Paraxial Approximations To The Acoustic Vti Wave Equation

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