Pure quasi-P wave forward modeling method in TI media and its application to RTM

Based on the exact dispersion relation proposed by Tsvankin, and adopting the approximate expanded method, this work derives the decoupled pure quasi-P wave equations in a TTI medium. Then we divide the pseudodifferential operator in the equations into a Laplace operator and a scalar operator to indicate the exact transmission direction of qP waves, and establish second order pure qP wave equations in the time domain. In this induction process, there is no need to set S wave velocity at 0, which can describe the kinetic features of qP waves in a more accurate way. Compared with the second-order decoupled qP wave equations in the wavenumber domain, this method has a higher computation efficiency and lower storage demand. While compared with the second-order pure qP wave equations in the time domain which is based on derivatibh from Alkhalifah dispersion relation, it has better suppression of artifacts and less numeral error, being more general. But using this method to solve wave vectors is asymptotic approximation to adopting first-order of wavefield gradients, which might cause inaccurate amplitude of qP waves perpendicular to the axis. In order to correct amplitude and apply the elliptical decomposition method to these equations, pure qP wave elliptical decomposition equations have been derived, achieving more balanced amplitude. Compared with equations proposed by Xu, the wavefield amplitude derived from pure qP wave elliptical decomposition equations established in this paper is more accurate. Firstly, we choose a homogeneous TTI medium to conduct forward modeling of qP waves, and analyze the amplitude of single trace of the qP wavefield, verifying the correctness and effectiveness of the qP wave equations and qP. wave elliptical decomposition equations constructed in this paper. Then, we choose the BP TTI model to conduct forward modeling of qP waves, and combine the results of stimulation and amplitude analysis of a homogeneous TTI medium, highlighting the advantages and adaptability of qP wave elliptical decomposition equations established in this paper. Lastly, we apply the qP wave elliptical decomposition wave equations derived in this paper to implement reverse time migration imaging for a thrust model and BP TTI model, which verifies feasibility of the equations and its applicability in RTM.