Lowrank Approximation for Time Domain Viscoacoustic Wave Equation With Spatially Varying Order Fractional Laplacians

Chen, Hanming (China University of Petroleum) | Zhou, Hui (China University of Petroleum) | Qu, Shan (China University of Petroleum)

OnePetro 

Summary

Recently a time domain nearly constant Q (NCQ) wave equation derived from Kjartansson’s constant Q model has been developed for modeling viscoacoustic wavefield. The wave equation introduces decoupled attenuation and dispersion terms based on two separate fractional Laplacians, which can be easily calculated by spatial Fourier pseudo-spectral method. The fractional orders of the Laplacians are related to Q, and that means the orders are actually spatially varying. However, no desirable approach is presented in the current literatures to handle the varying orders. The fractional Laplacian with a spatially varying order can be exactly represented by a wavenumber-space domain operator. In this abstract we use a lowrank decomposition method to approximate the mixed-domain operator, thus making the NCQ wave equation adapt to large Q contrasts. Additionally, we reformulate the existing velocity-stress-strain NCQ formulation as an equivalent compact velocity-pressure system. The staggered-grid pseudo-spectral (SGPS) method and unsplit convolutional perfectly matched layer (CPML) are adopted in numerical simulations.