高频渐近散射理论及其在地球物理场数值模拟与反演成像中的应用——研究历史与研究现状概述以及若干新进展

doi:10.13278/j.cnki.jjuese.201604303

摘要/Abstract

摘要：

为了对高频渐近散射理论及其在地球物理场数值模拟与反演成像中的应用有一个提纲挈领的了解，对与之有关的研究历史和研究现状进行了概述，并对近5年内笔者在这个领域中所取得的一些进展做了介绍。针对目前文献中所存在的一些问题，首先，对散射理论中的一些基本概念和基本公式进行了回顾，并对这些概念和公式的数学物理内涵进行了重申和强调；其次，对高频渐近散射理论的研究历史和研究现状及其在地球物理场数值模拟与反演成像中的应用成效进行了概述；再次，对近5年内笔者所取得的一些研究进展进行了介绍，其中包括对面积分方程的拟解析近似、广义Beam-Born（Beam-Rytov）型近似以及弱散射近似所引入的误差等等；最后，对高频渐进散射理论的自身发展及其在地球物理场数值模拟与反演成像中的应用前景进行了展望。无论是在历史上还是在现阶段，高频渐近散射理论在地球物理场数值模拟与反演成像中一直占有不可替代的地位，尤其是在反射地震偏移成像和全波形反演研究中更是如此。高频渐近散射理论的进一步发展依赖于对高频渐近Green函数的研究。随着相应研究的不断深入，高频渐近散射理论今后将会在地球物理场数值模拟与反演成像领域中发挥更大的作用。

关键词: 高频渐近散射理论, 数值模拟和成像, 研究历史, 研究现状, 发展趋势, 应用前景

Abstract:

To bring out the essentials of high-frequency asymptotic scattering theories and their applications in numerical modeling and imaging of geophysical fields, we give a brief overview of the corresponding research histories and the state-of-the-art. Also, we present some new developments that we have achieved in the last five years in the investigation of the high-frequency asymptotic scattering theories. Considering some problems in the literature, we first give a brief review of the basic concepts and formulas in the scattering theory; and reaffirm and underline the mathematical physics intensions of the concepts and formulas. Next, we give an overview of the research history and the state-of-the-art of the high-frequency asymptotic scattering theories, and make some comments on some related topics. Moreover, we present some new developments that we have achieved in the last five years in the corresponding studies, including the quasi-analytical approximation of the surface integral equation of the scattered waves, the generalized Beam-Born and Beam-Rytov type approximations, and so on. Finally, we give some prospects for the road ahead of the development of the high-frequency asymptotic scattering theories themselves and their application in numerical modeling and imaging of geophysical fields. Not only in history but also at present, play the asymptotic scattering theories an irreplaceable role in numerical modeling and imaging of geophysical fields, especially in migration of reflection seismic data and in full waveform inversion. In author's point of view, the further development of the high-frequency asymptotic scattering theories depends on the investigation of the Green's function. Along with the uninterrupted deep-going of the corresponding studies, the high-frequency asymptotic scattering theories will play a much more important role in numerical modeling and imaging of geophysical fields in future.

Key words: high-frequency asymptitics scattering theory, numerical modeling and imaging, research history, state-of-the-art, the road ahead, application prospects

中图分类号:

P631.4

孙建国. 高频渐近散射理论及其在地球物理场数值模拟与反演成像中的应用——研究历史与研究现状概述以及若干新进展[J]. 吉林大学学报(地球科学版), 2016, 46(4): 1231-1259.

Sun Jianguo. High-Frequency Asymptotic Scattering Theories and Their Applications in Numerical Modeling and Imaging of Geophysical Fields: An Overview of the Research History and the State-of-the-Art, and Some New Developments[J]. Journal of Jilin University(Earth Science Edition), 2016, 46(4): 1231-1259.

参考文献

1] Born M, Wolf E. Principles of Optics[M]. 6th ed. New York: Pergamon Press, 1980.

[2] Bowman J J, Senior T B A, Uslenghi P L E. Electromagnetic and Acoustic Scattering by Simple Shapes[M]. Amsterdam: North-Holland, 1969.

[3] Felsen L B, Marcuvitz. Radiation and Scattering of Waves[M]. Englewood Cliffs: Prentice-Hall, 1973.

[4] Hecht E. Optics. Beijing[M]. [S.l.]: Higher Education Press, 2005.

