基于小波分析的确1-10TeV宇宙线时间变化及气象效应研究
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摘要
宇宙线强度随时间的变化，是宇宙线物理、太阳地球物理和天体物理等交叉学科中的重要问题之一。通过宇宙线变化可以研究宇宙线的起源、传播以及受太阳的调制等等。但由于受到观测阈能和观测设备技术水平的限制，TeV到10TeV能区宇宙线变化的研究尚处于空白。
羊八井宇宙线观测站Tibet ASγ阵列海拔高度处于超高能宇宙线空气簇射发展极大附近，使在该处探测的簇射粒子密度高，阵列的观测阈能低，特别适合于研究1-10TeV能量的宇宙线变化。
本论文将小波变换与传统统计折叠法相结合作为数据分析方法，利用仿真实验信号检验了其有效性和优越性，发现这种方法可以更有效地从高噪声信号中提取弱周期信号，并给出周期变化的相位分布。且首次将该方法应用于羊八井宇宙线观测站Tibet AS γ阵列1997年11月到1998年6月的实验记录数据的周期分析，对1-10TeV宇宙线流强的时间变化及其气象影响进行了研究。
研究发现TeV和10TeV宇宙线流强中存在着太阳日和半太阳日周期变化。TeV宇宙线流强1d和0.5d周期变化的信噪比分别为9.8和12.9，其变化幅度分别为0.4±0.26％和0.3±0.18％，最大变化处的相位分别在约0.8(18h)和0.9(11h)。10TeV宇宙线流强1d和0.5d周期变化的信噪比分别为10.1和12.9，其变化幅度分别约为0.5±0.34％和0.35±0.23％，最大变化处的相位分别在约0.8(18h)和0.9(11h)。
应用上述方法分析了气象参量，包括观测面处大气压和室外温度的日变化和半日变化，接下来的关联分析和拟合计算表明：宇宙线流强的周期变化与气压和温度的周期变化显著相关。利用二元回归分析对小波变换后的宇宙线流强数据进行气象效应修正，并进行了修正检验，证明修正是有效的。
对气象效应修正后的宇宙线流强数据进行周期分析，发现TeV和10TeV宇宙线数据中存在半日、0.996和1.002日周期变化。10TeV宇宙线1.002日、0.996日和半日周期变化的信噪比分别为6.4、5.6和8.1，其变化幅度分别约为0.15±0.095％、0.15±0.087％和0.08±0.04％，最大值处的相位分别在约0.3(7h)、0.7(17h)和0.1(1h)。TeV宇宙线1.002日、0.996
西南交通大学硕士研究生学位论文第n页
日和半日周期变化的信噪比分别为6.1、5.1和7.1，其变化幅度分别约为
0.125士0.078%、0.1士0.068%和0.05士0.031%，最大值处的相位分别在约
0.3(7h)、0.7(17h)和0.9(11h).这些周期变化是如何引起的，还需要进一步
深入研究。
宇宙线的恒星日变化紧密联系于宇宙线的起源、其传播途径的性质，
以及宇宙线的加速机制等宇宙线物理中最基本的重大问题。通过对气象效
应修正后的宇宙线流强数据进行周期分析，发现了10TeV宇宙线流强的恒
星日(T== 0.997日)变化，其信噪比为5.0，变化幅度约为0.125士0.079%，
最大值处的相位约在0.45(11h)。相位基本与其它观测结果相符，而变化幅
度大1倍，我们的结果更接近于理论估计结果(0.17%)。TeV宇宙线恒星
日变化的信噪比为4.5，变化幅度约为0.1士0.062%，最大值处的相位约为
0 .45(1 lh)。
本论文采用信号处理中逐渐成熟且被大量采用的小波分析方法，并将
其与传统统计周期分析方法相结合，第一次来处理著名的羊八井宇宙线观
测站AS丫阵列的观测数据，具有重要的实际意义，可以为将来AS丫阵列
和ARGO实验的数据处理及分析打下良好的基础。
The time variation of the cosmic ray flux is one of crucial problems in the field of cosmic ray physics, solar geophysics and astrophysics, etc. The origin, propagation and modulation of cosmic ray can be studied through its variation. However, there is no information on the variation of 1-l0TeV cosmic ray because of the limit of the observation threshold energy and equipments.
