复杂非均匀介质伪谱法波场数值模拟
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摘要
在地震波场数值正演模拟方法的研究中,计算精度和计算效率是评价方法的有效性及优越性的2个关键问题。从—阶速度—应力弹性波动方程出发,利用伪谱法求解波动方程,对复杂非均匀介质模型中的波场进行了正演模拟,并利用经典的Mamousi速度模型验证了该方法所具有的优势及存在的问题。将伪谱法模拟结果与交错网格高阶有限差分法的模拟结果比较可知：对于较为简单的非均匀模型,伪谱法和交错网格高阶有限差分法生成了几乎相同的波场；而当模型非常复杂且存在变化较剧烈的速度间断面时,伪谱法的模拟结果比较差。尽管如此,伪谱法计算速度快,计算效率高,能够直观、高效地反映介质中波场的传播规律。因而仍不失为一种很好的地震波模拟方法。
Wave field numerical simulation is an important field in geo- physics.For the forward modeling,the computational precision and efficiency are two key issues in evaluating the validity and the superiority of the method.Based on the first order velocity-stress elastic wave equation,the wave field forward modeling with the pseudo-spectral method was carried out for complex heterogeneous medium.Meanwhile,the classical Marmousi model was utilized to verify the advantages and the existing problems of the method.By comparing the results of the pseudo-spectral method with the stag- gered-grid high-order finite difference approach,we can see that the two methods generate nearly the same wave field for the simple heterogeneous model.For the complex model,however,the mod- eling result of the pseudo-spectral method is worse than that of the staggered-grid high-order finite difference approach.Nevertheness, the pseudo-spectral method has a high computation speed and com- putational efficiency and can reflect the propagation rules of the wave field in medium visually and effectively.As a result,the pseudo-spectral method is still an effective method to model the heterogeneous seismic wave field.
Wave field numerical simulation is an important field in geo- physics.For the forward modeling,the computational precision and efficiency are two key issues in evaluating the validity and the superiority of the method.Based on the first order velocity-stress elastic wave equation,the wave field forward modeling with the pseudo-spectral method was carried out for complex heterogeneous medium.Meanwhile,the classical Marmousi model was utilized to verify the advantages and the existing problems of the method.By comparing the results of the pseudo-spectral method with the stag- gered-grid high-order finite difference approach,we can see that the two methods generate nearly the same wave field for the simple heterogeneous model.For the complex model,however,the mod- eling result of the pseudo-spectral method is worse than that of the staggered-grid high-order finite difference approach.Nevertheness, the pseudo-spectral method has a high computation speed and com- putational efficiency and can reflect the propagation rules of the wave field in medium visually and effectively.As a result,the pseudo-spectral method is still an effective method to model the heterogeneous seismic wave field.
引文
1张永刚．地震波数值模拟方法[J]．石油物探，2003，42(2)：143～148
2 Gazdag J.Modelling of the acoustic wave equation with transform method[J].Geophysics,1981,46(6):854～859
3 Kosloff D,Baysal E.Forward modeling by a Fourier method[J].Geophysics,1982,47(10):1 402～1 412
4 Fornberg K The pseudospectral method:Comparisons with finite difference for the elastic wave equation[J].Geophysics,1987,52(4):483～501
5 Virieux J.P-SV wave propagation in heterogeneous media:velocity-stress finite-difference method[J].Geophysics,1986,51(4):889～901
6 Koslof D,Moshe Reshef,Loewenthal D.Elastic wave calculations by the Fourier method[J].Bulletin of the Seismological Society of America,1984,74(3):875～891
7侯安宁，何樵登．各向异性介质中弹性波记录的傅里叶变换法正演模拟[J]．石油地球物理勘探，1994，29(1)：64～71
8张文生，何樵登．二维横向各向同性介质的伪谱法正演模拟[J]．石油地球物理勘探，1998，33(3)：310～319
9 Cerjan C,Kosloff D,kosloff R,et aL A nonreflecting boundary condition for discrete acoustic and elastic wave equation[J].Geophysics,1985,50(4):705～708
10程冰洁，李小凡，徐天吉．非均匀介质中交错网格高阶有限差分数值模拟[J]．物探化探计算技术，2006，28(4)：1～7
11牟永光，裴正林．三维复杂介质地震数值模拟[M]．北京：石油工业出版社，2005．41～43
2 Gazdag J.Modelling of the acoustic wave equation with transform method[J].Geophysics,1981,46(6):854～859
3 Kosloff D,Baysal E.Forward modeling by a Fourier method[J].Geophysics,1982,47(10):1 402～1 412
4 Fornberg K The pseudospectral method:Comparisons with finite difference for the elastic wave equation[J].Geophysics,1987,52(4):483～501
5 Virieux J.P-SV wave propagation in heterogeneous media:velocity-stress finite-difference method[J].Geophysics,1986,51(4):889～901
6 Koslof D,Moshe Reshef,Loewenthal D.Elastic wave calculations by the Fourier method[J].Bulletin of the Seismological Society of America,1984,74(3):875～891
7侯安宁，何樵登．各向异性介质中弹性波记录的傅里叶变换法正演模拟[J]．石油地球物理勘探，1994，29(1)：64～71
8张文生，何樵登．二维横向各向同性介质的伪谱法正演模拟[J]．石油地球物理勘探，1998，33(3)：310～319
9 Cerjan C,Kosloff D,kosloff R,et aL A nonreflecting boundary condition for discrete acoustic and elastic wave equation[J].Geophysics,1985,50(4):705～708
10程冰洁，李小凡，徐天吉．非均匀介质中交错网格高阶有限差分数值模拟[J]．物探化探计算技术，2006，28(4)：1～7
11牟永光，裴正林．三维复杂介质地震数值模拟[M]．北京：石油工业出版社，2005．41～43
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