The Wave-field Simulation And Decomposition By Rotated Staggered Grid Finite-difference In TTI Media

Seismic anisotropy and the viscosity of the medium in the Earth is prevalent, and which result in the coupling of the compression wave and shear wave and the splitting of the shear waves and the delay of wavelet and the decrease of the amplitude and the widen of the wavelet and the distortion of the waveform. The propagation of seismic waves in the medium with anisotropy and viscoelasticity is an important topic in seismology, it can testify the accuracy of the theory and help to recognize the different waves in the seismic records and help to design the shot and receiver system.The rotated staggered grid is a deformation of the classic staggered grid, it redefine the location of the wave-field components and the physical parameter. The axis of the coordinate system is still vertical and horizontal. The stress components and the physical parameters are located in the vertex of the grid, and the velocity components are located in another vertex of the gird along the diagonal. The computations of the derivatives along the axis are a linear combination of the derivatives along the diagonal. The average of the elastic constants is not needed in the simulation of the elastic waves, and this advantage is very important to simulate the propagate the waves in the viscoelastic medium and the anisotropic medium and pore medium, it overcomes the instability of the classic staggered grid in the wave-field simulation, and since it does not need the average of the physical parameters, the accuracy is improved.According to the anisotropy theory, the compressional waves and the shear waves are coupled with each other. The seismic wave-field obtained by the ordinary methods is a mixture of the compression waves and the shear waves, and this is the difficulty to research the propagation of pure compression waves and pure shear waves. The couple of compression waves and shear waves is a difficult point to obtain an accurate image of the earth, so we need to separate the compression and shear waves. In the anisotropic medium,the waves polarization vectors are not completely parallel or perpendicular to the wave vectors, so we cannot separate the compression waves and shear waves by the calculate of divergence and curl. In this paper, we separate the compression and shear waves by project the wave-field to the compression wave polarization vectors and project the wave-field to the shear wave polarization vectors, and through this way we obtained the pure snapshot and seismic records of pure compression waves and shear waves.In this paper, we obtained the snapshots and seismic records in the TTI medium(Titled Transverse Isotropy) by the rotated staggered grid high-order finite-difference method. And we separated the coupled compression and shear waves. Since the X and Z components are at the same position, the average or interposition of velocity component is not needed, so the simulation accuracy and computation speed is improved. In order to decrease the reflection from the man-made boundary, we applied the PML and CE boundary.