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 nonrectangular
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.