复杂地表条件下地震波走时计算方法研究
摘要
本项研究的目的是提出复杂地表条件下地震波走时计算方案。研究方法是将常规波前快速推进法(Fast marching method ,简写为FMM)和复杂地表问题相结合。主要研究内容是:(1)改进FMM的计算精度和计算效率;(2)在复杂地表条件下实现FMM和线性插值法。主要研究成果是:(1)通过对局部算法的改进在保证计算效率的情况下提高了FMM的精度;(2)通过对堆选排技术的改进大大地提高了FMM的计算效率;(3)利用线性插值技术解决了起伏地表点的走时计算问题,提出了复杂地表条件下地震波走时计算方案、实现算法和计算流程。有关数值实验证明:改进后的FMM计算精度和计算效率都有很大的提高,针对复杂地表提出的FMM计算方案是切实可行的,对速度模型的处理使计算方案对模型的不均匀性具有很强的适应能力,能很好地计算出地震波在复杂地表地区的传播情况。
A great quantity of geophysical prospecting work is carried out in complex surface areas in western china, compared with the plain areas, seismic exploration in complex surface areas is of a lot of problems, such as low signal to noise ratio, many types of interference of the collecting seismic data and the difficulties of imaging in data processing. Aiming at these problems, we should first solve the problems of the seismic wave field’s structure and propagation characteristics completely, and then research the collecting, processing and interpretation techniques of seismic data.
The research about the problems of the seismic wave field’s structure and propagation characteristics can start with many ways, and the seismic wave field forward modeling is a very effective way. The forward modeling based on ray theory has advantages of high efficiency and intuitive wave field. As a forward modeling tomography based on ray theory, the computation about the seismic traveltimes can be applied to tomography, Kirchhoff migration, velocity analysis, seismic modeling, and other fields and it will play a very important role in solving complex surface problems. In all, the computation of seismic traveltimes is developing to the direction of high accuracy, high efficiency, good flexibility and good stability, and a lot of computation technologies had developed relatively mature. However, so far, there is no the relevant research for complex surface seismic waves traveltimes computation which limits the existing technology applied in the mountains, hills and other complex surface areas.
The purpose of the study related to the content of this paper is to propose and implement seismic waves traveltimes computation program under the conditions of complex surface. In order to achieve this objective, we propose the following research ideas: Firstly, review the existing computation technologies of seismic traveltimes and select a optimal computation method (FMM) as the foundation of other follow-up methods; Secondly, study the FMM carefully and improve it in each aspect; Finally, integrate the improved FMM and the complex surface problems, we propose the implementation strategy of studying on the computation of seismic traveltimes in the condition of surface topography. Under the guidance of these ideas, we did the following three aspects of work:
①We review various traveltimes algorithms: First, classify various traveltimes algorithms; Second, state the basic principle and implementation strategy of various traveltimes algorithms; Third, compare these algorithms, we know the present situation and development trend of traveltimes algorithms by reviewing them; finally, we draw a conclusion: The finite-difference method is an optimal algorithm to calculating seismic traveltimes and FMM is an optimal finite-difference algorithm. So, we select FMM as the basic algorithm to study the computation of seismic traveltimes in the condition of surface topography.
②We further research the FMM: First, discuss the origin and development, basic principles and implementation, unconditional stability, computational accuracy and efficiency, et al of FMM in detail, and get the following conclude: The order of difference format is an important factor impacting the calculating accuracy of FFM, the order of difference scheme is higher, and the calculating accuracy is higher. The calculating accuracy of second-order scheme is higher than first-order scheme’s. Grid space is another important factor impacting calculating accuracy, the grid space is larger, the calculating accuracy is less, and vice versa. The heap sort technology is the most important factor impacting the calculating efficiency of FMM; Second, according to improving the algorithm of FMM form the local difference scheme, greatly enhance the computation accuracy of the algorithm; then start with improving the heap sort technology, greatly enhance the computation efficiency of the algorithm. Finally, a large number of examples about the computation of the FMM verify that the various measures for improving the effective and the results are very good.
