| The anisotropy of subsurface media has large effects on seismic wavefield propagation and reverse-time migration(RTM).Ignoring anisotropy will reduce the signal-to-noise ratio and the reliability of RTM imaging profile,which is difficult to meet the requirements of oil and gas exploration with high accuracy at present stage.Absorption and attenuation are the inherent properties of the medium.The amplitude attenuation and velocity dispersion usually occur to the seismic wave propagation due to the absorption and attenuation of the medium.In addition to velocity anisotropy,the absorption and attenuation are also anisotropic which has been demonstrated by experimental measurements and field observations.Therefore,it is of great significance to develop a Q-compensated RTM method with high accuracy in anisotropic media by taking the anisotropy of velocity and quality factor into consideration.Given the above-mentioned issues,this dissertation mainly focuses on the accurate and efficient numerical algorithms for solving the viscoelastic and viscoacoustic wave equations in vertical transversely isotropic(VTI)media and stable Q-compensated viscoacoustic RTM methods.The main achievements are as follows:Firstly,the fractional-order viscoelastic wave equation,the complex-velocity based viscoelastic wave equation and their decoupled formulations are derived based on the constant-Q theory.Using the accurate relation between angular frequency and reference velocity,the improved viscoelastic wave equations are further derived.On the condition of weak attenuation,two viscoelastic wave equations are proved to be equivalent.Both equations can well describe wave propagations and wavefield characteristics in viscoelastic media.Secondly,for the anisotropy of velocity and Q,the fractional-order viscoelastic and viscoacoustic wave equations are developed in two-dimensional(2D)VTI media.A least-squares fractional polynomial fitting algorithm and a Taylor-series expansion method are proposed to solve the equations.The new methods can effectively solve the fractional-order wave equations and realize the wavefield simulation in VTI attenuated media.Numerical modeling results show that the proposed schemes have good performances both on accuracy and efficiency in comparison with low-rank decomposition method.Thirdly,for the anisotropy of velocity and Q,a viscoelastic wave equation in 2D VTI media is derived based on the complex-velocity theory.Combining the anisotropic constitutive equation and P wave dispersion relation,the pseudo-viscoacoustic(PSVA)and pure-viscoacoustic(PUVA)wave equations are derived.Simulation results show that PSVA wavefield has serious SV wave noise which is not affected by P wave attenuation.While PUVA can completely eliminate the SV wave components and generate a PUVA wavefield.Fourthly,the conventional viscoacoustic and viscoelastic wave equations are usually discretized by the second-order accuracy finite-difference.It is easy to suffer from serious time dispersion or even instability when the time step is large.For viscoacoustic medium,a high temporal accuracy viscoacoustic wave equation is developed based on k-space operator and solved by low-rank decomposition.For viscoelastic medium,a high temporal accuracy viscoelastic wave equation is developed based on normalized pseudo-Laplacian operator and solved by least-squares finite-difference and low-rank decomposition.Compared with the conventional method,the new schemes can effectively suppress time dispersion and improve time accuracy of simulation results.Fifthly,seismic wave propagation in attenuated medium has the effects of amplitude attenuation and phase dispersion which lead to low signal-to-noise ratio and incorrect migrated position in RTM results.To solve the issue,a stable Q-compensated viscoacoustic RTM method in VTI media is studied.The acoustic and the compensated viscoacoustic wave equations are used during the RTM process.Meanwhile,the influences of velocity anisotropy and Q anisotropy on RTM results are investigated.The results show that the velocity anisotropy has a great influence on the RTM results,while the influence of Q anisotropy is relatively small.This conclusion is also related to the model parameters. |
