中文摘要：

声波在具有不规则自由表面的粘弹性介质传播的数值模拟工作在地震勘探，地震预测中非常重要，特别是当模型有起伏的自由界面和较强的衰减特性时更是如此。基于镜像方法和直接方法，本文发展了一种二维有限差分算法，可以模拟不规则自由表面引起的声波散射问题。该方法将自由表面条件与速度应力方程结合求解粘弹性波动方程，在垂直和水平自由段及拐点处设置相应的边界条件。该方法假设自由表面穿过剪切应力和相应参数的网格点。为了提高计算精度，分别计算了水平和垂直方向上应力镜像值，而对质点速度，采用先水平方向后垂直方向分析进行镜像计算和更新。将粘弹性水平自由表面镜像方法和不同倾斜度平滑自由表面的改进方法的数值结果进行对比，并验证了算法的精度。

英文摘要：

Modelling acoustic wave propagation in heterogeneous viscoelastic media with free-surfaces plays an important role in seismic exploration, earthquake prediction, especially for the model with a rugged free surface and strong attenuation. Based on imaging and direct methods, we have developed a new improved two-dimensional finite-difference algorithm for simulating acoustic wave scattering from an irregular free surface. The free surface conditions are combined with a velocity-stress formulation for full viscoelastic wave equations. The boundary conditions are implemented in the vertical and horizontal free surface segments and at their comers. The method assumes that the free surface passes through the grid points of shear stress and the corresponding shear memory variables. In order to increase accuracy, imaging isperformed for stress components in both horizontal and vertical directions independently. To update particle velocities, imaging and updating are first carded out in horizontal direction, and then, in vertical direction. Numerical results are compared for a viscoelastic fiat horizontal free surface with the imaging method and those for flat free surface of various slope angles with the improved method, and are shown to be in good agreement.