The development of EAS with ultrahigh energy reaches about its maximum at the altitude of the Yangbajing Cosmic Ray Observation Station Tibet ASy array where the density of shower particles is high, and the threshold energy is low. Therefore, it is propitious to study the variation of 1-lOTeV cosmic ray.
In this thesis, wavelet transform combining with epoch folding methods is used as the data analysis method, and its validity and superiority is proved by the simulated experiments. It shows that this method is able to detect low-power level periodic signals in data with low signal-noise ratio more effectively, and give the distribution of phase. It is the first time that the method is used to search for the periodic signals of 1-l0TeV cosmic ray in the data obtained with Tibet II /HD AS Array for December of 1997 to June of 1998 and study its meteorological effect.
Solar time semi-diurnal and diurnal variations have been detected with about signal-noise ratio 12.9 and 10 for the TeV and l0TeV cosmic ray flux respectively. The semi-diurnal variations are of an amplitude 0.3 ?.1 8%, a phase 0.9(llh) for TeV cosmic ray and 0.35?.23%, 0.9(llh) for lOTeV. The diurnal variations are of amplitude 0.4 ?.26%, 0.5 ?.34%, and phase 0.8(18h) for TeV and lOTeV cosmic ray respectively.
Using the method above, solar time semi-diurnal and diurnal variations of meteorological parameters, including the atmospheric pressure and the temperature out of the room are analyzed. The following correlation analysis and data fit show that the obvious correlation exist between the periodic variations of trigger rate and record rate of the cosmic ray observation experiment and of the atmospheric pressure and the temperature out of the
room at the level of observation. The meteorological effect of cosmic ray is corrected by using binary regression analysis. And the correction is proved to be effective by correction inspection.
The periodic analysis for the data of cosmic ray flux after meteorological effect inspection shows that solar time semi-diurnal, 0.996 and 1.002 diurnal variations exit in the data of TeV and lOTeV cosmic ray. These periodic variations have been detected with about signal-noise ratio 8.1, 5.6 and 6.4, with amplitude 0.08?.04%, 0.15 ?.087% and 0.150.095%, and phase O.l(lh), 0.7(17h) and 0.3(7h) for lOTeV cosmic ray flux respectively, and with signal-noise ratio 7.1, 5.1 and 6.1, with amplitude 0.05 + 0.031%, 0.1 0.068% and 0.125 + 0.078%, and phase 0.9(1 Ih), 0.7(17h) and 0.3(7h) for TeV cosmic ray flux respectively. The origin of these periodic variations needs more investigation.
The sidereal diurnal variation of cosmic ray ties up with the most basic and important problem in cosmic ray physics such as the origin, propagation and the acceleration mechanisms of cosmic ray. The sidereal diurnal variation (T=0.997d) for lOTeV cosmic ray has been detected with about signal-noise ratio 5.0, with amplitude 0.125 + 0.079% and phase 0.45(llh) by analyzing the data of cosmic ray flux after meteorological effect corrected. The phase accords with other observation results basically, while the amplitude of variation is double. Our result of the amplitude is more close to the theory value (0.17%). The sidereal diurnal variation for TeV cosmic ray has been detected with about signal-noise ratio 4.5, with amplitude 0.10.062% and phase 0.45(1Ih).
