Study On Method Of Forward Modeling And Reverse Time Migration In Viscous Media

Real earth media are anelastic, which affects both the kinematics and dynamics of propagating waves: waves are attenuated and dispersed. If anelastic effects are neglected, migration and inversion can yield erroneous results, and it is hard to obtain detailed subsurface information and high resolution image directly. The anelastic effects in real rocks can be well described by a viscoelastic model. And forward modeling is the base of migration and inversion. So the numerical simulation and reverse time migration in viscous media are researched and studied in this thesis.Starting from basic theory of viscoelastic media, we deduce the viscoelstic wave equation of GSLS, and develops and consummates the high-order staggered grid finite-difference method which solve the wave equation. We also establish overdetermined system of nonlinear equations using the Q formula of viscoacoustic/viscoelastic media with no approximation and assumption. And the nonlinear optimization method is adopted to directly compute the relaxation time to fitting the nearly constant Q model. For absorbing boundary condition, we combine the C-PML and M-PML to develop MC-PML which has both higher stability and better absorption effect.Then the dispersion and stability of above-mentioned difference method are analyzed. The discrete difference schemes are Fourier transformed to the frequency-wavenumber domain, where they are compared to the analytical dispersion of the viscoelastic media. The practical criterion is proposed through researching the numerical dispersion degree in different cases. The stability can be investigated through the roots of the Z-transformed and Fourier transformed difference scheme(modal equation), and the stability condition is obtained from the range of roots.P- and S-wave can be generated in viscoelatic media and only coupling wave field which contains both P- and S-wave is obtained when original viscoelastic wave equation is used for numerical simulation. Based on the previous research, this thesis gives an equivalent equation which contains variables of both the hybrid wavefield and the pure P- and S-wave wavefield. Using the finite difference method to solve the wave equation, we obtain perfectly separated wavefield of pure P- and S-wave while obtaining hybrid wavefield. And the information of mutual transformation of P- and S-wave energy is preserved.Viscous effects can influence wave propagation, and there is no exception in migration. These unwanted effects are prefered to be corrected in a prestack depth migration. Based on the dispersion relation in a viscoacoustic model of SLS, we derive a viscoacoustic wave equation in time domain. The equation includes a fractional Laplician operator for viscosity. And then a Q-RTM method is developed to compensate the influence of viscosity. Two regularization method are introduced to stabilize the extrapolating process. And the numerical test shows the validity.