Seismic Full Waveform Modeling & Imaging in Attenuating Media
Abstract
Seismic attenuation strongly affects seismic waveforms by amplitude loss and velocity dispersion. Without proper inclusion of Q parameters, errors can be introduced for seismic full waveform modeling and imaging. Three different (Carcione's, Robertsson's, and the generalized Robertsson's) isotropic viscoelastic wave equations based on the generalized standard linear solid (GSLS) are evaluated. The secondorder displacement equations are derived, and used to demonstrate that, with the same stress relaxation times, these viscoelastic formulations are equivalent. By introducing separate memory variables for P and S relaxation functions, Robertsson's formulation is generalized to allow different P and S wave stress relaxation times, which improves the physical consistency of the Qp and Qs modelled in the seismograms.The three formulations have comparable computational cost. 3D seismic finitedifference forward modeling is applied to anisotropic viscoelastic media. The viscoelastic Tmatrix (a dynamic effective medium theory) relates frequencydependent anisotropic attenuation and velocity to reservoir properties in fractured HTI media, based on the mesoscale fluid flow attenuation mechanism. The seismic signatures resulting from changing viscoelastic reservoir properties are easily visible. Analysis of 3D viscoelastic seismograms suggests that anisotropic attenuation is a potential tool for reservoir characterization. To compensate the Q effects during reversetime migration (RTM) in viscoacoustic and viscoelastic media, amplitudes need to be compensated during wave propagation; the propagation velocity of the Qcompensated wavefield needs to be the same as in the attenuating wavefield, to restore the phase information. Both amplitude and phase can be compensated when the velocity dispersion and the amplitude loss are decoupled. For wave equations based on the GSLS, because Q effects are coupled in the memory variables, Qcompensated wavefield propagates faster than the attenuating wavefield, and introduce unwanted phase shift. Numerical examples show that there are phase (depth) shifts in the Qcompensated RTM images from the GSLS equation. An adjointbased leastsquares reversetime migration is proposed for viscoelastic media (QLSRTM), to compensate the attenuation losses in P and S images. The viscoelastic adjoint operator, and the P and S modulus perturbation imaging conditions are derived using the adjointstate method and an augmented Lagrangian functional. QLSRTM solves the viscoelastic linearized modeling operator for synthetic data, and the adjoint operator is used for back propagating the data residual. QLSRTM is capable of iteratively updating the P and S modulus perturbations,in the direction of minimizing data residuals, and attenuation loss is iteratively compensated. A novel Q compensation approach is developed for adjoint seismic imaging by pseudodifferential scaling. With a correct Q model included in the migration algorithm, propagation effects, including the Q effects, can be compensated with the application of the inverse Hessian to the RTM image. Pseudodifferential scaling is used to efficiently approximate the action of the inverse Hessian. Numerical examples indicate that the adjoint RTM images with pseudodifferential scaling approximate the true model perturbation, and can be used as wellconditioned gradients for leastsquares imaging.
 Publication:

Ph.D. Thesis
 Pub Date:
 2017
 Bibcode:
 2017PhDT.......123G
 Keywords:

 Geophysics