It has practical significance to process the data obtained with the famous Yangbajing Cosmic Ray Observation Station ASy array for the first time using the technique of wavelet analysis which is maturing and used largely in the signal processing combining with classical epoch folding methods, and will lay the
羊八井宇宙线观测站Tibet ASγ阵列海拔高度处于超高能宇宙线空气簇射发展极大附近，使在该处探测的簇射粒子密度高，阵列的观测阈能低，特别适合于研究1-10TeV能量的宇宙线变化。
本论文将小波变换与传统统计折叠法相结合作为数据分析方法，利用仿真实验信号检验了其有效性和优越性，发现这种方法可以更有效地从高噪声信号中提取弱周期信号，并给出周期变化的相位分布。且首次将该方法应用于羊八井宇宙线观测站Tibet AS γ阵列1997年11月到1998年6月的实验记录数据的周期分析，对1-10TeV宇宙线流强的时间变化及其气象影响进行了研究。
研究发现TeV和10TeV宇宙线流强中存在着太阳日和半太阳日周期变化。TeV宇宙线流强1d和0.5d周期变化的信噪比分别为9.8和12.9，其变化幅度分别为0.4±0.26％和0.3±0.18％，最大变化处的相位分别在约0.8(18h)和0.9(11h)。10TeV宇宙线流强1d和0.5d周期变化的信噪比分别为10.1和12.9，其变化幅度分别约为0.5±0.34％和0.35±0.23％，最大变化处的相位分别在约0.8(18h)和0.9(11h)。
应用上述方法分析了气象参量，包括观测面处大气压和室外温度的日变化和半日变化，接下来的关联分析和拟合计算表明：宇宙线流强的周期变化与气压和温度的周期变化显著相关。利用二元回归分析对小波变换后的宇宙线流强数据进行气象效应修正，并进行了修正检验，证明修正是有效的。
对气象效应修正后的宇宙线流强数据进行周期分析，发现TeV和10TeV宇宙线数据中存在半日、0.996和1.002日周期变化。10TeV宇宙线1.002日、0.996日和半日周期变化的信噪比分别为6.4、5.6和8.1，其变化幅度分别约为0.15±0.095％、0.15±0.087％和0.08±0.04％，最大值处的相位分别在约0.3(7h)、0.7(17h)和0.1(1h)。TeV宇宙线1.002日、0.996
西南交通大学硕士研究生学位论文第n页
日和半日周期变化的信噪比分别为6.1、5.1和7.1，其变化幅度分别约为
0.125士0.078%、0.1士0.068%和0.05士0.031%，最大值处的相位分别在约
0.3(7h)、0.7(17h)和0.9(11h).这些周期变化是如何引起的，还需要进一步
深入研究。
宇宙线的恒星日变化紧密联系于宇宙线的起源、其传播途径的性质，
以及宇宙线的加速机制等宇宙线物理中最基本的重大问题。通过对气象效
应修正后的宇宙线流强数据进行周期分析，发现了10TeV宇宙线流强的恒
星日(T== 0.997日)变化，其信噪比为5.0，变化幅度约为0.125士0.079%，
最大值处的相位约在0.45(11h)。相位基本与其它观测结果相符，而变化幅
度大1倍，我们的结果更接近于理论估计结果(0.17%)。TeV宇宙线恒星
日变化的信噪比为4.5，变化幅度约为0.1士0.062%，最大值处的相位约为
0 .45(1 lh)。
本论文采用信号处理中逐渐成熟且被大量采用的小波分析方法，并将
其与传统统计周期分析方法相结合，第一次来处理著名的羊八井宇宙线观
测站AS丫阵列的观测数据，具有重要的实际意义，可以为将来AS丫阵列
和ARGO实验的数据处理及分析打下良好的基础。
The time variation of the cosmic ray flux is one of crucial problems in the field of cosmic ray physics, solar geophysics and astrophysics, etc. The origin, propagation and modulation of cosmic ray can be studied through its variation. However, there is no information on the variation of 1-l0TeV cosmic ray because of the limit of the observation threshold energy and equipments.
The development of EAS with ultrahigh energy reaches about its maximum at the altitude of the Yangbajing Cosmic Ray Observation Station Tibet ASy array where the density of shower particles is high, and the threshold energy is low. Therefore, it is propitious to study the variation of 1-lOTeV cosmic ray.
In this thesis, wavelet transform combining with epoch folding methods is used as the data analysis method, and its validity and superiority is proved by the simulated experiments. It shows that this method is able to detect low-power level periodic signals in data with low signal-noise ratio more effectively, and give the distribution of phase. It is the first time that the method is used to search for the periodic signals of 1-l0TeV cosmic ray in the data obtained with Tibet II /HD AS Array for December of 1997 to June of 1998 and study its meteorological effect.
