复杂地表边界元-体积元波动方程数值模拟

摘要

复杂近地表引起来自深部构造的地震反射信号振幅和相位的异常变化,是影响复杂近地表地区地震资料品质的主要原因.本文采用边界元-体积元方法,通过求解含复杂地表的波动积分方程,来模拟地震波在复杂近地表构造中的传播.其中,边界元法模拟地形起伏和表层地质结构对地震波传播的影响；体积元法模拟起伏地表下非均质低降速层的影响.与其他数值模拟方法比较,其主要优点为几何上精确描述不规则地表界面,实现精确模拟自由表面对地震波的边界散射；显式应用近地表地层界面的连续边界条件,实现半解析的数值模拟；分区处理近地表复杂结构,有效模拟复杂地表下非均匀介质对地震波场的体散射.数值试验结果表明了该方法的实用性和有效性.%Complex near surface causes the anomalous variation of the amplitude and phase of seismic reflection signal from deep structures, and it is the most important factor to degrade the quality of seismic data. In this paper, we use the boundary-volume integral equation technique to simulate the seismic wave propagation in the complex near surface structure by solving the wave propagation equation with complex near surface condition. In the boundary-volume integral equation technique, the boundary element method can simulate irregular surface and geological structure for seismic wave propagation, and the volume element method can simulate the effect of the heterogeneous medium in low subweathered zone for the seismic wave propagation. Compared with other numerical simulation methods, the main advantage of the boundary-volume integral equation technique is its accurate geometric description of irregular surface and interface to simulate the boundary scattering waves by the free surface; it explicitly applies the continuous boundary conditions of the complex near surface to implement the semi-analytical numerical simulation; it can deal with the complex near surface structure piecewise and effectively simulate the scattering body wave field caused by the inhomogeneous medium under the complex near surface. Numerical results show that the method is practical and effective.