[5] Ishimaru A. Electromagnetic Waves Propagation, Radiation, and Scattering[M]. Englewood Cliffs: Prentice-Hall, 1991.

[6] Kline M, Kay I W. Electromagnetic Theory and Geometrical Optics[M]. New York: Interscience, 1965.

[7] Kravtsov Yu A, Orlov Yu I. Geometrical Optics of Inhomogeneous Media[M]. Berlin: Springer-Verlag, 1990.

[8] Mcnamara D A, Pistorius C W I, Malherbe J A G. Introduction to the Uniform Geometrical Theory of Diffraction[M]. Norwood: Artech House, 1990.

[9] Born M, Wolf E. 光学原理:上、下[M]. 7版. 北京:电子工业出版社,2006. Born M, Wolf E,Principles of Optics: Volumes 1 and 2[M]. 7th ed. Beijing:Publishing House of Electronics Industry,2006.

[10] ?ervený V. Seismic Ray Theory[M]. Cambridge: Cambridge University Press, 2001.

[11] 李永俊. 电磁理论的高频方法[M]. 武汉:武汉大学出版社,1999. Li Yongjun. High-Frequency Methods of Electromagnetic Theory[M]. Wuhan: Wuhan University Press, 1999.

[12] 汪茂光. 几何绕射理论[M]. 2版. 西安:西安电子科技大学出版社,1994. Wang Maoguang. Geometrical Theory of Diffraction[M]. Xi'an: Xi Dian University Press, 1994.

[13] Coates R T, Chapman C H. Generalized Born Scattering of Elastic Waves in 3-D Media[J]. Geophysical Journal International, 1991, 107: 231-263.

[14] Senior T B A, Uslenghi P L E. Experimental Detection of the Edge-Diffracted Cone[J]. Proceedings of the IEEE, 1972,60(11): 1448.

[15] Luneburg R K. Mathematical Theory of Optics[M]. Berkley: University of California Press, 1964.

[16] Aki K, Richards P G. Quantitative Seismology Theory and Methods: Volume 1 and 2[M]. San Francisco: W H Freeman and Co,1980.

[17] Keller J B. Geometrical Acoustics: I: The Theory of Weak Shock Waves[J]. Journal of Applied Physics, 1954, 25(8): 116-130.

[18] 长春地质学院,成都地质学院,武汉地质学院合编. 地震勘探:原理和方法[M]. 北京:地质出版社,1980. Compiled By Changchun College of Geology, Chengdu College of Geology, and Wuhan College of Geology. Seismic Exploration: Principles and Methods[M]. Beijing: Geological Publishing House, 1980.

[19] Keller J B.Geometrical Theory of Diffraction[J]. Jo-urnal of Optical Society of America, 1962, 52: 116-130.

[20] Karal F G, Keller J B, Elastic Wave Propagation in Homogeneous and Inhomogeneous Media[J]. Journal of Acoustic Society of American, 1959, 3: 694-705.

[21] Goodman J W. Introduction to Fourier Optics[M]. 3rd ed. Roberts and Company Publishers, 2005.

[22] Hill R. Prestack Gaussian-Beam Depth Migration[J]. Geophysics, 2001, 66(4): 1240-1250.

[23] Chew W C.Waves and Fields in Inhomogeneous Media[M]. New York: Van Nostrand Reinhold, 1990.

[24] Devaney A J.Geophysical Diffraction Tomography[J]. IEEE Transactions on Geosciences and Remote Sensing, 1984, GE-22:3-13.

[25] Stratton J A. Electromagnetic Theory[M]. [S. l. ]: Mcgraw-Hill Book Company, 1941.

[26] 孙建国. 声波散射数值模拟的两种新方案[J]. 吉林大学学报(地球科学版),2006,36(5):863-868. Sun Jianguo.Two New Schemes for Numerical Mo-deling of Acoustic Scattering[J]. Journal of Jilin University (Earth Science Edition), 2006, 36(5):863-868.

[27] Zhdanov M S, Dmitriev V I, Fang S, et al. Quasia-nalytical Approximations and Series in Electromagnetic Modeling[J]. Geophysics, 2000, 65: 1746-1757.

[28] Zhdanov M S, Fang S. Three-Dimensional Quasi-Linear Electromagnetic Modeling and Inversion[M]//Oristaglio M, Spies B. Three-Dimensional Electromagnetics. Tulsa: Society of Exploration Geophysicists, 1999: 233-255.