Solar time semi-diurnal and diurnal variations have been detected with about signal-noise ratio 12.9 and 10 for the TeV and l0TeV cosmic ray flux respectively. The semi-diurnal variations are of an amplitude 0.3 ?.1 8%, a phase 0.9(llh) for TeV cosmic ray and 0.35?.23%, 0.9(llh) for lOTeV. The diurnal variations are of amplitude 0.4 ?.26%, 0.5 ?.34%, and phase 0.8(18h) for TeV and lOTeV cosmic ray respectively.
Using the method above, solar time semi-diurnal and diurnal variations of meteorological parameters, including the atmospheric pressure and the temperature out of the room are analyzed. The following correlation analysis and data fit show that the obvious correlation exist between the periodic variations of trigger rate and record rate of the cosmic ray observation experiment and of the atmospheric pressure and the temperature out of the
room at the level of observation. The meteorological effect of cosmic ray is corrected by using binary regression analysis. And the correction is proved to be effective by correction inspection.
The periodic analysis for the data of cosmic ray flux after meteorological effect inspection shows that solar time semi-diurnal, 0.996 and 1.002 diurnal variations exit in the data of TeV and lOTeV cosmic ray. These periodic variations have been detected with about signal-noise ratio 8.1, 5.6 and 6.4, with amplitude 0.08?.04%, 0.15 ?.087% and 0.150.095%, and phase O.l(lh), 0.7(17h) and 0.3(7h) for lOTeV cosmic ray flux respectively, and with signal-noise ratio 7.1, 5.1 and 6.1, with amplitude 0.05 + 0.031%, 0.1 0.068% and 0.125 + 0.078%, and phase 0.9(1 Ih), 0.7(17h) and 0.3(7h) for TeV cosmic ray flux respectively. The origin of these periodic variations needs more investigation.
The sidereal diurnal variation of cosmic ray ties up with the most basic and important problem in cosmic ray physics such as the origin, propagation and the acceleration mechanisms of cosmic ray. The sidereal diurnal variation (T=0.997d) for lOTeV cosmic ray has been detected with about signal-noise ratio 5.0, with amplitude 0.125 + 0.079% and phase 0.45(llh) by analyzing the data of cosmic ray flux after meteorological effect corrected. The phase accords with other observation results basically, while the amplitude of variation is double. Our result of the amplitude is more close to the theory value (0.17%). The sidereal diurnal variation for TeV cosmic ray has been detected with about signal-noise ratio 4.5, with amplitude 0.10.062% and phase 0.45(1Ih).
It has practical significance to process the data obtained with the famous Yangbajing Cosmic Ray Observation Station ASy array for the first time using the technique of wavelet analysis which is maturing and used largely in the signal processing combining with classical epoch folding methods, and will lay the
引文
[1] V. Hess, Phys. Z., 13(1912)1084
[2] W. Baade and F. Zwicky, Phys. Rev., 46, (1934)76
[3] M.V. Fouseca. Nucl. Phys. B (proc. Suppl.) 114(2003)233
[4] M.S. Longair, High Energy Astrophysics, Cambridge, Cambridge University Press, 1981, p. 117.
[5] N. L. Grigorov et al., Proc. 12nd Int. Cosmic Ray Conf., Vol.2 (1983) 135
[6] T.H. Bumett et al., Proc. 23rd Int. Cosmic Ray Conf. Vol.2 (1993) 5
[7] M. Ichimura et al., Phys. Rev., 48(1993) 1994
[8] M. Nagano et al., J. Phys., G10 (1984) 1295
[9] J. Linsley, et al., Proc.18th Int. Cosmic Ray Conf., Vol.12 (1983) 135
[10] E. Fermi, Phys. Rev., 75,1949,p.1169.
