Accurate seismic exploration demands sophisticated seismic techniques that can be applied to any complex geological structures. The key of most recent seismic processing techniques is wave propagation modelling. For accurate simulation of the seismic wavefield, the characteristics of the real Earth media should be appropriately considered, such as attenuation effects and anisotropy.
This dissertation aims to address the attenuation problems in seismic wavefield modelling in attenuative media and its related applications. My work presented in this dissertation includes
1. A viscoelastic wave equation for isotropic media is proposed. The attenuation operator applied in the wave equation consists of separate terms, which are related to velocity dispersion and energy absorption effects respectively. It is derived that the two effects are completely decoupled.
2. A numerical scheme based on low-rank approximation is presented for wave simulation in heterogeneous attenuative media. This method can achieve very high accuracy while the computational cost is greatly reduced compared with conventional method.
3. In order to take account of the anisotropic attenuation, a generalized viscoelastic wave equation is presented. The velocity dispersion and energy absorption effects are also decoupled in the encapsulated attenuation operators. Based on this, the seismic wave propagation in arbitrary anisotropic media with anisotropic attenuation can be accurately simulated.
4. Q-compensated reverse-time migration (RTM) is investigated. It is shown that the velocity dispersion and energy absorption effects should be taken care of separately. Attributed to the completed decoupled attenuation effects in the derived viscoelastic wave equation, the \Q-compensation operator is derived. As a result, the dispersion correction and energy compensation is successfully separated and can be implemented simultaneously. Based on this, different \Q-compensation schemes are analysed and compared.