Abstract
At present, it is generally assumed that the quality factor Q is frequency independent in the seismic exploration band and the attenuation is isotropic. In reality, like the velocity anisotropy, the attenuation anisotropy cannot be ignored. In this paper, we combine the attenuation anisotropy and velocity anisotropy with the constant-Q model to establish a viscoelastic vertical transversely isotropic (VTI) attenuative model. Based on the fractional time derivatives theory, the corresponding constitutive relation and wave equations are proposed. The analytical expressions of the quality factor, complex, phase, and energy velocities for the quasi-compressional wave qP, the quasi-shear wave qSV, and the pure shear wave SH, respectively, are derived from the homogeneous plane wave analysis and Poynting theorem. The correctness of the presented model is numerically verified, and the propagation characteristics of the qP, qSV, and SH waves are analyzed. The results of numerical experiments indicate that the given m