[11] R. Blandford & D. Eichler, Phys. Rep., 154(1987) 1
[12] W. I. Axford, Astrophys. J. Suppl., 90(1994) 937
[13] C. T. Hill & D.N. Schramm, Phys. Rev., D31(1984)564
[14] Nagashima K, Mori S. Galactic and Heliotail-in Anisotropies of Cosmic Rays as the Origin of Sidereal Daily Variation in the Energy Region <10~GeV. Proc. of the Int. Cosmic Ray Sym. on High Energy Cosmic Ray Modulation, Tokyo, 1976,326
[15] Fichtel C E, Linsley J. High-energy and Ultra-high-energy Cosmic Rays. Astrophys. J., 1986,300:474
[16] Amenomori M, Cao Z, Ding L K et al. Search for Steady Emission of 10TeV Gamma Ray from the Crab Nebula,Cyg X-3 and Her X-1 Using the Tibet Air Shower Array. Phys. Rev. Lett., 1992,69:2468
[17] Amenomori M, Cao Z, Dai B Z et al. The Cosmic-ray Energy Spectrum Between 10~(14.5) and 10~(16.3) eV Covering the "Knee" Region. Astrophys. J., 1996,461:408
[18] Amenomori M, Ayabe S, Cao P Y et al. Detection of Multi-TeV Gamma Rays from Markarian 501 During an Unforeseen Flaring State in 1997 with the Tibet Air Shower Array. Astrophys. J., 2000,532:302
[19] Amenomori M, Ayabe S, Cui S W. et al. Observation of Multi-TeV Diffuse Gamma Rays from the Galactic Plane with the Tibet Air Shower Array. Astrophys. J., 2002,580:887
[20] 杨福生．小波变换的工程分析与应用．北京：科学出版社，1999，2．
[21] Otazu X, Ribo M, Peracaula M. Detection of superimposed periodic signals using wavelets, arXiv: astro-ph/0202107
[22] Lewis M J, Freesc K: A Wavelet Analysis of Solar Climate Forcing: I) Solar Cycle Timescales arXiv: astro-ph/0203497
[23] 胡昌华等．基于MATLAB的系统分析与设计一小波分析．西安：西安电子科技大学出版社，1999，12．
[24] Mallat,S. A theory of multi-resolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Machine Intell. 11,1989.
[25] Daubechies, I. Orthonormal bases of compactly supported wavelets. Comm. Pure and Appl. Math.41, 1988.
[26] Mallat, S. and Hwang, W. L. Singularity detection and processing with wavelets. IEEE Trans.on Information Theory, 1992,38.
[27] 龚怀云，寿纪麟，王绵森．应用泛函分析．西安：西安交通大学出版社，1985．
[28] 赵纪元，何正嘉等．小波包—自回归谱分析及在振动诊断中的应用．振动工程学报，1995(8)．
[29] 董新洲，耿中行，葛耀中，张伏生，徐丙垠．小波变换应用于电力系统故障信号分析初探．中国电机工程学报，1997，(6)．
[30] 董新洲等．小波变换．继电器．1997，27(1)
[31] 秦前清，杨宗凯．实用小波分析．西安：西安电子科技大学出版社，1998，1．
[32] 程正兴．小波分析算法与应用．西安：西安交通大学出版社，1998，5．
[33] 张贤达、保铮著．非平稳信号分析与处理．北京：国防工业出版社，1998．9
[34] 宋建社．小波分析及其应用选例．北京：现代出版社，1998．5
[35] 刘贵忠、邸双亮．小波分析及其应用．西安：西安电子科技大学出版社，1997．3
[36] L．科恩著。时-频分析：理论与应用．自居宪译．西安：西安交通大学出版社．1998．3
[37] Chui C K and Wang J Z. A cardinal spline approach to wavelets. Proc.
Amer. Math. Soc., 1991.