[29] Zhdanov M S, Fang S, Hurs'An G. Electromagnetic Inversion Using Quasi-Linear Approximation[J]. Geophysics, 2000, 65: 1501-1513.

[30] Zhdanov M S, Tartaras E. Three-Dimensional Inversion of Multitransmitter Electromagnetic Data Based on the Localized Quasilinear Approximation[J]. Geophysical Journal International, 2002, 148: 506-519.

[31] Beylkin G. Imaging of Discontinuities in the Inverse Scattering Problem by Inversion of a Causal Generalized Radon Transform[J]. Journal of Mathematical Physics, 1985, 26: 99-108.

[32] Beylkin G. Mathematical Theory for Seismic Migration and Spatial Resolution[M]// Worthington M H. Deconvolution and Inversion. Oxford: Blackwell Scientific Publications, 1987, 291-304.

[33] 仇庆玖,陈恕行,是嘉鸿,等. 傅里叶积分算子及其应用[M]. 北京:科学出版社,1985. Qiu Qingjiu, Chen Shuxing, Shi Jiahong, et al. The Fourier Integral Operator and Its Applications[M]. Beijing: Science Press, 1985.

[34] Bleistein N, Gray S H. An Extension of the Born Inversion Method to a Depth Dependent Reference Profile[J]. Geophysical Prospecting, 1985, 33: 999-1022.

[35] Bleistein N. On the Imaging of Reflectors in the Earth[J]. Geophysics, 1987,52: 931-942.

[36] Bleistein N, Cohen J K, Hagin F G. Two and One-Half Dimensional Born Inversion with an Arbitrary Reference[J]. Geophysics, 1987, 52: 26-36.

[37] Bleistein N,Cohen J K, Stockwell J W,Mathematics of Multidimensional Seismic Imaging Migration, and Inversion[M]. New York: Springer-Verlag,2001.

[38] LambarÉG. Sterotomography[J]. Geophysics, 2003, 73(5): VE25-VE34.

[39] Schleicher J, Tygel M, Hubral P. Seismic True-Amplitude Imaging[M]. SEG, 2007.

[40] Wapenaar C P A, Berkhout A J. Elastic Wave Field Extrapolation[M]. Amsterdam: Elsevier, 1989.

[41] Zhdanov M S.Integral Transforms in Geophysics[M]. Berlin: Springer, 1988.

[42] Virieux J, Operto S. An Overview of Full-Waveform Inversion in Exploration Geophysics[J]. Geophysics, 2009, 74(6): WCC127-WCC152.

[43] Etgen J, Gray S H, Zhang Y. An Overview of Depth Imaging in Exploration Geophysics[J]. Geophysics, 2009, 74(6): WCA5-WCA17.

[44] Thierry P G, Lambaré P, Podvin, et al. 3-D Preserved Amplitude Prestack Depth Migration on a Workstation[J]. Geophysics, 1999, 64: 222-229.

[45] Thierry P, Operto S, Lambar G. Fast 2D Ray-Born Inversion/Migration in Complex Media[J]. Geophysics, 1999, 64: 62-181.

[46] Schuster G T. Reverse-Time Migration=Generalized Diffraction Stack Migration[C]// Abstract of SEG Annual Meeting. Houston: SEG, 2009: 1280-1283.

[47] Zhan G, Dai W, Zhou M, et al. Generalized Diffraction-Stack Migration and Filtering of Coherent Noise[J]. Geophysical Prospecting, 2014, 62: 1-16.

[48] Sun H, Schuster G T. 2-D Wave Path Migration[J]. Geophysics, 2001, 66: 1528-1537.

[49] Woodward M J. Wave-Equation Tomography[J]. Geophysics, 1992, 57: 15-26.

[50] Woodward M J, Nichols D, Zdraveva O, et al. A Decade of Tomography[J]. Geophysics, 2008, 73(5): VE5-VE11.

[51] Ursin B, Tygel M. Reciprocal Volume and Surface Scattering Integrals for Anisotropic Elastic Media[J]. Wave Motion, 1997, 26: 31-42.

[52] Schleicher J, Tygel M, Ursin B, et al. The Kirchhoff-Helmholtz Integral for Anisotropic Elastic Media[J]. Wave Motion, 2001,34: 353-364.

