起伏地表二阶弹性波方程差分策略稳定性分析

Stability analysis of differential strategy for rugged topography by secondorder elastic wave equation based on coordinate transformation

1.西安石油大学地球科学与工程学院，陕西西安710065;2.中国石油大学(北京)CNPC物探重点实验室，北京102249

Tang Wen, Key Laboratory of Geophysical Exploration,CNPC,China University of Petroleum (Beijing),Beijing 102249,China

采用坐标变换的思想将起伏地表情况的曲线网格变换成水平地表情况的矩形网格，推导出了变换后的二阶弹性波动方程，研究了基于坐标变换的起伏地表二阶弹性波场有限差分数值模拟方法。重点针对起伏地表变换成水平地表后的3种不同特点的自由边界条件，包括隐式、单边伪节点和混合自由地表边界条件的处理，并给出了具体的差分格式。数值模拟结果表明，起伏地表二阶弹性波方程模拟方法是有效可行的，但不同的地表处理方法对模拟结果有不同的影响。在这3种自由地表处理方法中，隐式的自由地表边界条件有最好的稳定性。

Curved grid with undulating surface is transformed into rectangular grid with horizontal surface and secondorder elastic wave equation based on the idea of coordinate transformation is deduced.The finite difference numerical simulation method of elastic wavefield including rugged topography by the transformed secondorder elastic wave equation is studied.Three kinds of free boundary conditions of the flat surface,including implicit,unilateral pseudo node and mixed free surface boundary conditions are introduced and the concrete difference schemes are given.Numerical simulation results show that the secondorder elastic wave equation simulation method including rugged topography is effective and feasible and different free surface processing methods have different influences on the stability of simulation results.The implicit free boundary condition is more stable than the other two surface boundary conditions.

陕西省教育厅专项科研计划项目(2013JK0845)、国家重点基础研究发展计划(973)项目(2013CB228600)和国家自然科学基金项目(41372118)共同资助。

10.3969/j.issn.10001441.2013.05.003