Research On Numerical Simulation For Pure P-wave In Anisotropic Medium And Reverse Time Migration

Seismic numerical simulation is not only an important method to study the propagation characteristics of seismic waves in subsurface, but also an effective tool to analyze bedding structures and fine-structures of the deep. Seismic numerical simulation has attracted more and more attention in the field of hydrocarbon exploration and thus has been used extensively in various steps of seismic exploration including data acquisition, processing and interpretation. Anisotropic medium are distributed widely in subsurface due to inducing stress, oriented linear fracture, etc. Meanwhile, the propagation and imaging of seismic waves are affected by stratigraphic anisotropy. Therefore, seismic numerical simulation of anisotropic medium plays a vital role in the exploration of complex structure of subsurface.Conventional numerical simulation of elastic wave equation has been developed maturely, However, numerous parameters, large calculation and memory space are needed in the computational process, which made the method time-consuming. Gradually, numerical simulation of acoustic wave equation had been widely used. Acoustic approximation assumption is adopted in this paper. To simplify the acoustic wave equation, S-wave velocities along the symmetry axis were set zero. Derived acoustic wave equation not only preserved useful information of P-waves, but also reduced the computing time substantially and enhanced the computational efficiency under the same simulation precision.The most practical method is the finite difference method of seismic wave equation numerical solution, because of its simple algorithm and high computational efficiency. Based on acoustic approximation assumption, acoustic wave equations of VTI, TTI anisotropic medium were derived in this paper, combined with numerical simulation using finite difference method(FDM). However, unfavorable result with severe frequency dispersion was got. Although increasing finite difference order can diminish frequency dispersion, such method would result in the decrease of computational efficiency, the augment of computer memory space, and the wave front of S-wave in numerical simulation results. Subsequently, based on wave field extrapolation theory, pure P-wave equation in time-wavenumber domain was derived in this paper, followed with solving method of Fourier finite-difference(FFD). The wave front of S-wave was removed effectively in this numerical simulation results, but frequency dispersion still existed to a certain extent. Finally, based on the precise phase velocity expression proposed by Tsvankin, by using approximation of square root, pure P-wave equation of 2D TTI medium was derived, after that, rapid expansion method(REM) was used to proceed numerical simulation. By this way, the computational efficiency and simulation accuracy had achieved very good results.Reverse time migration is one of the most common types of migration. It is accomplished through wave equation by reverse extrapolation of seismic data on timelines. In the process of reverse time migration, noise attenuation can be achieved. Additionally, this method can be used regardless of the limitation of dip angle in the process of imaging, which is more suitable in complex geological structure imaging. Finally, We have been achieved good results in a simple model by the trial of reverse-time migration in the 2D pure P-wave equation of TTI medium...