Sensitive kernel of complex traveltime of seismic wave with respect to elastic moduli and Q-factors in viscoelastic VTI media

Anisotropy of velocity and attenuation is often observed in seismic data. Investigation of high-frequency seismic wave propagation in viscoelastic anisotropic media helps understand seismic wave propagation in such media. Based on the analytic eigenvalues of Christoffel matrix for viscoelastic VTI media, we demonstrate the real ray-tracing method to calculate the ray velocity, ray attenuation, and ray quality factor. Then the sensitivity kernels of the real traveltime and imaginary traveltime (attenuation) with respect to elastic moduli and Q-factors are discussed. We apply these theoretical formulas to rock samples. The computational results of the sensitivity kernels indicate that the real traveltime is more sensitive to elastic moduli, while the ray attenuation is almost equally sensitive to elastic moduli and Q-factors. This study can provide the theoretical foundation for seismic ray tracing and traveltime and attenuation tomography in viscoelastic VTI media.