[38] 徐长发，李国宽．实用小波方法．武汉：华中科技大学出版社，2001．
[39] 李建平等．小波分析与信号处理．重庆：重庆大学出版社，2001．
[40] 郑治真等．小波变换及其MATLAB工具的应用．北京：地震出版社，2001．
[41] JIA Huan Yu, WANG Shun Jin. Study of the Time Variation of 10TeV Cosmic Ray. High Energy Phys. And Nucl. Phys., 2001,25:277(in Chinese)(贾焕玉，王顺金．10TeV宇宙线时间变化研究．高能物理与核物理，2001，25：277)
[42] P. Bassi et al., Phys. Rev., 92(1953)441
[43] M. Amenomori et al., Nucl. Instr. Meth. Phys. Res., A285(1990)619
[44] A.H. Compton & I.A. Getting, Phys. Rev., 47No. 11 (1984)314
[45] M.S. Vallarta et al., Phys. Rev., 55(1939)1
[46] A. Daudin & M. I. Daudin, Comp. Rend. Acad. Sci. 234(1952)1551
[47] F. Farley & I. Storley, Nature 173(1954)445
[48] G. Cocconi, Phys. Rev., 83(1951)1193
[49] N.Sherman, Phys. Rev., 89(1953)25
[50] C. P. Barret et al., Phys. Rev., 95(1954)1571
[51] T. E. Cranshaw & W. Galbraith, Phil. Mag., 45(1954) 1109
[52] Amenomori M, Ayabe S, Cao P Yet al: Observation of Multi-TeV Gamma Rays from the Crab Nebula Using the Tibet Air Shower Array. Astrophys. J., 1999,525:L93
[53] XU Xian Wu, DING Lin Kai, CAO Pei Yuan. Search for TeV Gamma Rays from the Crab Nebula with Tibet Ⅱ/HD AS Array. High Energy Phys. And Nucl. Phys., 2000,24:473(in Chinese)(徐贤武，丁林垲，曹培圆等．Tibet Ⅱ／HD阵列寻找来自蟹壮星云的TeVγ射线．高能物理与核物理，2000，24：473)
[54] L. Myssowsky & L.Tuwin, Z. Phys.,39:No. 2-3(1926)146
[55] A. H. Compton et al., Rev. Sci. Instrum., 5:No.12(1934)415
[56] W. Galbraith, Extensive Air Showers, Butterworths Seie. Publi., (1958)123
[57] L.I. Dorman, Cosmic Rays Variations. and Space Explorations, North Holland Publi. Comp., (1974) 106
[58] 贾焕玉等，高能物理与核物理，18(1994)788
[59] H. P.William, Numerical Recipes in C, Cambridge Univ.Pre.,Second Edi.
[2] W. Baade and F. Zwicky, Phys. Rev., 46, (1934)76
[3] M.V. Fouseca. Nucl. Phys. B (proc. Suppl.) 114(2003)233
[4] M.S. Longair, High Energy Astrophysics, Cambridge, Cambridge University Press, 1981, p. 117.
[5] N. L. Grigorov et al., Proc. 12nd Int. Cosmic Ray Conf., Vol.2 (1983) 135
[6] T.H. Bumett et al., Proc. 23rd Int. Cosmic Ray Conf. Vol.2 (1993) 5
[7] M. Ichimura et al., Phys. Rev., 48(1993) 1994
[8] M. Nagano et al., J. Phys., G10 (1984) 1295
[9] J. Linsley, et al., Proc.18th Int. Cosmic Ray Conf., Vol.12 (1983) 135
[10] E. Fermi, Phys. Rev., 75,1949,p.1169.
