SEGJ Technical Conference

Viscoelastic wave equation in the tau-p domain for a vertically inhomogeneous medium and its FDTD computation

Abstract We have derived the viscoelastic wave equations in the tau-p domain (plane-wave domain) by applying the Radon transform to the 3D viscoelastodynamic equation for 1D structures, and developed an efficient algorithm to calculate the plane-wave response of a vertically heterogeneous attenuative medium. Arbitrary Qp and Qs are incorporated into the wave equations via a general standard linear solid rheological model. A finite-difference time-domain (FDTD) staggered-grid technique is used for numerical solution of the derived plane-wave equations. The scheme uses a 1D grid, which allows for significant reduction in computation time and memory requirements compared to the corresponding 2D or 3D computations. In the proposed algorithm the domain boundaries are only at the top and bottom. The lack of artificial side reflections is another advantage of this approach.