横向各向同性介质地震波场数值模拟研究

地震波场数值模拟是理解地震波在地下介质中的传播特点，帮助解释观测数据的有效手段，而提高计算精度和运算效率是所有波场数值模拟方法研究所追求的目标.有限差分技术是求解波动方程计算效率最高、应用最为广泛的方法之一.但传统的有限差分技术计算过程中的数值频散问题影响了该技术的计算精度与计算效率.本文通过交错网格高阶有限差分技术与通量校正传输方法（Flux|corrected transport method，FCT）相结合, 对横向各向同性介质（Transverse isotropic medium，TI）一阶速度|应力弹性波动方程组进行了数值求解研究.波场快照数值模拟结果表明，本文研究的数值模拟方法与波动方程二阶有限差分方法、交错网格四阶有限差分方法相比，在压制网格数值频散方面有明显的优势，计算精度提高，而且可以利用较大的空间步长，提高计算效率.

Study on seismic wave field numerical simulation in transverse isotropic medium

Seismic wave field numerical simulation is one of effective methods for understanding seismic wave characterization during spreading in underground medium,and for helping to interpret the recording data.Improving computation precision and efficiency is the main objective of wave field numerical simulation studies.As one of the most efficient methods,the finite difference technique is widely used in wave equation solution.But the shortcoming of the traditional numerical frequency dispersion during wave equation finite difference solvingt affects the calculation efficiency and precision.In the paper,one-order velocity-stress elastic wave equations in transverse isotropic medium are solved by a staggered-grid high-order difference flux-corrected transport method.The snapshots computed by different difference methods show that the method study in the paper work more favorable in decreasing grid dispersion and improving computation precision compared with two-order and staggered-grid four-order difference methods.Therefore the longer spatial step length can be utilized to improve computation efficiency.