Ultra Efficient Methods of Seismic Wave Modeling for Waveform Tomography

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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.