Finite Difference Numerical Modeling Of Seismic Wavefields In Tansversely Isotropic Media With A Vertical Axis

Seismic numerical modeling is an improtant tool to understand the wave propagation characteristics in anstropic medium. In the numerical simulation field, by virtue of its high efficiency and easy implementation of boundary conditions, the finite difference method is attrative. However, it has two key questions, which are called numerical dispersion and aritifical boundary conditions. Based on the theory of staggered-grid finite difference, firstly, we focus on the numerical dispersion as well as the artifical boundary conditons, and put forward the corresponding improvement strategies; Secondly, we simulate seismic wave propagation in 2D vertical transversely isotropic media, and analyze the seismic numerical modeling results; Finally, we successfully separate the elastic wavefield.To deal with the numerical dispersion, firstly, by combining the staggered-grid technology with the compact finite difference scheme, we derive a compact staggered-grid finite difference scheme in vertical transverse isotropic medium from the first-order velocity-stress wave equations. With the comparison of the principal truncation error terms of the compact staggered-grid finite difference scheme, the staggered-grid finite difference scheme and the compact finite difference scheme, the thesis analyzes the approximation accuracy of the above three schemes through Fourier analysis. Secondly, based on the optimization theory, we construct two forms of Lagrange function by introducing strong and weak constraint, respectively, and further obtain the optimization operator for staggred-grid finite difference via the solution of conditional extremum value, which is also compared with the normal Taylor expansion operator.In order to weaken the artifical boundary reflection, we summarize several kinds of typical artifical boundary conditions, and point out their shortcomings, respectively. After analyzing the influence factors of the sponge methods in detail, we present the improved damping functions and their application principles. The perfectly matched layer (PML) absorbing boundary condition (ABC) has been widely used for seismic numerical modeling. In the paper, we implement the split PMLs for the velocity-stress formulation of elastodynamics, and adapt the proposed application principles to the PMLs. The simulation results have shown the vadity of the improved sponge methods as well as the PMLs.In order to analyze the wave propagation characteristics easily, it's necessary to carry out the separation of the wavefields. Taking the divergence and the curl of the vectorial wavefield during the finite difference modeling, we separate P- and converted SV-waves in 2D elastic seismograms and get clear wavefields by introducing optimal difference operator. The rusults has also proved the validity of the improved strategies.