起伏地表条件下的地震波场数值模拟
摘要
本文的研究目的是提出一种解决起伏地表条件下地震波场数值模拟的方案。研究方法是将网格映射和有限积分变换-有限差分法(FIFT—FD)相结合。
全文共分六章,第一章对现有的起伏地表地震波场数值模拟方法进行了概述;第二章介绍了有限积分变换方法的原理,此方法在数学物理问题中和在地球物理学中的发展概况;波动方程FIFT-FD法应用在第三章进行了讨论,在这一章给出了水平和起伏地表条件下的波动方程FIFT—FD法的离散方程形式;第四章首先讨论震源函数类型,然后对震源的限积分变换处理进行说明;第五章主要对FIFT-FD法解弹性波方程时出现的高振荡函数积分进行计算并编制程序,给出算法的实例并分析其近似效果;第六章根据导出来的变换域波动方程的FIFT-FD法对水平地表的情况进行地震波场数值模拟;最后,在第七章对全文的研究结果做了总结,提出了对今后进一步深入研究的方向。
Seismic exploration is an important geophysical methods. The useful geological information was carried from seismic waves, so the characteristics of the seismic wave field awareness is very important.
Generally, the study seismic waves There are two ways: physical methods and mathematical methods, often referred to as the physical simulation and numerical simulation. Physical simulation is by a certain scale, with certain materials to and the actual geological body in shape, structure and properties, and so on the main features of proportion to the physical models in the laboratory simulation of this physical model of seismic exploration of the field work, Various methods of data collection, given the necessary seismic records and collection of data and make the appropriate process. Physical simulation was accomplished in the laboratory. Beacuase the physical parameters, structural and tectonic patterns of physical model was known, and the sources can be controlled, the seismic wave field reflects the characteristics clearly, and help us to interpret the actual formation lithology and structure.
In contrast with the physical simulation, numerical simulation is in a given mathematical model (such as elastic wave equation, acoustic equation, etc.), the source, and underground geometry interface, physical parameters (rock density, velocity, etc.). studied acoustic or elastic waves’dynamic features. Numerical simulation can be intuitive understanding of seismic wave field, and provide the necessary basis for exploration seismic data inversion (the so-called inversion is the methods of using the observation wells in the ground or the data or physical phenomena within the media to speculate the Earth's physical state).
Seismic wave field of numerical simulation in seismic data processing method plays a very important role, it is one of the means to study and understand the importance of seismic wave field, in the oil and gas exploration and development occupies a very important and irreplaceable status. On the one hand, use of numerical simulation of seismic records, test results of the seismic data processing quality and effectiveness of the treatment. On the other hand, forward modeling can be used as the basis of the study inversion. In this paper, the limited integral transformation - finite difference method (FIFT-FD) is one of the many numerical simulation technologies.
Called combination of finite integral Fourier transform and finite difference technique (FIFT-FD) will be researched in this paper. The method was firstly proposed byМихайленко.Б.Г.firstly, based on the principles of the method, two versions are deduced for acoustic wave equations. Then finite difference equations are created for the methods. At last, utilizing appropriate source functions, seismic responses are calculated for homogeneous and layered earth. Based on the same principle, the method is adapted to elastic wave equations for many other earth models, And discrete forms of the equations are deduced.
This article combinated mesh mapping and limited integral transformation - finite difference, a surface mapping will be ups and downs to the rules of a rectangular grid coordinate system, according to transform guided by the use of the limited domain wave equation integral transformation finite difference method Seismic wave field of numerical simulation methods to solve the rugged surface under conditions of simulated. Through this work, the limited DCT-based Fourier Fourier limited or sine-wave seismic methods numerical simulation was more widely applied.
By the work of this thesis, the new characters of FIFT-FD method can be gained:
(1)Finite sine/cosine transform belongs to classical method of solution partial differential equation(PDE). It can decrease the PDE’s spacial dimension, that is able to transform the PDE to ordinary differential equation(ODE), which would be more easy to solve.
(2) The FIFT-FD used to model SH wave. We found it could be applied widely. For example we used this method to model acoustic wave equation. It also adapted to the elastical wave equation in isotropic medium. The only difference was the given medium parameter.
(3)The method enabled extend the model to infinite in transform direction, so that was suitable for large scale problems. When dealed with arbitrary velocity or density distribution, this method nearly no computation increment.
