井中和井间地震波场正演模拟
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摘要
研究井中和井间地震波场的形成过程以及波场分量的转换规律,对于指导实际井中地震测量工作有着十分重要的意义。为此,采用变间距交错网格有限差分方法,进行了单井慢速地层和快速地层半空间模型以及井间快速地层半空间模型的地震波场正演模拟。给出了方法的基本原理,讨论了算法的边界条件和自由界面问题,阐述了可变空间步长和可变时间步长的实现方法。采用变间距交错网格、完全匹配层吸收边界条件和Xu等提出的利用声学和弹性介质界面近似代替自由界面的方法,很好地模拟了波场的形成过程,获得了信息丰富的弹性波波场快照。对模拟结果进行了分析,认为井间地震记录是各类波组干涉的结果。
Study on the build-up process of borehole and crosshole seismic wave field and transformation rule of wave field components is important for guiding actual logging.Therefore,the finite-difference method with variable grid and variable-space staggered grid is used for seismic wave field forward modeling on single borehole semi-spatial model with soft formation and fast formation,as well as crosshole semi-spatial model with fast formation.Firstly,the basic principles are given.Then,the boundary conditions and free interface of the algorithm are discussed.Some methods(including staggered grid with variable time step,perfectly matched layer absorption boundary conditions.the free interface approximately replaced by acoustics and elastic medium interfaee proposed by Xu et al)were used to effectively stimulate the build-up process of wave field and obtain elastic wave field snapshot with abundant information. The simulated result was analyzed;it is thought that the seismic logging recordistheinterference result of all kinds ofwave groups
Study on the build-up process of borehole and crosshole seismic wave field and transformation rule of wave field components is important for guiding actual logging.Therefore,the finite-difference method with variable grid and variable-space staggered grid is used for seismic wave field forward modeling on single borehole semi-spatial model with soft formation and fast formation,as well as crosshole semi-spatial model with fast formation.Firstly,the basic principles are given.Then,the boundary conditions and free interface of the algorithm are discussed.Some methods(including staggered grid with variable time step,perfectly matched layer absorption boundary conditions.the free interface approximately replaced by acoustics and elastic medium interfaee proposed by Xu et al)were used to effectively stimulate the build-up process of wave field and obtain elastic wave field snapshot with abundant information. The simulated result was analyzed;it is thought that the seismic logging recordistheinterference result of all kinds ofwave groups
引文
1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,2005.14-36,125-148
2张永刚.地震波场数值模拟方法[J].石油物探,2003, 42(2):143-148
3 Virieux J.P-SV wave propagation in heterogeneous media:velocity-stress finite-difference method[J].Geophysics, 1986,51(4),889-901
4 Carcione J M,Helle H B.Numerical solution of the poroviscoelastic wave equation on a staggered mesh[J]. Journal of Computational Physics.,1999,154(2):520- 527
5 Janstram C,Tessmer E.Elastic modeling on a grid with vertically raring spacing[J].Geophysical Prospecting, 1994,42(4):357-370
6 Oprasl I,Zahradnik J.Elastic finite-difference method for irregular grids[J].Geophysics,1999,64(1):240- 250
7 Pitarka A.3-D elastic finite-difference modeling of seismic motion using staggered grids with nonuniform spacing[J].Bulletin of the Seismological Society of America, 1999,89(1):54-68
8 Nordstrom J,Carpenter M H.High-order finite difference methods,multidimensional linear problems and curvilinear coordinates[J].Journal of Computational Physics,2001,173(1):149-174
9 Falk J,Tessmer E,Gajewski D.Efficient finite-difference ?? modeling of seismic waves using locally adjustable time steps[J].Geophysical Prospecting,1998,46(6): 603-616
10 Ivo O,Jirl Z.Elastic finitic-difference method for irregular grids[J].Geophysics,1999,64(1):240-250
11 Wu C L.Efficient seismic modeling in multi-scale heterogeneous media[D].California:Stanford University, 2005
12张海澜,李明轩.慢速地层井孔瞬态声场的数值研究[J].地球物理学报,1993,36(1):80-86
13宋长喻,裴正林.井间地震粘弹性波场特征的数值模拟研究[J].石油物探,2006,45(5):508-513
14孙成禹,李胜军,倪长宽,等.波动方程变网格步长有限差分数值模拟[J].石油物探,2008,47(2):123-127
15孔庆丰.井间地震波场数值模拟技术研究与应用[J].勘探地球物理进展,2006,29(5):333-337
16裴正林.三维各向同性介质弹性波场交错网格高阶有限差分方法模拟[J].石油物探,2005,44(4):308-315
