An Anisotropic Acoustic Wave Equation for VTI Media

Here we propose a new anisotropic acoustic wave equation based on the same dispersion relation as Alkhalifah’s (2000), but introducing an auxiliary function which allows the original fourth-order differential equation to become a coupled system of lower-order differential equations. Of these two equations, one equation can be considered as a hyperbolic wave equation for elliptical anisotropy, but with a correction term that compensates for the loss of anisotropy for VTI media, while the other can be considered as the additional expansion or contraction of the wavefront in the lateral directions. This two-way anisotropic wave equation can be used for both modeling and reverse-time migration.<br><br>The new anisotropic acoustic equation has the obvious physical meaning and is much easier to implement. Impulse responses for both modeling and migration have been shown to validate the proposed anisotropic acoustic equation. <br>