[53] Tygel M, Schleicher J, Hubral P. The Kirchhoff-Helmholtz Integral Pair[J].Journal of Computational Acoustics, 2001, 9(4): 1383.

[54] Huang X, Sun H, Sun J. Born Modeling for Heterogeneous Media Using the Gaussian Beam Summation Based Green's Function[J]. Journal of Applied Geophysics, 2016, 131:191-201.

[55] Huang X, Sun J, Sun Z. Local Algorithm for Computing Complex Travel Time Based on the Complex Eikonal Equation[J]. Physical Review E, 2016, 93(4): 043307.

[56] Berkhout A J, Verschuur D J. Full Wavefield Migration, Utilizing Surface and Internal Multiple Scattering[C]// Abstract of SEG Annual Meeting. San Antonio: SEG, 2011: 3212-3215.

[57] Davydenko M, Verschuur D J. Full Wavefield Migration, Using Internal Multiples for Undershooting[C]// Abstract of SEG Annual Meeting. Houston: SEG, 2013: 3741-3744.

[58] Weglein A B. Multiples: Signal or Noise?[C]// Abstract of SEG Annual Meeting. Denver: SEG, 2014: 4393-4398.

[59] Weglein A B. Multiples Can Be Useful (at Times) to Enhance Imaging, by Providing an Approximate Image of an Unrecorded Primary, But Its Always Primaries That Are Migrated or Imaged[C]//Abstract of SEG Annual Meeting. New Orleans: SEG, 2015:4033-4037.

[60] 朗道, 栗夫席兹. 理论物理学教程:第三卷:量子力学(非相对论部分)[M]. 6版. 北京:高等教育出版社,2008. Landau L D, Lifshits E M. Theoretical Physics:III. Quantum Mechanics (Non-Relativity Theory)[M]. 6th ed. Beijing: Higher Education Press, 2008.

[61] Mavko G, Mukerji T, Dvorikin J. The Rock Physics Handbook: Tools for Seismic Analysis in Porous Media[M]. Cambridge: Cambridge University Press, 1998.

[62] Bleistein N. Mathematical Methods for Wave Phenomena[M]. New York: Academic Press Inc, 1984.

[63] James G L. Geometrical Theory of Diffraction for Electromagnetic Waves[M]. Stevenage: Peter Peregrinus Ltd, 1976.

[64] Jaramillo H H, Bleistein N. The Link of Kirchhoff Migration and Demigration to Kirchhoff and Born Modeling[J]. Geophysics, 1999,64 (6): 1793-1805.

[65] Courant R,Hilbert D.Methods of Mathematical Phy-sics: Volume II[M]. New York: Wiley, 2008.

[66] Popov M M. A New Method of Computation of Wave Fields Using Gaussian Beams[J]. Wave Motion, 1982, 4: 85-97.

[67] Popov M M, Semtchenok N M, Popov P M, et al. Depth Migration by the Gaussian Beam Summation Method[J]. Geophysics, 2010, 75(2): S81-S93.

[68] Babich V M, Buldyrev V S. Short-Wavelength Diffraction Theory: Asymptotic Methods[M]. Berlin: Springer Verlag, 1990.

[69] Brekhovskikh L M. Waves in Layered Media[M]. Academic Press, 1960.

[70] Chapman C H, Drummond R. Body-Wave Seismograms in Inhomogeneous Media Using Maslov Asymptotic Theory[J]. Bulletin of the Seismological Society of America, 1982, 72: S277-S317.

[71] White S, Norris A, Bayliss A, Burridge R. Some Remarks on the Gaussian Beam Summation Method[J]. Geophys J R Astr Soc, 1987, 89: 579-636.

[72] Bortfeld R K, Geometrical Ray Theory: Rays and Traveltimes in Seismic Systems (Second-Order Approximation of the Traveltimes)[J]. Geophysics, 1989, 54: 342-349.

[73] Hubral P, Schleicher J, Tygel M. Three-Dimensional Paraxial Ray Properties: I: Basic Relations[J]. Journal of Seismic Exploration, 1992, 1: 265-279.

[74] Hubral P, Schleicher J, Tygel M. Three-Dimensional Paraxial Ray Properties: II: Applications[J]. Journal of Seismic Exploration, 1992, 1: 347-362.

