Modeling viscoacoustic wave propagation using a new spatial variable-order fractional Laplacian wave equation

Abstract

We have developed a new time-domain viscoacoustic wave equation for simulating wave propagation in anelastic media. The new wave equation is derived by inserting the complex-valued phase velocity described by the Kjartansson attenuation model into the frequency-wavenumber domain acoustic wave equation. Our wave equation includes one second-order temporal derivative and two spatial variable-order fractional Laplacian operators. The two fractional Laplacian operators describe the phase dispersion and amplitude attenuation effects, respectively. To facilitate the numerical solution for our wave equation, we use the arbitrary-order Taylor series expansion (TSE) to approximate the mixed-domain fractional Laplacians and achieve the decoupling of the wavenumber and the fractional order. Then, our viscoacoustic wave equation can be directly solved using the pseudospectral method. We adopt a hybrid pseudospectral/finite-difference method (HPSFDM) to stably simulate wave propagation in arbitrarily complex media. We validate the high accuracy of our approximate dispersion term and approximate the dissipation term in comparison with the accurate dispersion term and accurate dissipation term. The accuracy of the numerical solutions is evaluated by comparison with the analytical solutions in homogeneous media. Theory analysis and simulation results indicate that our viscoacoustic wave equation has higher precision than the traditional fractional viscoacoustic wave equation in describing constant- Q attenuation. For a model with Q\xa0<\xa010, the calculation cost for solving the new wave equation with TSE HPSFDM is lower than that for solving the traditional fractional-order wave equation with TSE HPSFDM under the high numerical simulation precision. Furthermore, we examine the accuracy of HPSFDM in heterogeneous media using several numerical examples.