Paraxial Approximations To The Acoustic Vti Wave Equation

Many migration methods are based on paraxial approximations to the wave equation. These approximations are used to describe the wave propagation in a preferred direction. We apply the idea of a directed propagation to the so-called anisotropic acoustic wave equation. We derive paraxial approximations for this equation, the first ones being generalizations of the 15◦ and 45◦ approximations to the isotropic acoustic wave equation. Moreover, we derive higher-order approximations using Pad´e approximations. A set of numerical experiments demonstrates that our paraxial equations provide reasonable approximations to the solution of the full equation. Moreover, their computational execution is cheaper than using a direct implementation.