Research On Pre-stack Time Migration In Anisotropic Media

Seismic migration is a wave-equation-based process that removes distortions fromreflection records by moving events. Pre-stack time migration is an effective tool for imagingseismic wave field in complex medium. A transversely isotropic (TI) model with a tiltedsymmetry axis is regarded as one of the most effective approximations to the earth subsurface,especially for imaging purposes. The propagation of seismic wave is unique in anisotropicmedia. The conventional seismic migration methods based on isotropic theory cannot solvethe migration of seismic wave in anisotropic media effectively, causing lower imagingprecision. While the migration methods based on anisotropic theory can overcome the defectand improve imaging precision. Only migration methods based on the anisotropic mediumcan increase migration accuracy. Therefore, with the development of anisotropy andmulti-component exploration, it is essential to develop anisotropic pre-stack time migrationmethod. The goal of this paper is to image the seismic wave field in transversely isotropicmedia with a vertical symmetry axis (VTI) accurately. On the basis of theoretical analysis andnumerical simulation, the research of this paper is focused on the algorithm of pre-stack timemigration based on anisotropic theory.In pre-stack time migration, computation of travel-time is the precondition of goodmigration result. So when the layers have the anisotropic properties，seismic wave’s velocityand move-out will become complex.It needs to acquire the anisotropic move-out formulasand the connection of layers parameters with velocity. We are using seismic wave informationsufficiently to analyses the seismic data. Kirchhoff pre-stack time migration for transverselyisotropic media with a vertical symmetry axis (VTI media) may be implemented using theoffset-midpoint travel-time equation proposed by Alkhalifah (2000). The derivation of suchequation for VTI media requires approximations that pertain to high frequency and weakanisotropy. Yet the resultant offset-midpoint travel-time equation for VTI media is accuratefor even strong anisotropy. This equation is also dependent on two parameters: normalmove-out velocity and the anisotropy parameter.The migration equation takes a formsimilar to conventional Kirchhoff migration. In this paper, I describe the mechanics ofmigration (the algorithms) as well as some of the problems related to anisotropy, such as travel-time accuracy and efficiency, and anisotropic parameter estimation. Pre-stack timemigration imaging factors were systematically studied in this paper. On the basis of literaturesappeared，for the vertical transverse isotropy layers，firstly learn the hyperbolic approximationformula about the reflection move-out on short-spreads; Secondly derivate the non-hyperbolicapproximation formula about the reflection move-out on intermediate-spreads andlong-spreads detailed gain the high precise formula about P wave, and Converted wave. At thesame time get the connection of layer’s anisotropic parameters with move-out curve andvelocity by the numbers. At present, multi-component seismic exploration is being widelyused. This paper presents a method for elastic imaging of multi-component seismic data. Themethod is based on Claerbout’s survey-sinking concept and the elastic Kirchhoff integral forthe displacement field. The main advantage of multi-component Kirchhoff time migrationmethod is numerical efficiency rather than high accuracy. It may be of interest for pre-stackimaging of large data volumes and fast computation of the first pre-stack images ofmulti-component data.Based on the theory above, this paper developed a2-D pre-stack time migrationalgorithm in the anisotropic medium. The algorithm was applied to synthetic records and thereal data. The results show that this approach can produce clear images, remove the effect ofanisotropic, and have satisfactory practical application effect.