Seismic Wavefield Modeling And Migration Method In Anisotropic Attenuation Media

Due to the aligned fluid-filled or gas-bearing fractures and thin-layers with different velocity and attenuation properties,the actual earth media may exhibit anisotropic absorption effects,causing the velocity and attenuation of seismic wave to vary with direction.The attenuation anisotropy may be more significant than velocity anisotropy,which affects the kinematic and dynamic characteristics of seismic wave propagation(such as amplitude,phase/travel time)and the quality of seismic migration imaging.Therefore,the development of wave equation theory and forward modeling method for anisotropic absorbing media that can quantitatively describe arbitrary attenuation anisotropy characteristics can more accurately understand the propagation law of seismic waves in actual subsurface media.Stable and efficient anisotropic attenuation compensation reverse time migration imaging method can provide higher-resolution seismic data for complex structure and lithological reservoir exploration(such as unconventional reservoirs,fractured reservoirs).The study of seismic attenuation and anisotropy is of vital importance in earthquake seismology and exploration seismology.This paper first numerically analyzes the anisotropic absorption effect of the medium under the two theoretical mechanisms of thin-layer equivalence and fracture induction.I show that the attenuation anisotropy may be stronger than the velocity anisotropy,and there is a certain similarity in symmetry of the quality factor and velocity anisotropy.Then,based on the viscoelastic theory,I extend the constant-Q attenuation model to anisotropic media and derive the viscoelastic anisotropic wave equation involving fractional time derivative or fractional Laplace operator.In order to reduce the complexity of considering anisotropic viscoelasticity in practical applications,based on the acoustic anisotropic approximate assumption,starting from the constant-Q viscoelastic anisotropic constitutive equation and the q P wave complex dispersion equation,I further derive the pseudo-and pure-viscoacoustic anisotropic wave equations with fractional Laplaces,which are used in only P-wave propagation simulation.The Laplace operator wave equation can be solved accurately and efficiently in the time domain using the generalized pseudospectral method.Finally,based on the derived viscoacoustic anisotropy equation propagation operator,an anisotropic attenuation compensated reverse-time migration imaging method was developed.Through a series of numerical experiments and theoretical analysis,the influence of attenuation anisotropy effect on seismic wavefield is illustrated,and the applicability of the new equation and forward modeling algorithm in complex media is proved.The research results show that the new equation can accurately describe the constant-Q attenuation and arbitrary attenuation anisotropy characteristics of seismic waves.The wave equation with fractional Laplacian operator can model the decoupled amplitude loss and velocity dispersion effects.The attenuation anisotropy compensation reverse time migration method based on the new equation propagation operator can compensate the anisotropic amplitude attenuation and correct the phase dispersion effect at the same time.Compared with conventional reverse time migration method under the assumption of acoustic and isotropic attenuation media,it can obtain migration results with more balanced amplitude energy,higher resolution and more accurate imaging position.