Abstract:Based on the elastic wave theory, we first derive in this paper a quasi-acoustic equation in VTI medium which expressed by velocity and stress. Then we popularize it into TTI media with coordinate transformation. The energy conservation proves that the velocity-stress equations derived from elastic theory are more stable than equations derived from the dispersion relation. For model with anisotropic parameters , the issue about residual shear instability can be solved by introducing a shear correction. Numerical simulation shows that the new equation can not only describe the kinematic characteristics of qP wave, and also adapt well to TTI media. Furthermore, the numerical examples verify the stability of the equations.
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