A new highly accurate and efficient pure visco‐acoustic wave equation for tilted transversely isotropic attenuating media

Abstract

AbstractThe propagation of seismic waves in attenuating anisotropic media exhibits amplitude dissipation and phase dispersion. To describe its effects, the fractional Laplacian pure visco‐acoustic wave equations capable of producing stable and noise‐free wavefields have been derived. However, except for acoustic approximation, previous wave equations utilize the approximations with lower accuracy in simplifying the denominator of the approximate complex‐valued dispersion relation, resulting in reduced accuracy. To address this concern, we use a combination of complex stiffness coefficients to replace the denominator term of the approximate complex‐valued dispersion relation. This approximation effectively reduces the loss of accuracy caused by ignoring the influence of the velocity anisotropy parameter ε and the attenuation anisotropy parameter εQ in the denominator term, leading to a wave equation with high accuracy in media with large anisotropic parameters ε and δ. In addition, the new wave equation only contains two high‐order spatial partial derivatives and has high computational efficiency. Theoretical analysis and numerical examples demonstrate that the proposed pure visco‐acoustic tilted transversely isotropic wave equation outperforms the previous pure visco‐acoustic wave equation in terms of simulation accuracy. The newly developed wave equation is well suited for the application of Q‐compensated reverse time migration and full waveform inversion in attenuating anisotropic media.