Solving fractional laplacian viscoacoustic wave equation using hermite distributed approximating functional method

Accurate seismic modeling in realistic media severs the basis of seismic inversion and imaging. Recently viscoacoustic seismic modeling incorporating attenuation effects was done by solving a fractional Laplacian viscoacoustic wave equation. In this equation, attenuation, being spatially heterogeneous, is represented partially by the spatially varying power of the fractional Laplacian operator previously approximated by the global Fourier method. In this paper, we present a local spectral approach, based on Hermite distributed approximating functional (HDAF) method, to implement the fractional Laplacian in the viscoacoustic wave equation. The proposed approach combines local methods' simplicity and global methods' accuracy. Several numerical examples are presented to demonstrate the feasibility and accuracy of using the HDAF method for the frequency-independent Q fractional Laplacian wave equation.