Modeling Pure qP-wave in Attenuative TI Media Using Complex-Valued Fractional Viscoacoustic Wave Equation

Abstract

Seismic anisotropy, characterized by direction-dependent seismic velocity and atten- uation, is a fundamental property of the Earth, widely observed in both field and lab measurements. This anisotropy significantly influences seismic wavefield attributes, such as amplitude, phase, and traveltime. Accurate quantification of anisotropy-related seismic wave propagation is essential for global and regional scale studies in seismology, including imaging and inversion. Since the elastic assumption of the Earth requires contending with shear waves, which are often weak in our seismic recording, thus we derive a new general complex-valued spatial fractional Laplacian (SFL) viscoacoustic anisotropic pure quasi-P (qP) wave equation (WE) in attenuative TI (A-TI) media under the acoustic assumption, and employ the fixed-order SFL operator to quantify seismic wave propagation in heteroge- neous media. The proposed WE accurately captures anisotropic effects in seismic velocity and attenuation, even in strongly attenuative and anisotropic environments. It also de- scribes the decoupled energy attenuation and velocity dispersion behaviors of the frequency independent quality factor Q, beneficial for seismic imaging and inversion. Compared with existing viscoacoustic anisotropic pure qP WEs in A-TI media, our WE simplifies computa- tional complexity and is easy to implement, as it decomposes into a complex-valued scalar operator and two differential operators. The evaluated dispersion curves further confirm the accuracy of our proposed approach. Numerical examples in complex geological settings demonstrate the new equation’s precision, stability and efficiency in modeling seismic wave propagation.