利用组合质量矩阵压制数值频散

Using combined mass matrix to suppress numeric dispersion

波动方程数值模拟一直受到频散效应的影响。利用有限元模拟声波方程时,协调质量矩阵和集中质量矩阵对频散误差起着相反的作用:协调质量矩阵使频散误差领先于真实信号,而集中质量矩阵使频散误差落后于真实信号。因此利用两种质量矩阵的线性组合能有效压制数值频散。速度对组合系数的影响很小,在2500～4000m/s范围内,最优组合系数均约为0.5。这种压制数值频散的方法,具有不增加额外计算量且不导致算法复杂的特点,能够适应变速模型。

The numeric simulation of wave equation always suffers from the dispersion effect.Using finite-element simulation of acoustic wave equation, the consistent mass matrix plays an opposite role to lumped mass matrix in dispersion error,consistent mass matrix makes the dispersion error to be ahead of the true signal,while the lumped mass matrix makes it to fall behind.Using linear combination of two mass matrixes can effectively suppress numeric dispersion.The velocity has little influence on combining coefficient,and optimal combining coefficient is about 0.5 when the velocity is in 2500～4000 m/s.Using the method for suppressing numeric dispersion is characteristics of neither adding extra computational efforts nor leading the algorithm to complex,which can be adaptive to velocity-changing model.