An Anisotropic Acoustic Wave Equation For Modeling And Migration In 2D TTI Media

In this abstract, we propose a new anisotropic acoustic wave equation for 2D TTI media. This is the extension of our previous work on VTI media to TTI media. Similar to VTI case, we follow the same procedures as Zhou et al. (2006), by the introduction of an auxiliary function, the original fourth-order differential equation becomes a coupled system of lower-order differential equations. However, unlike VTI case, a cross-derivative term has been added to each of the coupled system of the hyperbolic differential equations because of its TTI characteristics. Of these two equations, one equation plays a key role in governing the propagation of the wavefront, with the other equation compensating for the loss of anisotropy for TTI media not only in the lateral but also in the depth directions. The new anisotropic acoustic wave equation has the obvious physical meaning and is much easier to implement. Impulse responses for both modeling and migration have been tested to show the validation of the proposed anisotropic acoustic wave equation.