起伏地表复杂介质波动方程有限元数值模拟方法

波动方程数值模拟是深入研究地震波传播规律的有效方法.有限差分法因其方法简单、精度高而得到了广泛的应用.但其缺点是不能准确模拟具有复杂几何形态的物性界面.因而当遇到起伏地表或复杂构造时，求解精度低.为了准确模拟起伏地形、复杂构造和复杂介质条件下的地震波场，本文采用有限元法模拟二维声波方程.用三角形单元模拟地形和速度界面；把单元内的场和波速均看作单元上的线性函数，以适应复杂介质压制边角散射；采用吸收边界条件去除来自截断边界上的反射；采用集中质量矩阵和集中阻尼矩阵使得显式时间递推无需对矩阵求逆，提高了计算效率.对模型的计算表明该方法正确有效.

Wave equation finite-element modeling including rugged topography and complicated medium

Wave equation modeling is a effective means of research the wave propagate phenomena.Because of simpleness and high-accuracy,finite-difference modeling has been applied wildly.As a result of difficult to deal with complex geometry interface,finite-difference has low-accuracy when encountering rugged topography or complicated structure.In order to accurately modeling wave field including complicated geology,this paper presents finite-element method solving 2-D acoustic wave equation.Triangular elements were adopted for approximating free surface and velocity interfaces.Both field and velocity were regarded as linear functions in elements to adapt to complex medium.Absorbing boundary conditions were employed for eliminating reflection from truncation boundaries.In order to improving computation efficiency,lumped mass matrix and lumped damp matrix were adopted for reason of enable avoid matrix inversion.The modeling results of examples proved the method's validity.