(4)The FIFT-FD transformed function to sine/cosine functions, then accumulated the function series. Not like pseudospectral method, it had no folding effect resulted from the periodicity of Fourier transform, and it had infinite order accuracy.
(5)The selection of surface function was very important when the surface was irregular, and it effected the equation’s difference scheme and the accuracy of solution.
Anyway we can draw a conclusion that the FIFT-FD was a simple, efficient and parsimonious method. However, its disadvantage was not neglectable. Because it included the finite integral of derivative of wave equation parameter, so the given parameter model must sufficient smooth.
In this paper, the method of study on a formula derived and the computation of integral of high-oscillation function. Because of the time relatively tight, the specific examples of calculation the rugged surface models have not given, but given the plane surface examples. The rugged surface of the calculation example would be research and analysis in the further.
全文共分六章,第一章对现有的起伏地表地震波场数值模拟方法进行了概述;第二章介绍了有限积分变换方法的原理,此方法在数学物理问题中和在地球物理学中的发展概况;波动方程FIFT-FD法应用在第三章进行了讨论,在这一章给出了水平和起伏地表条件下的波动方程FIFT—FD法的离散方程形式;第四章首先讨论震源函数类型,然后对震源的限积分变换处理进行说明;第五章主要对FIFT-FD法解弹性波方程时出现的高振荡函数积分进行计算并编制程序,给出算法的实例并分析其近似效果;第六章根据导出来的变换域波动方程的FIFT-FD法对水平地表的情况进行地震波场数值模拟;最后,在第七章对全文的研究结果做了总结,提出了对今后进一步深入研究的方向。
Seismic exploration is an important geophysical methods. The useful geological information was carried from seismic waves, so the characteristics of the seismic wave field awareness is very important.
Generally, the study seismic waves There are two ways: physical methods and mathematical methods, often referred to as the physical simulation and numerical simulation. Physical simulation is by a certain scale, with certain materials to and the actual geological body in shape, structure and properties, and so on the main features of proportion to the physical models in the laboratory simulation of this physical model of seismic exploration of the field work, Various methods of data collection, given the necessary seismic records and collection of data and make the appropriate process. Physical simulation was accomplished in the laboratory. Beacuase the physical parameters, structural and tectonic patterns of physical model was known, and the sources can be controlled, the seismic wave field reflects the characteristics clearly, and help us to interpret the actual formation lithology and structure.
In contrast with the physical simulation, numerical simulation is in a given mathematical model (such as elastic wave equation, acoustic equation, etc.), the source, and underground geometry interface, physical parameters (rock density, velocity, etc.). studied acoustic or elastic waves’dynamic features. Numerical simulation can be intuitive understanding of seismic wave field, and provide the necessary basis for exploration seismic data inversion (the so-called inversion is the methods of using the observation wells in the ground or the data or physical phenomena within the media to speculate the Earth's physical state).
Seismic wave field of numerical simulation in seismic data processing method plays a very important role, it is one of the means to study and understand the importance of seismic wave field, in the oil and gas exploration and development occupies a very important and irreplaceable status. On the one hand, use of numerical simulation of seismic records, test results of the seismic data processing quality and effectiveness of the treatment. On the other hand, forward modeling can be used as the basis of the study inversion. In this paper, the limited integral transformation - finite difference method (FIFT-FD) is one of the many numerical simulation technologies.
Called combination of finite integral Fourier transform and finite difference technique (FIFT-FD) will be researched in this paper. The method was firstly proposed byМихайленко.Б.Г.firstly, based on the principles of the method, two versions are deduced for acoustic wave equations. Then finite difference equations are created for the methods. At last, utilizing appropriate source functions, seismic responses are calculated for homogeneous and layered earth. Based on the same principle, the method is adapted to elastic wave equations for many other earth models, And discrete forms of the equations are deduced.
This article combinated mesh mapping and limited integral transformation - finite difference, a surface mapping will be ups and downs to the rules of a rectangular grid coordinate system, according to transform guided by the use of the limited domain wave equation integral transformation finite difference method Seismic wave field of numerical simulation methods to solve the rugged surface under conditions of simulated. Through this work, the limited DCT-based Fourier Fourier limited or sine-wave seismic methods numerical simulation was more widely applied.
