A Modified Pure P-Wave Equation and RTM for TTI Media

For the study of reverse-time migration, the stimulation of the comprehensive wave-field plays an important role. Therefore, an accurate and fast pure P-wave equation for anisotropic media is the basis of P-wave reverse-time migration. Based on the hybrid pseudo-spectral and finite-difference theory, we deduce an efficient pure P-wave equation in TTI media. We obtain a simplified approximation representation of the P-wave velocity following the exact phase velocity representation. We then use the rotated wave-number to improve the validity of simplified representation. The phase angle is replaced by the wave-number term which is subsequently rotated referring to the dip angle. Since the equation only contains a pair of Fourier transform and inverse transform, its computational efficiency is significantly improved. We analyze the accuracy of the proposed velocity representation. The results show that it coincides the exact phase velocity better. We then test the forward modeling and reverse-time migration in BP 2007 TTI model. The results show that the proposed pure P-wave equation can stimulate the comprehensive wavefield accurately and efficiently. It also can be applied in reverse-time migration for complex TTI media.