Abstract：Wave equation decomposition means wave equation decomposed from elastic wave equation to describe individual wavefield independent propagation. In anisotropic medium, P-wave and S-wave are coupling propagation and without decoupling nature generally. The paper carried out elastic wave equation decomposition in 3-D TTI medium from two ways: Thomsen weak anisotropic approximation and acoustic hypothesis approximation. Using eigenvalue method to solve the Christoffel equation of elastic wave equation in 3-D TTI medium and to get precious dispersion relation equation describing SH wave, qP-wave and qSV-wave, and the wave equation in time-space domain describing qP-wave and qSV-wave propagation in weak anisotropic condition was deduced by Thomsen weak anisotropic theory; the wave equation describing qP-wave propagation in 3-D TTI medium was deduced based on acoustic synthesis theory and starting from dispersion relation equation coupling qP-wave to qSV-wave in 3-D TTI medium. The numeric case showed the wave equation of qP-wave and qSV-wave in 3-D TTI medium by wave equation decomposition has higher precision, laid theoretical foundation for studying forward simulation and depth migration algorithm of qP-wave and qSV-wave in 3-D TTI medium.
