2.5D modelling of elastic waves in transversely isotropic media using the spectral element method

The spectral-element method provides an accurate alternative to the finite-element method for modelling elastic waves in anisotropic media. With the aim of reducing the high computational overheads of 3D modelling, we have implemented 2.5D spectral-element modelling of elastic waves, initially for vertically transversely isotropic media, and then extended to a tilted transversely isotropic medium with a dipping symmetry-axis. We have investigated different categories of absorbing boundaries to minimise artificial boundary reflections, including viscous boundary conditions and two distinct 2.5D formulations of perfectly matched layers (PMLs). Both PML methods use complex coordinate stretching, but the first method is only applicable in the frequency-domain. The other method uses the decomposed gradient operator and can be applied in both the time-domain and frequency-domain. Traditional 2D modelling exhibits cylindrical wave propagation characteristics from a line source. Our 2.5D modelling results, presented as images of seismic wavefields, illustrate the more realistic spherical propagation from a point source.