[75] Tygel M, Schleicher J, Hubral P. A Unified Approach in 3-D Seismic Reflection Imaging, Part II: Theory[J]. Geophysics, 1996, 61(3): 759-775.

[76] De Hoop M V, Bleistein N. Generalized Radon Transform Inversions for Reflectivity in Anisotropic Elastic Media[J]. Inverse Problems, 1997, 13: 669-690.

[77] Alkhalifah T. Gaussian Beam Depth Migration for Anisotropic Media[J]. Geophysics, 1995, 60(5): 1474-1484.

[78] Albertin U, Yingst D, Kitchenside P. True Amplitude Beam Migration[C]// Abstract of SEG Annual Meeting. Denver: SEG, 2004: 398-401.

[79] Gray S H, Bleistein N. True-Amplitude Gaussian-Beam Migration[J]. Geophysics, 2009, 74(2): S11-S23.

[80] Han J, Wang Y, Lu J. Multi-Component Gaussian Beam Prestack Depth Migration[J]. Journal of Geophysics and Engeneering, 2013, 10: 1-10.

[81] Hill N R. Prestack Gaussian-Beam Depth Migration[J]. Geophysics, 2001, 66(4): 1240-1250.

[82] Protasov M I, Tcheverda V A. True Amplitude Elastic Gaussian Beam Imaging of Multicomponent Walkaway Vertical Seismic Profiling Data[J]. Geophysical Prospecting, 2012, 60: 1030-1042.

[83] Protasov M I,Tcheverda V A. True Amplitude Imaging by Inverse Generalized Radon Transform Based on Gaussian Beam Decomposition of the Acoustic Green?s Function[J]. Geophysical Prospecting, 2011, 59(2): 197-209.

[84] ?ervený V, Pšen?i K I. Gaussian Beams in Inhomogeneous Anisotropic Layered Structures[J]. Geophy-sical Journal International, 2010, 180: 798-812.

[85] ?ervený V. Synthetic Body Wave Seismograms for Laterally Varying Layered Structures by the Gaussian Beam Method[J]. Geophys J Roy Astr Soc, 1983, 73: 389-426.

[86] Frazer L N, Sen M K. Kirchhoff-Helmholtz Reflection Seismograms in a Laterally Inhomogeneous Multi-Layered Elastic Medium-I. Theory[J]. Geophys J R Astr Soc, 1985, 80: 121-147.

[87] Sen M K, Frazer L N. Kirchhoff-Helmholtz Reflection Seismograms in a Laterally Inhomogeneous Multi-Layered Elastic Medium: Part II: Computations[J]. Geophys J Roy Astr Soc, 1985, 82: 415-437.

[88] Sun J. The Relationship Between the First Fresnel Zone and the Normalized Geometrical Spreading Factor[J]. Geophysical Prospecting, 1996, 44(3): 351-374.

[89] Sun J. 3-D Crosswell Transmissions: Paraxial Ray Solutions and Reciprocity Paradox[J]. Geophysics, 1995, 60(3): 810-820.

[90] Cohen J K,Hagin F G,Bleistein N. Threedimensional Born Inversion with an Arbitrary Reference[J]. Geophysics, 1986, 51: 1552-1558.

[91] Coates R T, Chapman C H. Ray Perturbation Theory and the Born Approximation[J]. Geophysical Journal International, 1990, 100: 379-392 .

[92] Xu S, Lambar G. Fast Migration/Inversion with Multivalued Ray Fields: Part 1: Method, Validation Test, and Application in 2D to Marmousi[J]. Geophysics, 2004, 69(5): 1311-1319.

[93] Xu S, Chauris H, Lambaré G, Noble M. Common-Angle Migration: A Strategy for Imaging Complex Media[J]. Geophysics, 2001, 66: 1877-1894.

[94] Miller D, Oristaglio M, Beylkin G. A New Slant on Seismic Imaging: Migration and Integral Geometry[J]. Geophysics, 1987, 52 (7): 943-964.

[95] Tygel M, Ursin B. Weak-Contrast Edge and Vertex Diffractions in Anisotropic Elastic Media[J]. Wave Motion, 1999, 29(4): 363-373.

[96] Yu G X, Fu L Y. Rytov Series Approximation for Rough Surface Scattering[J]. Bulletin of the Seismological Society of America, 2012, 102(1): 42-52.

[97] Marks D L. A Family of Approximations Spanning the Born and Rytov Scattering Series[J]. Optics Express, 2006, 14(19): 8837-8848.