③The implementation of the computing seismic traveltimes in the condition of surface topography: First, establish a reasonable, complex physical model of the surface corresponding to the mathematical model; Second, the model is complete, introduce FMM to solve complex surface problems and propose the implementation strategy about the seismic waves traveltimes computation in the complex surface condition. and set up implementation process framework; Third, through processing the velocity model and making interpolation processing near interface and surface, compute the traveltimes on interface and surface more reasonably; Finally, a large number of examples of computation and analysis confirmed that the implementation strategy about the seismic time computation which is presented in this paper is feasible, the results of computation can well describe propagating process of seismic wave at complicated surface area.
The main innovation of results of the research as follows:①Through changing the partial algorithm, we enhance the accuracy of the FMM;②Through developing the heap sort technology, we greatly enhance the computation efficiency of FMM;③We first present a technical scheme of the seismic traveltimes computation in surface topography condition, set up implementation process framework and compily complete program code.
The main results of the research have great significance to study on the structure and propagation characteristics of seismic wave field under the condition of complex surface topography, lay the theoretical foundation for the research of seismic data collecting, processing and interpreting in complex surface technology condition and have a very important theoretical significance for the hydrocarbon exploration in complex surface area(especially in the western mountains).
A great quantity of geophysical prospecting work is carried out in complex surface areas in western china, compared with the plain areas, seismic exploration in complex surface areas is of a lot of problems, such as low signal to noise ratio, many types of interference of the collecting seismic data and the difficulties of imaging in data processing. Aiming at these problems, we should first solve the problems of the seismic wave field’s structure and propagation characteristics completely, and then research the collecting, processing and interpretation techniques of seismic data.
The research about the problems of the seismic wave field’s structure and propagation characteristics can start with many ways, and the seismic wave field forward modeling is a very effective way. The forward modeling based on ray theory has advantages of high efficiency and intuitive wave field. As a forward modeling tomography based on ray theory, the computation about the seismic traveltimes can be applied to tomography, Kirchhoff migration, velocity analysis, seismic modeling, and other fields and it will play a very important role in solving complex surface problems. In all, the computation of seismic traveltimes is developing to the direction of high accuracy, high efficiency, good flexibility and good stability, and a lot of computation technologies had developed relatively mature. However, so far, there is no the relevant research for complex surface seismic waves traveltimes computation which limits the existing technology applied in the mountains, hills and other complex surface areas.
The purpose of the study related to the content of this paper is to propose and implement seismic waves traveltimes computation program under the conditions of complex surface. In order to achieve this objective, we propose the following research ideas: Firstly, review the existing computation technologies of seismic traveltimes and select a optimal computation method (FMM) as the foundation of other follow-up methods; Secondly, study the FMM carefully and improve it in each aspect; Finally, integrate the improved FMM and the complex surface problems, we propose the implementation strategy of studying on the computation of seismic traveltimes in the condition of surface topography. Under the guidance of these ideas, we did the following three aspects of work:
①We review various traveltimes algorithms: First, classify various traveltimes algorithms; Second, state the basic principle and implementation strategy of various traveltimes algorithms; Third, compare these algorithms, we know the present situation and development trend of traveltimes algorithms by reviewing them; finally, we draw a conclusion: The finite-difference method is an optimal algorithm to calculating seismic traveltimes and FMM is an optimal finite-difference algorithm. So, we select FMM as the basic algorithm to study the computation of seismic traveltimes in the condition of surface topography.
②We further research the FMM: First, discuss the origin and development, basic principles and implementation, unconditional stability, computational accuracy and efficiency, et al of FMM in detail, and get the following conclude: The order of difference format is an important factor impacting the calculating accuracy of FFM, the order of difference scheme is higher, and the calculating accuracy is higher. The calculating accuracy of second-order scheme is higher than first-order scheme’s. Grid space is another important factor impacting calculating accuracy, the grid space is larger, the calculating accuracy is less, and vice versa. The heap sort technology is the most important factor impacting the calculating efficiency of FMM; Second, according to improving the algorithm of FMM form the local difference scheme, greatly enhance the computation accuracy of the algorithm; then start with improving the heap sort technology, greatly enhance the computation efficiency of the algorithm. Finally, a large number of examples about the computation of the FMM verify that the various measures for improving the effective and the results are very good.
