摘要
随着油气勘探工作的深入,现代油气勘探工作正面临着越来越复杂的目标和越来越高的勘探精度要求。激发、接收和观测系统是地震资料采集的3个主要组成部分。三维观测系统优化设计的水平直接影响地下构造的成像质量,特别是在复杂地区。如何筛选出一个优化的观测系统成为地震勘探中的一个重要的课题。
荷兰Delft大学教授Berkhout提出了基于WRW模型双聚焦理论的面向目标点叠前成像质量的观测系统评价方法。根据WRW模型理论,地震波的传播可以划分为5个独立的步骤:1、震源激发,用激发算子S进行抽象表示;2、地震波向下传播,用下行传播算子Ws进行抽象表示;3、地震波在界面反射,用反射算子R进行抽象表示;4、地震波向上传播,用上行传播算子Wd进行抽象表示;5、观测系统检波器对地震波场的采集,用采集算子D进行抽象表示。这5个算子的乘积就构成了WRW模型。同时,定义两个聚焦算子:震源聚焦算子Fs和检波器聚焦算子Fd。这两个算子分别实现震源和检波器的聚焦。用震源聚焦算子实现对地震波场的聚焦后,再向下延拓波场到成像面就得到检波器阵列聚焦束。同理,用检波器聚焦算子实现对地震波场的聚焦后,再向下延拓波场到成像平面就得到震源阵列聚焦束。它们分别反映检波器和震源对目标点的成像分辨率。检波器阵列聚焦束和震源阵列聚焦束相乘得到单个模板的分辨率。整个观测系统所有模板的分辨率为所有单个模板分辨率相加。在整个计算过程中,波场外推是最为重要的环节。
本文在消化吸收A.J.Berkhout提出的基于WRW模型的双聚焦理论基础上,为了适应当前计算机计算能力和实际生产需要,我们对此方法做了一些简化和改进。编写了能适应任意复杂模型的“二维观测系统分辨率评估系统”软件和能适应相对简单的层状介质的“三维观测系统分辨率评估系统”软件。通过理论模型和实际模型的计算,可以看出这种简化方法的可行性和实用行。
With the development and progress of oil-gas exploration, the challenge of increasingly complicated target points and increasingly high precision demands is faced in modern oil-gas exploration. Seismic data acquisition includes exploding, receiving and acquisition geometry. The level of the optimum designing 3D acquisition geometry can directly affect the imaging quality of subsurface structure, especially, in some complicated regions. It is an important theme how to sieve an optimal acquisition geometry.
Professor Berkhout has developed an approach for estimating acquisition geometry that is guided by prestack imaging quality of target points based on the double focusing theory of the WRW model. According to the theory of the WRW model, the process of seismic wave propagation can be divided into 5 independent procedures: 1) sources explode, which can be signified by operator S; 2) seismic wave propagates downward, which can be signified by operator Ws ; 3) seismic wave is reflected at the subsurface, which can be signified by operator R ; 4) seismic wave propagates upward, which can be signified by operator Wd ; 5) receivers acquire the seismic wave, which can be signified by operator D . The product of the 5 operators is the WRW model. We define two focusing operators: focal source operator Fs and focal detector operator Fd . The two operators separately implement focusing on sources and detectors. Focused the seismic wave field by Fs , and then downward continue the wave field to image subsurface, thus get focal detector beam. Likewise, Focused the seismic wave field by Fd , and then downward continue the wave field to image subsurface, thus get focal shot beam. They separately indicate imaging resolution of detectors and sources to target points. The resolution of a single spread is the product of focal detector beam and focal source beam. The total resolution of the whole acquisition geometry is the summation of resolutions of all the single spreads. Extrapolating wave field is most important in the whole process.
Based on Berkhout’s theory of double focusing of the WRW model, in order to adapt to the calculating ability of current computers and actual needs of production, this dissertation has made some simplifications and improvements. The software of“assessment system of 2D acquisition geometry’s resolution”can be adapted to an arbitrarily complicated geology model. The software of“assessment system of 3D acquisition geometry’s resolution”can be adapted to a relatively simple geology model. Calculation of theoretic and actual models indicates feasibility and practicality of the simplified approach.
引文
[1]Berkhout, A. J.,1985, Seismic migration: Imaging of acoustic energy by wavefield extrapolation: Elsevier Science Publishers B.V.
[2]Berkhout, A. J.,1997, Pushing the limits of seismic imaging, Part I: Prestack migration in terms of double dynamic focusing: Geophysics, Vol 62, No. 3: 937-954
[3]Berkhout, A. J.,1997, Pushing the limits of seismic imaging, Part II: Integration of prestack migration, velocity estimation, and AVO analysis: Geophysics, Vol 62, No. 3: 954-969
[4]A.J. Berkhout, L. Ongkiehong. Comprehensive assessment of seismic acquisition geometries by focal beams—part I: Theoretical considerations, Geophysics, 2001, 66 (3): P911-917
[5]A.W.F. Volker, G. Blacquière. Comprehensive assessment of seismic acquisition geometries by focal beams—part II: Practical aspects and examples, Geophysics, 2001, 66 (3): P918-931
[6]Cerjan C, Kosloff D, Kosloff R, et a. A nonreflecting boundary condition for discrete acoustic and elastic wave equations. Geophysics, 1985, 50:705-708
[7]Kosloff D, Kosloff R. Absorbing boundaries for wave propagation problems, J, Comput. Phys. , 1986,63:363-376
[8]Jean-Pierre Berenger. A Perfectly matched layer for the absorption of electromagnetic waves, Journal of computational physics,1994,114: 185-200
[9]Francis Collino, Chrysoula Tsogka. Application of the perfectly matched absorbing layer model to the linear elastodynamic problemin anisotropic heterogeneous media, Geophysics, 2001, 66 (1): P294-307
[10]Clayton R, Engquist B. Absorbing boundary conditions for acoustic and elastic wave equations. Bull. Seism. Soc. Am., 1977, 67: 1529- 1540
[11]Higdon R L. Absorbing bonndary conditions for elastic waves. Physics, 1991, 56: 231-241
[12]Randall C J. Absorbing boundary condition for the elastic wave equation. Geophysics, 1988, 53: 611-624
[13]Reynolds. Boundarv conditions for the numerical solution of wave propagation problems. Geophysics, 1978, 43: 1099
[14]刘洋,李承楚,牟永光.任意偶阶精度有限差分法数值模拟,石油地球物理勘探,33(1),1998
[15]Fornberg, B., A practical guide to pseudospectral methods, Cambridge University Press, 1996
[16]王守东.声波方程完全匹配层吸收边界,石油地球物理勘探,38(1),2003
[17]马在田.地震成像技术——有限差分法偏移,石油工业出版社,1989
[18]李荣华.微分方程数值解法,高等教育出版社,1996
[19]徐士良.常用算法程序集(C 语言描述),清华大学出版社,2006
[20]裴正林.三维各向同性介质弹性波方程交错网格高阶有限差分法模拟,石油物探,44(4),2005