Viscoacoustic wave equation for qP-wave in transversely isotropic media

Abstract

The wave equation acts a pivotal part in seismic data processing. We derived two time-domain pure qP viscoacoustic wave equations suitable for attenuation anisotropic media, providing a choice for pure qP-wave forward modeling and inversion in attenuation anisotropic media. Our new qP-wave equation in vertical transversely isotropic (VTI) media are based on the dispersion relation for qP-wave in VTI media and obtained by the relaxation functions of the standard linear solid model and the Kjartansson's constant Q model respectively. Anelasticity including amplitude attenuation and phase dispersion can be dealt with by the proposed wave equation separately. With the coordinate transform, the corresponding two pure qP-wave viscoacoustic anisotropic wave equations for titled transversely isotropic media also are derived. Different from the common viscoacoustic anisotropic wave equation (a coupled second-order partial differential equations system), the new wave equations are simplified by decomposing the original pseudo-differential operator into a differential and a scalar opera- tors. For numerical calculation, the new wave equations can be solved more efficiently than the coupled wave equations. Meanwhile the new wave equations could simulate pure qP-wave steadily in attenuation anisotropic media without quasi-SV wave artifacts. Some synthetic examples, including attenuation Hess and Marmousi-2 models, demonstrate the feasibility of the derived pure qP-wave viscoacoustic wave equations in transversely isotropic media.