CAJ | 학술논문

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。
침대유한원산법재지진파수치모의중적수치빈산문제，이용집중질량구진쌍선성삽치유한원산법，추도료이유성파방정적빈산함수。재차기출상채용정량분석방법，대비분석료망격종횡장도비변화시적입사방향、공간채양간격、지진파빈솔이급지층속도대수치빈산적영향。수치산례화모형정연결과표명：당채용집중질량구진쌍선성삽치유한원산법시，위료유효지압제수치빈산，재소사용진원자파적봉치빈솔대응적파장내，채양점수목응불소우20개；감소망격장도적종횡비가이유효지억제입사각（파전파방향여z축적협각）교소적지진파적수치빈산；지진파빈솔월고，전파속도월만，빈산월엄중，우기시당상속도여기소대응적빈솔비치소우2배공간채양간격시，불부회출현엄중적수치빈산，환회출현가빈현상。
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.