By the work of this thesis, the new characters of FIFT-FD method can be gained:
(1)Finite sine/cosine transform belongs to classical method of solution partial differential equation(PDE). It can decrease the PDE’s spacial dimension, that is able to transform the PDE to ordinary differential equation(ODE), which would be more easy to solve.
(2) The FIFT-FD used to model SH wave. We found it could be applied widely. For example we used this method to model acoustic wave equation. It also adapted to the elastical wave equation in isotropic medium. The only difference was the given medium parameter.
(3)The method enabled extend the model to infinite in transform direction, so that was suitable for large scale problems. When dealed with arbitrary velocity or density distribution, this method nearly no computation increment.
(4)The FIFT-FD transformed function to sine/cosine functions, then accumulated the function series. Not like pseudospectral method, it had no folding effect resulted from the periodicity of Fourier transform, and it had infinite order accuracy.
(5)The selection of surface function was very important when the surface was irregular, and it effected the equation’s difference scheme and the accuracy of solution.
Anyway we can draw a conclusion that the FIFT-FD was a simple, efficient and parsimonious method. However, its disadvantage was not neglectable. Because it included the finite integral of derivative of wave equation parameter, so the given parameter model must sufficient smooth.
In this paper, the method of study on a formula derived and the computation of integral of high-oscillation function. Because of the time relatively tight, the specific examples of calculation the rugged surface models have not given, but given the plane surface examples. The rugged surface of the calculation example would be research and analysis in the further.
引文
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2 吴永刚, 吴清岭. 有限差分法弹性波场数值模拟.大庆石油地质与开发[J], 1994, 13(3): P1~6.
3 林小竹, 姚本全. 弹性波虚谱法模拟. 石油地球物理勘探[J], 1991, 26(6): P688~699.
4 薛东川, 王尚旭, 焦淑静. 起伏地表复杂介质波动方程有限元数值模拟方法. 地球物理学进展[J], 2007, 22(2): P522~529.
5 张剑峰. 弹性波数值模拟的非规则网格差分法, 地球物理学报[J], 1998(增刊),41:P357~366.
6 徐世浙, 地球物理中的有限单元法(第一版), 科学出版社[M], 1994.
7 张宝琳, 袁国兴, 刘兴平. 偏微分方程并行有限差分方法. 科学出版社[M], 1994.
8 佘德平. 波场数值模拟技术. 勘探地球物理进展[J], 2004, 27(1): P16~21.
9 张中杰. 2D和3D横向各向同性波动问题研究. 长春地质学院博学位士论文, 1991: P55~79.
10 克莱鲍特 J F. 地震成像理论及方法(第一版), 石油工业出版社[M], 1991: P61~69.
11 张伟, 陈晓非. 中国地球物理学会年刊. 2001—三维交错网格有限差分方法及其在模拟地震波传播问题中的应用. 云南科技出版社[M], P351.
12 Kelly K R, Ward R W, Sven Treitel, Alford R M. Synthetic seismograms: afinite-difference approach. Geophysics [J], 1946, 41(1): P2~27.
13 裴正林. 任意起伏地表弹性波方程交错网格高阶有限差分法数值模拟. 石油地球物理勘探[J], 2004, 39(6): P629~634.
14 Kindelan M, Kamel A, Sguazzero P. On the construction and efficiency of staggered numerical differentiators for the wave equation. Geophysics[J], 1990, 55(1): P107~110.
15 桂志先. 2n 阶有限差分的计算与复杂介质波场数值模拟. 石油天然气学报(江汉石油学院学报) [J], 2005, 27(3): P334~337.
16 李信富, 李小凡.伪谱法地震波场数值模拟. 桂林工学院学报[J], 2007, 27(2): P178~181.
17 Gazdag J. Modelling of the acoustic wave equation with transform method. Geophysics[J], 1981, 46(6): P854~859.
18 Kosloff D, Baysal E. Forward modeling by a Fourier method. Geophysics[J], 1982,47(10): P1402～1412.
19 Kindelan M, Kamel A, Sguazzero P. On the construction and efficiency of staggered numerical differentiators for the wave equation. Geophysics[J], 1990, 55(1): P107~110.
20 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. 地震学报[J], 2000, 22(2): P132~138.
21 程冰洁, 李小凡, 徐天吉. 复杂非均匀介质伪谱法波场数值模拟.石油物探[J], 2007, 46(1): P16~19.
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