Locally solving fractional Laplacian viscoacoustic wave equation using Hermite distributed approximating functional method

Accurate seismic modeling in realistic media serves as the basis of seismic full-waveform inversion and imaging. Recently, viscoacoustic seismic modeling incorporating attenuation effects has been performed 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. We have developed a local-spectral approach, based on the Hermite distributed approximating functional (HDAF) method, to implement the fractional Laplacian in the viscoacoustic wave equation. Our approach combines local methods' simplicity and global methods' accuracy. Several numerical examples are developed to evaluate the feasibility and accuracy of using the HDAF method for the frequency-independent Q fractional Laplacian wave equation.