Modeling the wave propagation in viscoacoustic media: An efficient spectral approach in time and space domain

We present an efficient and accurate modeling approach for wave propagation in anelastic media, based on a fractional spatial differential operator. The problem is solved with the Fourier pseudo-spectral method in the spatial domain and the REM (rapid expansion method) in the time domain, which, unlike the finite-difference and pseudo-spectral methods, offers spectral accuracy. To show the accuracy of the scheme, an analytical solution in a homogeneous anelastic medium is computed and compared with the numerical solution. We present an example of wave propagation at a reservoir scale and show the efficiency of the algorithm against the conventional finite-difference scheme. The new method, being spectral in the time and space simultaneously, offers a highly accurate and efficient solution for wave propagation in attenuating media.