三维波动方程的数值频散关系及其叠前和叠后数值模拟
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摘要
采用适于三维各向同性介质正演的有限差分格式 ,对声波方程进行了差分离散 ,导出了差分格式的数值频散关系。研究表明 ,三维正演的数值频散主要受差分精度及网格空间步长的影响 ,尤以后者影响更甚。在相同的条件下 ,剖分步长越大及差分精度越低 ,数值频散现象越明显。研究还表明 ,剖分网格有低通滤波作用 ,因而在正演时应使激发源的主要频率远离网格的截止频率 ,以保证精度。在此基础上对某地质模型进行了叠前和叠后数值模拟。计算结果表明 ,叠前模拟能够比较真实地反映地震波在地下介质中的传播规律 ,但计算量过大 ;叠后模拟时 ,爆炸界面法能较好地反映地下反射界面形状 ,但不宜计算较大的模型 ;平面波照射法可用于计算较大的模型 ,且能较好地反映波的动力学特征 ,但不能精确地反映界面形态
By using high accurate finite difference to approximate the derivative of 3 D acoustic wave equation, a forward modeling technique applicable for anisotropic media called high order difference scheme of 3 D seismic simulation is established. A numerical dispersion relationship is proposed, which is mainly influenced by both the finite difference accuracy and the grid size. The latter factor has more influence on it. In the same conditions, the numerical dispersion will worsen when the grid becomes bigger or difference accuracy becomes lower. It is indicated that the grid space has a function of low pass filter, so the main frequency component of the hypocenter should be far away from the cut frequency to insure the accuracy of results. The technique is used for prestack and afterstack numerical simulation for a geologic model. The simulation results indicate that the prestack modeling can simulate the procedure of wave propagation faithfully, whereas its workload is much higher than that of the other two methods. The explosive interface method can image the shape of interface with a good accuracy. In the case of a bigger model, the method is very difficult to be used because it needs a large EMS memory. The plane wave radiation method can calculate a large model and describe the dynamics characteristic of waves. However it can not describe the shape of interface accurately.
By using high accurate finite difference to approximate the derivative of 3 D acoustic wave equation, a forward modeling technique applicable for anisotropic media called high order difference scheme of 3 D seismic simulation is established. A numerical dispersion relationship is proposed, which is mainly influenced by both the finite difference accuracy and the grid size. The latter factor has more influence on it. In the same conditions, the numerical dispersion will worsen when the grid becomes bigger or difference accuracy becomes lower. It is indicated that the grid space has a function of low pass filter, so the main frequency component of the hypocenter should be far away from the cut frequency to insure the accuracy of results. The technique is used for prestack and afterstack numerical simulation for a geologic model. The simulation results indicate that the prestack modeling can simulate the procedure of wave propagation faithfully, whereas its workload is much higher than that of the other two methods. The explosive interface method can image the shape of interface with a good accuracy. In the case of a bigger model, the method is very difficult to be used because it needs a large EMS memory. The plane wave radiation method can calculate a large model and describe the dynamics characteristic of waves. However it can not describe the shape of interface accurately.
引文
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[3] 杜世通 .地震波动力学 [M ].东营 :石油大学出版社 ,1996 .
[4 ] 刘洋 ,李承楚 ,牟永光 .任意偶数阶精度的有限差分法数值模拟 [J].石油地球物理勘探 ,1998,33(1) :1- 10 .
[5 ] 罗大清 ,宋炜 ,吴律 ,柏森林 .加权方向校正及插值预测吸收边界条件的三维波动方程叠前数值模拟 [J].石油地球物理勘探 ,1999,34(3) :2 75 - 2 84.
[6 ] FORNBERGB .The pseudospectralmethod comparisonswithfinitedifferencesfortheelasticwaveequation[J].Geophysics,1987,5 2 (4 ) :483- 5 0 1.
[7] 范书蕊 .有限元地震模拟的点状振源 [J].石油地球物理勘探 ,1992 ,2 7(2 ) :2 2 3 - 2 2 9.
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