③The implementation of the computing seismic traveltimes in the condition of surface topography: First, establish a reasonable, complex physical model of the surface corresponding to the mathematical model; Second, the model is complete, introduce FMM to solve complex surface problems and propose the implementation strategy about the seismic waves traveltimes computation in the complex surface condition. and set up implementation process framework; Third, through processing the velocity model and making interpolation processing near interface and surface, compute the traveltimes on interface and surface more reasonably; Finally, a large number of examples of computation and analysis confirmed that the implementation strategy about the seismic time computation which is presented in this paper is feasible, the results of computation can well describe propagating process of seismic wave at complicated surface area.
The main innovation of results of the research as follows:①Through changing the partial algorithm, we enhance the accuracy of the FMM;②Through developing the heap sort technology, we greatly enhance the computation efficiency of FMM;③We first present a technical scheme of the seismic traveltimes computation in surface topography condition, set up implementation process framework and compily complete program code.
The main results of the research have great significance to study on the structure and propagation characteristics of seismic wave field under the condition of complex surface topography, lay the theoretical foundation for the research of seismic data collecting, processing and interpreting in complex surface technology condition and have a very important theoretical significance for the hydrocarbon exploration in complex surface area(especially in the western mountains).
引文
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[2] Aki K, Christoffersson A, Husebye E S. Determination of the three- dimensional seismic structure of the lithosphere[J]. J Geophys Res, 1977, 82: 277-296.
[3] Thurber C H. Earthquake locations and three-dimensional crustal structure in the Coyote Lake area, central California[J]. J Geophys Res, 1983, 88: 8226-8236.
[4] Hole J A, Clowes R M, Ellis R M. Interface inversion using broadside seismic refraction data and three-dimensional traveltime calculations[J]. J Geophys Res, 1992, 97: 3417-3429.
[5] Eberhart-Phillips D, Michael A J. Three-dimensional velocity structure, seismicity, and fault structure in the Parkfield Region, central California[J]. J Geophys Res, 1993, 98: 15737-15758.
[6] Graeber F M, Asch G. Three-dimensional models of P wave velocity and P-to-S velocity ratio in the southern central Andes by simultaneous inversion of local earthquake data[J]. J Geophys Res, 1999, 104: 20237-20256.
[7] Zelt B C, Ellis R M, Zelt C A, Hyndman R D, Lowe C, Spence G D, Fisher M A. Three-dimensional crustal velocity structure beneath the Strait of Georgia, British Columbia[J]. Geophys J Int, 2001, 144: 695-712.
[8] Graeber F M, Houseman G A, Greenhalgh S A. Regional teleseismic tomography of the western Lachlan Orogen and the Newer Volcanic Province, southeast Australia[J]. Geophys J Int, 2002, 149: 249-266.
[9] Widiyantoro S, Van Der Hilst R. Mantle structure beneath Indonesia inferred from high-resolution tomographic imaging[J]. Geophys J Int,1997, 130: 167-182.
[10] Gorbatov A, Widiyantoro S, Fukao Y, Gordeev E. Signature of remnant slabs in the North Pacific from P-wave tomography[J]. Geophys J Int, 2000, 142: 27-36.
[11] Gorbatov A, Fukao Y, Widiyantoro S, Gordeev E. Seismic evidence for a mantle plume oceanwards of the Kamchatka-Aleutian trench junction[J]. Geophys J Int, 2001, 146: 282-288.
[12] Dziewonski A M, Woodhouse J H. Global images of the Earth's interior[J]. Science, 1987, 236: 37-48.
[13] Van Der Hilst R D, Widiyantoro S, Engdahl E R. Evidence for deep mantle circulation from global tomography[J]. Nature, 1997, 386: 578-584.
[14] Bijwaard H, Spakman W. Non-linear global P-wave tomography by iterated linearized inversion[J]. Geophys J Int, 2000, 141: 71-82.
[15] Sena A G, Toksoz M N. Kirchhoff migration and velocity analysis for converted and nonconverted waves in anisotropic media[J]. Geophysics, 1993, 58: 265-276.
