均匀性，可以近似为方位对称的波在地球上传播的影响。我们应用本方法来研究地球局部非均匀性的影响，通过在IASP 91地球模型中添加核幔边界（CMB）上方的低速扰动。
SUMMARY We present a method for modelling seismic wave propagation in a whole-earth model by solving the elastodynamic equations in 2-D cylindrical coordinates (r, h) using the Fourier pseudospectral method (PSM). In solving the 2-D cylindrical elastodynamic equations for a whole-earth model, a singularity arises at the centre (r=0) of the earth. To avoid the singularity, we develop a scheme that uses extension of field variables in the radial direction, with which computation of the wavefield at the centre is avoided, so that the wave propagation through the centre can be calculated. The time interval used in the calculation is determined by the smallest lateral grid spacing around the centre in the model. In a cylindrical coordinate system, the smallest lateral grid spacing is generally so small that the calculation is too time-consuming to be realistically carried out even on a supercomputer. We adopt a multidomain scheme to increase the smallest lateral grid spacing and avoid the oversampling of the physical domain around the centre of the earth. A smoothing scheme in the wavenumber domain is also proposed, which enables us to use a large enough time interval to allow the calculation for the whole-earth model on a desktop workstation. The waveforms calculated by the present method are compared with those obtained by the Direct Solution Method (DSM) to demonstrate their high accuracy. This method significantly reduces the computer memory and computation time required and makes it possible to study the effects of small-wavelength heterogeneities that can be approximated as azimuthally symmetric on wave propagation in the earth. We apply the present method to study the effects of local heterogeneity in the earth by adding a low-velocity perturbation above the core‐mantle boundary (CMB) to the IASP91 earth model.