Abstract
For seismic waveform simulation in tilted transversely isotropic (TTI) media, we derive explicitly the numerical dispersion relation and the stability condition for the computation of a 2D pseudo-acoustic wave equation. The numerical dispersion relation indicates that the number of sampling points per wavelength has the greatest influence on the dispersion, while the anisotropic parameters of the TTI media and the mesh rotation angle have little influence on the dispersion. Given an appropriate spatial sampling, the stability condition is for the selection of the time step for the implementation of the TTI wave equation. We partition a numerical model using quadrangle grids in Cartesian coordinates, and map it to a computing model in which any non-rectangular meshes in Cartesian coordinates become rectangular meshes. Then we reformulate the pseudo-acoustic wave equation for the TTI media accordingly in the computational space. We implement seismic waveform simulation using the second-order finite-difference method straightforwardly, and show examples with a desirable accuracy using a model with non-rectangular meshes in Cartesian coordinates along a curved surface and fluctuating interfaces in the TTI media.
Highlights
Seismic anisotropy commonly exists in the Earth’s subsurface media (Tsvankin et al 2010; Takanashi and Tsvankin 2012)
Accurate waveform simulation in tilted transversely isotropic (TTI) media is of importance for seismic waveform inversion
The P-wave and S-wave are coupled in the elastic wave equation in TTI media, we can have a pseudo-acoustic wave equation if the S-wave velocity is fixed along the axis of symmetry (Alkhalifah 1998; Fletcher et al 2009)
Summary
Seismic anisotropy commonly exists in the Earth’s subsurface media (Tsvankin et al 2010; Takanashi and Tsvankin 2012). Accurate waveform simulation in tilted transversely isotropic (TTI) media is of importance for seismic waveform inversion The latter reconstructs the subsurface velocity model quantitatively based on seismic waveform data. In the context of seismic waveform inversion, Pratt and Shipp (1999) and Rao and Wang (2011) use an acoustic wave equation defined by a single anisotropic parameter e. For the reformulated TTI wave equation, we analytically derive the corresponding numerical dispersion relation and stability condition, which provide the basis of finite-difference parameter selection of the TTI media waveform simulation
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