17 Mittet R.Free-surface boundary conditions for elastic staggered-grid modeling schemes[J].Geophysics,2002, 67(5):1616-1623
18 Collino F,Tsogka C.Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media[J]. Geophysics,2001,66(1):294-307
19 Carey M,Kim O.On the implementation of perfectly matched layers in a three-dimensional fourth-order velocity -stress finite difference scheme[J].Journal of Geophysical Research,2003,108(B5):2276
20 Abarbanel S,Gottlieb D.A mathematical analysis of the PML method[J].Journal of Computational Physics, 1997,134(2):357-363
21 Levander A R.Fourth-order finite-difference P-SV seismograms[J].Geophysics,1988,53(11):1425- 1436
22 Robertsson J O.A numerical free-surface condition for elastic/viscoelastic finite difference modeling in the presence of topography[J].Geophysics,1996,61(6): 1921-1934
23 Zahradnik J,Priolo E.Heterogeneous formulations of elastodynamic equations and finite-difference schemes [J].Geophysical Journal International,1995,120(3): 663-676
24 Aki K,Richards P G.Quantitative Seismology[M]. San Francisco:W H Freeman and Company,1980. 286-368
25 Xu Y X,Xia J H,Richard D M.numerical investigation of implementation of air/earth boundary by acoustic/elastic boundary approach[J].Geophysics,2007,72(5): SM147-SM153
2张永刚.地震波场数值模拟方法[J].石油物探,2003, 42(2):143-148
3 Virieux J.P-SV wave propagation in heterogeneous media:velocity-stress finite-difference method[J].Geophysics, 1986,51(4),889-901
4 Carcione J M,Helle H B.Numerical solution of the poroviscoelastic wave equation on a staggered mesh[J]. Journal of Computational Physics.,1999,154(2):520- 527
5 Janstram C,Tessmer E.Elastic modeling on a grid with vertically raring spacing[J].Geophysical Prospecting, 1994,42(4):357-370
6 Oprasl I,Zahradnik J.Elastic finite-difference method for irregular grids[J].Geophysics,1999,64(1):240- 250
7 Pitarka A.3-D elastic finite-difference modeling of seismic motion using staggered grids with nonuniform spacing[J].Bulletin of the Seismological Society of America, 1999,89(1):54-68
8 Nordstrom J,Carpenter M H.High-order finite difference methods,multidimensional linear problems and curvilinear coordinates[J].Journal of Computational Physics,2001,173(1):149-174
9 Falk J,Tessmer E,Gajewski D.Efficient finite-difference ?? modeling of seismic waves using locally adjustable time steps[J].Geophysical Prospecting,1998,46(6): 603-616
10 Ivo O,Jirl Z.Elastic finitic-difference method for irregular grids[J].Geophysics,1999,64(1):240-250
11 Wu C L.Efficient seismic modeling in multi-scale heterogeneous media[D].California:Stanford University, 2005
12张海澜,李明轩.慢速地层井孔瞬态声场的数值研究[J].地球物理学报,1993,36(1):80-86
13宋长喻,裴正林.井间地震粘弹性波场特征的数值模拟研究[J].石油物探,2006,45(5):508-513
14孙成禹,李胜军,倪长宽,等.波动方程变网格步长有限差分数值模拟[J].石油物探,2008,47(2):123-127
15孔庆丰.井间地震波场数值模拟技术研究与应用[J].勘探地球物理进展,2006,29(5):333-337
16裴正林.三维各向同性介质弹性波场交错网格高阶有限差分方法模拟[J].石油物探,2005,44(4):308-315
17 Mittet R.Free-surface boundary conditions for elastic staggered-grid modeling schemes[J].Geophysics,2002, 67(5):1616-1623
18 Collino F,Tsogka C.Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media[J]. Geophysics,2001,66(1):294-307
19 Carey M,Kim O.On the implementation of perfectly matched layers in a three-dimensional fourth-order velocity -stress finite difference scheme[J].Journal of Geophysical Research,2003,108(B5):2276
20 Abarbanel S,Gottlieb D.A mathematical analysis of the PML method[J].Journal of Computational Physics, 1997,134(2):357-363
21 Levander A R.Fourth-order finite-difference P-SV seismograms[J].Geophysics,1988,53(11):1425- 1436
22 Robertsson J O.A numerical free-surface condition for elastic/viscoelastic finite difference modeling in the presence of topography[J].Geophysics,1996,61(6): 1921-1934
23 Zahradnik J,Priolo E.Heterogeneous formulations of elastodynamic equations and finite-difference schemes [J].Geophysical Journal International,1995,120(3): 663-676
24 Aki K,Richards P G.Quantitative Seismology[M]. San Francisco:W H Freeman and Company,1980. 286-368
25 Xu Y X,Xia J H,Richard D M.numerical investigation of implementation of air/earth boundary by acoustic/elastic boundary approach[J].Geophysics,2007,72(5): SM147-SM153
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