Using PSPI to accelerate seismic Q-modeling based on Hermite distributed approximating functional

The attenuation effect of seismic waves has been recently incorporated into a fractional Laplacian viscoacoustic wave equation. Solving this equation requires a special treatment for the fractional Laplacian operators. The previous promising approach involves using a Hermite distributed approximating functional (HDAF). As a local-spectral method, HDAF method possesses the accuracy of a global method. However, the computational cost of the HDAF method increases dramatically as the complexity of the Q model increases. In this paper, we propose to use a phase shift plus interpolation (PSPI) technique to reduce the computational expense of HDAF method. The basic idea is to compute reference wavefileds for a set of reference Q⁰s and estimate the final wavefield using interpolation. Synthetic examples demonstrate the PSPI technique can greatly reduce the computational cost of HDAF method while preserving the accuracy.