针对有限元算法在地震波数值模拟中的数值频散问题，利用集中质量矩阵双线性插值有限元算法，推导了二维声波方程的频散函数。在此基础上采用定量分析方法，对比分析了网格纵横长度比变化时的入射方向、空间采样间隔、地震波频率以及地层速度对数值频散的影响。数值算例和模型正演结果表明：当采用集中质量矩阵双线性插值有限元算法时，为了有效地压制数值频散，在所使用震源子波的峰值频率对应的波长内，采样点数目应不少于20个；减小网格长度的纵横比可以有效地抑制入射角（波传播方向与z轴的夹角）较小的地震波的数值频散；地震波频率越高，传播速度越慢，频散越严重，尤其是当相速度与其所对应的频率比值小于2倍空间采样间隔时，不仅会出现严重的数值频散，还会出现假频现象。%This paper focuses on the dispersion problems of finite element algo-rithm in numerical simulation of seismic wave,and the dispersion function of two-dimensional acoustic wave equation is derived by employing lumped mass matrix and bilinear interpolation finite element algorithm.And,we compared quantitatively the effect of incident direction with the variable ratio of vertical to horizontal grid,spatial sampling interval,seismic wave frequency,and forma-tion velocity on numerical dispersion.The numerical examples and the forward modeling indicate,if we want to suppress the numerical dispersion effectively, it should not be less than 20 samples within the wavelength corresponding to peak frequency of source wavelet;reducing the ratio of vertical to horizontal grid can suppress the numerical dispersion with small incident angle (the angle between the direction of wave propagation and the z axis)remarkably;the slo-wer the propagation velocity of the seismic wave with higher frequency,the more serious its dispersion is;when the ratio of phase velocity to the corre-sponding frequency is less than twice of spatial sampling interval,not only the numerical dispersion becomes very serious,but also the aliasing phenomenon will happen.
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