[98] Vidale J.Finite-Difference Calculation of Travel Ti-mes[J]. Bulletin of the Seismological Society of America, 1988, 78: 2062-2076.

[99] Vinje V, Iversen E, Gjoystdal H. Traveltime and Amplitude Estimation Using Wavefront Construction[J]. Geophysics, 1993, 58: 1157-1166.

[100] Sethian J A. A Fast Marching Level Set Method for Monotonically Advancing Fronts[J]. Proceedings of the National Academy of Sciences of the United States of America, 1996, 93: 1591-1595.

[101] Sethian J A. Fast Marching Methods[J]. SIAM Review, 1999, 41: 199-235.

[102] Sethian J A. Evolution, Implementation, and Application of Level Set and Fast Marching Methods for Advancing Fronts[J]. Journal of Computational Physics, 2001, 169: 503-555.

[103] Sethian J A, Popovici A M. 3-D Traveltime Computation Using the Fast Marching Method[J]. Geophysics, 1999, 64: 516-523.

[104] Rawlinson N, Sambridge M. Multiple Reflection and Transmission Phases in Complex Layered Media Using a Multistage Fast Marching Method[J]. Geophysics, 2004, 69: 1338-1350.

[105] Rawlinson N, Sambridge M. Wave Front Evolution in Strongly Heterogeneous Layered Media Using the Fast Marching Method[J]. Geophysical Journal International, 2004, 156, 631-647.

[106] Sun J, Sun Z, Han F. A Finite Difference Scheme for Solving the Eikonal Equation Including Surface Topography[J]. Geophysics, 2011, 76(4): T53-T63.

[107] Leung S, Qian J, Burridge R. Eulerian Gaussian Beams for High-Frequency Wave Propagation[J]. Geophysics, 2007, 72(5): SM61-SM76.

[108] Li S,Fomel S. Improving Wave-Equation Fidelity of Gaussian Beams by Solving the Complex Eikonal Equation[C]// Abstract of SEG Annual Meeting. San Antonio: SEG, 2011: 3829-3833.

[109] ?ervený V. The Appliocation of Ray Tracing to the Propagation of Shear Waves in Complex Media[M]// Dohr G P. Seismic Share Waves. London: Geophysical Press,1985: 1-124.

[110] Slaney S M, Kak A C, Larsen L E. Limitations of Imaging with First-Order Diffraction Tomography[J]. IEEE Transactions on Microwave Theory and Techniques, 1984, MTT-32: 860-874.

[111] 《数学手册》编写组. 数学手册[M]. 北京:高等教育出版社,1979. Compile Group of Handbook of Mathematics. Handbook of Mathematics[M]. Beijing: Higher Education Press,1979.

[112] 石秀林,孙建国,孙辉,等. 基于Delta波包叠加的时间域深度偏移[J]. 地球物理学报,2016, 59(7):2641-2649. Shi Xiulin, Sun Jianguo, Sun Hui, et al. The Time-Domain Depth Migration by the Summation of Delta Packets[J]. Chinese Journal of Geophysics, 2016, 59(7): 2641-2649.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

[1]	方石, 赵云. 比较沉积学概念体系的厘定与重构[J]. 吉林大学学报(地球科学版), 2020, 50(2): 480-499.
[2]	任军平, 王杰, 刘晓阳, 贺福清, 何胜飞, 左立波, 许康康, 龚鹏辉, 孙凯, 刘宇. 非洲中南部铜多金属矿床研究现状及找矿潜力分析[J]. 吉林大学学报(地球科学版), 2017, 47(4): 1083-1103.
[3]	林君, 张扬, 张思远, 舒旭, 杜文元, 林婷婷. 强电磁干扰下磁共振地下水探测噪声压制方法研究进展[J]. 吉林大学学报(地球科学版), 2016, 46(4): 1221-1230.
[4]	孙建国. Kirchhoff型偏移理论的研究历史、研究现状与发展趋势展望——与光学绕射理论的类比、若干新结果、新认识以及若干有待于解决的问题[J]. J4, 2012, 42(5): 1521-1552.
[5]	林君, 蒋川东, 段清明, 王应吉, 秦胜伍, 林婷婷. 复杂条件下地下水磁共振探测与灾害水源探查研究进展[J]. J4, 2012, 42(5): 1560-1570.