Research On Prestack Reverse-time Depth Mgration OfQuai-P Wave Equations VTI Media

Elastic anisotropy is ubiquitous in subsurface media, the propagation of seismic wave is unique in anisotropic media. The conventional seismic migration methods based on isotropic theory can not solve the migration of seismic wave in anisotropic media effectively, causing lower imaging precision. While the migration methods based on anisotropic theory can overcome the defect and improve imaging precision. Prestack depth migration is an effective tool for imaging seismic wave field in complex medium, migration algorithm and its theoretical basis is the key to determine the effect of migration results. Prestack reverse-time depth migration based on the two-way wave equation is widely recognized by people for its advantages such as no dip restriction and high imaging precision. The goal of this paper is to image the seismic wave field in transversely isotropic media with a vertical symmetry axis(VTI) accurately. On the basis of theoretical analysis and numerical simulation, the research of this paper is focused on the algorithm of prestack reverse-time depth migration based on anisotropic theory .In the aspect of theoretical analysis, based on the basic theories of elastic wave in anisotropic media, the phase velocity and group velocity of TTI media and VTI media are obtained by solving the Christoffel equation in TTI media, and the effect of the change of elastic constant on the wave field in anisotropic media is discussed. In the aspect of numerical simulation, according to the one-order qP wave equations in VTI media, a high-order finite-difference scheme in staggered-grid is derived, the perfectly matched layer (PML) absorbing boundary condition is adopted to resolve the artificial boundary problem. Based on them, the forward modeling of the equations is carried out.In the aspect of migration algorithm, based on the one-order qP wave equations in VTI media, high-order finite-difference schemes in staggered-grid for reverse-time extrapolation of the equations and the PML absorbing layer boundary equation are derived. Prestack reverse-time depth migration of qP wave equations in VTI media is carried out using maximum amplitude method of down-going wave-field and normalized cross-correlation imaging conditions. The impulse response of prestack reverse-time depth migration of the equations in different models and the effect of anisotropy on migration results according to model test are analyzed. Through the research and analysis above, some conclusions are obtained:1. High-order finite-difference method in staggered-grid can simulate the propagation of qP wave in VTI media accurately and obtain results with high precision; PML absorbing boundary condition can suppress the reflection of artificial boundary effectively, proving that it is a perfect boundary condition; One-order qP wave equations can describe the kinematic characteristics of qP wave in VTI media with sufficient precision and has a good approximation of the dynamic characteristics of qP wave in VTI media.2. Prestack reverse-time depth migration can image structures with intense lateral velocity variation and steep dip properly and has good imaging effect for complex models; Reverse-time migration imaging condition using normalized cross-correlation has better imaging ability. The impact of anisotropy can not be ignored in the migration of seismic data in anisotropic media. Better imaging results can be obtained using anisotropic migration algorithm for P-wave data acquired in anisotropic regions.