双相各向同性介质伪谱法地震波场数值模拟
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摘要
伪谱法是一种模拟精度和计算效率都较高的地震波场数值模拟方法。该方法通过对空间坐标的快速傅里叶变换实现数值计算,在时间域直接采用差分运算代替导数的求解,避免了求偏导数;不存在有限差分和有限元等方法对高频成分限制的问题,可以实现全频带地震波场模拟;对内存容量的需求远远低于有限元法。利用伪谱法实现双相各向同性介质地震波场数值模拟的基本原理是:首先基于Biot模型给出双相各向同性介质弹性波波动方程;然后推导出二维双相各向同性介质的伪谱法计算公式;最后对给定的介质模型进行模拟试算。模拟结果表明,弹性波在双相各向同性介质中以快纵波、横波和慢纵波3种方式传播。基于模拟结果,分析了各类波的传播规律,讨论了耗散系数和孔隙度对地震波传播的影响。
Pseudo spectral method has high simulating accuracy and high computational efficiency.Compared to finite difference method and finite element method,it has such advantages:1)it uses fast Fou- rier transform in space coordinate to calculate the time in time do- main and can avoid computing the partial derivative;2)it can real- ize complete frequency band seismic wave simulation without any limitation by finite difference method and finite element method on high frequency component;and 3)it has a lower dispersion and needs only a small memory requirements.So the pseudo spectral method has been used in the wave field simulation of isotropic two- phase media.Firstly,elastic wave equation of isotropic two-phase media was given based on Biot model.Then,the iterative formu- late of pseudo spectral method was derived for 2-D isotropic two- phase media.Finally,the wave field simulation for the given media model was realized.Simulation results show that the elastic wave propagates in fast P-wave,S-wave,and slow P-wave in isotropic two-phase media.Based on simulation results,the propagation laws of various wave was analyzed and the effect of dissipation co- efficient and porosity on seismic wave propagation discussed.
Pseudo spectral method has high simulating accuracy and high computational efficiency.Compared to finite difference method and finite element method,it has such advantages:1)it uses fast Fou- rier transform in space coordinate to calculate the time in time do- main and can avoid computing the partial derivative;2)it can real- ize complete frequency band seismic wave simulation without any limitation by finite difference method and finite element method on high frequency component;and 3)it has a lower dispersion and needs only a small memory requirements.So the pseudo spectral method has been used in the wave field simulation of isotropic two- phase media.Firstly,elastic wave equation of isotropic two-phase media was given based on Biot model.Then,the iterative formu- late of pseudo spectral method was derived for 2-D isotropic two- phase media.Finally,the wave field simulation for the given media model was realized.Simulation results show that the elastic wave propagates in fast P-wave,S-wave,and slow P-wave in isotropic two-phase media.Based on simulation results,the propagation laws of various wave was analyzed and the effect of dissipation co- efficient and porosity on seismic wave propagation discussed.
引文
1 Gassmann F.Elastic waves through a packing of spheres[J].Geophysics,1951,16(4):673～685
2 Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid,PartⅠ:Low frequency range[J].The Journal of the Acoustic Society of A- merica,1956,28(2):168～178
3 Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid,PartⅡ:high frequency range[J].The Journal of the Acoustic Society of America,1956,28(2):179～191
4 Dvorkin J,Nur A.Dynamic poroelasticity:A unified model with squirt and the Biot mechanisms[J].Geo- physics,1993,58(4):524～533
5张应波．Biot理论应用于地震勘探的探索[J]．石油物探，1994，33(4)：29～38
6刘克安，郭萍．双相介质二维波动方程三参数同时反演正则迭代法[J]．石油地球物理勘探，1997，32(2)：615～622
7杨顶辉，张中杰，腾吉文，等．双相各向异性研究、问题与应用前景[J]．地球物理学进展，2000，15(2)：7～21
8孟庆生．基于BISQ机制双相裂隙介质弹性波场正演及其方位属性研究[D]．长春：吉林大学，2003
9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，2005．114～125
10杨顶辉．基于BISQ模型的弹性波理论和有限元法[D]．北京：中国石油大学(北京)，1998
11朱建伟．基于BISQ机制的含油水孔隙介质地震波波动方程[J]．石油物探，2001，40(4)：8～13
12杜世通．地震波动力学[M]．东营：石油大学出版社，1996．305～311
13傅旦丹，何樵登．正交各向异性介质地震弹性波场的伪谱法正演[J]．石油物探，2001，40(3)：8～14
14耿书启．伪谱法波动方程正演模拟方法研究[D]．东营：中国石油大学(华东)，2001
15刘洋，李承楚．双相各向异性介质中弹性波传播伪谱法数值模拟研究[J]．地震学报，2000，22(2)：132～138
2 Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid,PartⅠ:Low frequency range[J].The Journal of the Acoustic Society of A- merica,1956,28(2):168～178
3 Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid,PartⅡ:high frequency range[J].The Journal of the Acoustic Society of America,1956,28(2):179～191
4 Dvorkin J,Nur A.Dynamic poroelasticity:A unified model with squirt and the Biot mechanisms[J].Geo- physics,1993,58(4):524～533
5张应波．Biot理论应用于地震勘探的探索[J]．石油物探，1994，33(4)：29～38
6刘克安，郭萍．双相介质二维波动方程三参数同时反演正则迭代法[J]．石油地球物理勘探，1997，32(2)：615～622
7杨顶辉，张中杰，腾吉文，等．双相各向异性研究、问题与应用前景[J]．地球物理学进展，2000，15(2)：7～21
8孟庆生．基于BISQ机制双相裂隙介质弹性波场正演及其方位属性研究[D]．长春：吉林大学，2003
9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，2005．114～125
10杨顶辉．基于BISQ模型的弹性波理论和有限元法[D]．北京：中国石油大学(北京)，1998
11朱建伟．基于BISQ机制的含油水孔隙介质地震波波动方程[J]．石油物探，2001，40(4)：8～13
12杜世通．地震波动力学[M]．东营：石油大学出版社，1996．305～311
13傅旦丹，何樵登．正交各向异性介质地震弹性波场的伪谱法正演[J]．石油物探，2001，40(3)：8～14
14耿书启．伪谱法波动方程正演模拟方法研究[D]．东营：中国石油大学(华东)，2001
15刘洋，李承楚．双相各向异性介质中弹性波传播伪谱法数值模拟研究[J]．地震学报，2000，22(2)：132～138
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