[16] Gray S H, May W P. Kirchhoff migration using eikonal equation traveltimes[J]. Geophysics, 1994, 59: 810-817.
[17] Epili D, Mcmechan G A. Implementation of 3-D prestack Kirchhoff migration, with application to data from the Ouachita frontal thrust zone[J]. Geophysics, 1996, 61: 1400-1411.
[18] Buske S. 3-D prestack Kirchhoff migration of the ISO89-3D data set, Pure appl[J]. Geophys, 1999, 156: 157-171.
[19] Julian B R, Gubbins D. Three-dimensional seismic ray tracing[J]. J Geophys, 1977, 43: 95-113.
[20] Rawlinson N, Houseman G A, Collins C D N. Inversion of seismic refraction and wide-angle reflection traveltimes for 3-D layered crustal structure[J]. Geophys J Int, 2001, 145: 381-401.
[21] Um J, Thurber C. A fast algorithm for two-point seismic ray tracing[J]. Bull Seism Soc Am, 1987, 77: 972-986.
[22] Prothero W A, Taylor W J, Eickemeyer J A. A fast, two- point,three- dimensional raytracing algorithm using a simple step search method[J]. Bull Seism Soc Am, 1988, 78: 1190-1198.
[23] Grechka V Y, Mcmechan G A. 3-D two-point ray tracing for heterogeneous,weakly transversely isotropic media[J]. Geophysics, 1996, 61: 1883-1894.
[24] Pereyra V, Lee W H K, Keller H B. Solving two-point seismicray tracing problems in a heterogeneous medium[J]. Bull Seism Soc Am, 1980, 70: 79-99.
[25] Zhao D, Hasegawa A, Horiuchi S. Tomographic imaging of Pand S wave velocity structure beneath Northeastern Japan[J]. J Geophys Res, 1992, 97: 19909-19928.
[26] Cassell B R. A method for calculating synthetic seismograms in laterally varying media[J]. Geophys J R Astr Soc, 1982, 69: 339-354.
[27] Sambridge M S, Kennett B L N. Boundary value ray tracing in a heterogeneous medium: a simple and versatile algorithm[J]. Geophys J Int, 1990, 101: 157-168.
[28] Bulant P. Two-point ray tracing in 3-D, Pure appl[J]. Geophys, 1996, 148: 421-447.
[29] Asakawa E K T. Seismic ray tracing using linear traveltime interpolation [J ]. Geophysical Prospecting, 1993, 41(1): 99-111.
[30] 涂齐催,刘怀山. 利用线性旅行时插值射线追踪计算近地表模型初至波走时[J]. 物探与化探, 2006, 30(2): 148-153.
[31] 彭直兴,张芬. 地震波旅行时非线性/线性联合插值法[J]. 成都理工大学学报, 2005, 32(3): 322-324.
[32] 聂建新,杨慧珠. 地震波旅行时二次/线性联合插值法[J]. 清华大学学报, 2003, 43(11): 1495-1498.
[33] 赵改善,陈伟等. 基于旅行时线性插值的地震射线追踪算法[J]. 石油物探, 1998, 37(2): 14-24.
[34] Nakanishi I, Yamaguchi K. A numerical experiment on nonlinear image reconstruction from first-arrival times for two-dimensional island arc structure[J]. J Phys Earth, 1986, 34: 195-201.
[35] Moser T J. Shortest path calculation of seismic rays[J]. Geophysics, 1991, 56: 59-67.
[36] Fischer R, Lees J M. Shortest path ray tracing with sparse graphs[J]. Geophysics, 1993, 58: 987-996.
[37] Cheng N, House L. Minimum traveltime calculations in 3-D graph theory[J]. Geophysics, 1996, 61: 1895-1898.
[38] 刘洪,李幼铭等. 计算最小走时和路径的界面网全局方法[J]. 地球物理学报, 1995, 38(6): 823-831.
[39] 张建中,陈世军等. 最短路径射线追踪方法及其改进[J]. 地球物理学进展, 2003, 18(1): 146-150.
[40] Vinje V E A. 3-D ray modellingby wavefront construction in open models[J]. Geophys Prospect, 1993, 64: 1912-1919.
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