[11] R. Blandford & D. Eichler, Phys. Rep., 154(1987) 1
[12] W. I. Axford, Astrophys. J. Suppl., 90(1994) 937
[13] C. T. Hill & D.N. Schramm, Phys. Rev., D31(1984)564
[14] Nagashima K, Mori S. Galactic and Heliotail-in Anisotropies of Cosmic Rays as the Origin of Sidereal Daily Variation in the Energy Region <10~GeV. Proc. of the Int. Cosmic Ray Sym. on High Energy Cosmic Ray Modulation, Tokyo, 1976,326
[15] Fichtel C E, Linsley J. High-energy and Ultra-high-energy Cosmic Rays. Astrophys. J., 1986,300:474
[16] Amenomori M, Cao Z, Ding L K et al. Search for Steady Emission of 10TeV Gamma Ray from the Crab Nebula,Cyg X-3 and Her X-1 Using the Tibet Air Shower Array. Phys. Rev. Lett., 1992,69:2468
[17] Amenomori M, Cao Z, Dai B Z et al. The Cosmic-ray Energy Spectrum Between 10~(14.5) and 10~(16.3) eV Covering the "Knee" Region. Astrophys. J., 1996,461:408
[18] Amenomori M, Ayabe S, Cao P Y et al. Detection of Multi-TeV Gamma Rays from Markarian 501 During an Unforeseen Flaring State in 1997 with the Tibet Air Shower Array. Astrophys. J., 2000,532:302
[19] Amenomori M, Ayabe S, Cui S W. et al. Observation of Multi-TeV Diffuse Gamma Rays from the Galactic Plane with the Tibet Air Shower Array. Astrophys. J., 2002,580:887
[20] 杨福生．小波变换的工程分析与应用．北京：科学出版社，1999，2．
[21] Otazu X, Ribo M, Peracaula M. Detection of superimposed periodic signals using wavelets, arXiv: astro-ph/0202107
[22] Lewis M J, Freesc K: A Wavelet Analysis of Solar Climate Forcing: I) Solar Cycle Timescales arXiv: astro-ph/0203497
[23] 胡昌华等．基于MATLAB的系统分析与设计一小波分析．西安：西安电子科技大学出版社，1999，12．
[24] Mallat,S. A theory of multi-resolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Machine Intell. 11,1989.
[25] Daubechies, I. Orthonormal bases of compactly supported wavelets. Comm. Pure and Appl. Math.41, 1988.
[26] Mallat, S. and Hwang, W. L. Singularity detection and processing with wavelets. IEEE Trans.on Information Theory, 1992,38.
[27] 龚怀云，寿纪麟，王绵森．应用泛函分析．西安：西安交通大学出版社，1985．
[28] 赵纪元，何正嘉等．小波包—自回归谱分析及在振动诊断中的应用．振动工程学报，1995(8)．
[29] 董新洲，耿中行，葛耀中，张伏生，徐丙垠．小波变换应用于电力系统故障信号分析初探．中国电机工程学报，1997，(6)．
[30] 董新洲等．小波变换．继电器．1997，27(1)
[31] 秦前清，杨宗凯．实用小波分析．西安：西安电子科技大学出版社，1998，1．
[32] 程正兴．小波分析算法与应用．西安：西安交通大学出版社，1998，5．
[33] 张贤达、保铮著．非平稳信号分析与处理．北京：国防工业出版社，1998．9
[34] 宋建社．小波分析及其应用选例．北京：现代出版社，1998．5
[35] 刘贵忠、邸双亮．小波分析及其应用．西安：西安电子科技大学出版社，1997．3
[36] L．科恩著。时-频分析：理论与应用．自居宪译．西安：西安交通大学出版社．1998．3
[37] Chui C K and Wang J Z. A cardinal spline approach to wavelets. Proc.
Amer. Math. Soc., 1991.
[38] 徐长发，李国宽．实用小波方法．武汉：华中科技大学出版社，2001．
[39] 李建平等．小波分析与信号处理．重庆：重庆大学出版社，2001．
[40] 郑治真等．小波变换及其MATLAB工具的应用．北京：地震出版社，2001．
[41] JIA Huan Yu, WANG Shun Jin. Study of the Time Variation of 10TeV Cosmic Ray. High Energy Phys. And Nucl. Phys., 2001,25:277(in Chinese)(贾焕玉，王顺金．10TeV宇宙线时间变化研究．高能物理与核物理，2001，25：277)
[42] P. Bassi et al., Phys. Rev., 92(1953)441
[43] M. Amenomori et al., Nucl. Instr. Meth. Phys. Res., A285(1990)619
[44] A.H. Compton & I.A. Getting, Phys. Rev., 47No. 11 (1984)314
[45] M.S. Vallarta et al., Phys. Rev., 55(1939)1
[46] A. Daudin & M. I. Daudin, Comp. Rend. Acad. Sci. 234(1952)1551
[47] F. Farley & I. Storley, Nature 173(1954)445
[48] G. Cocconi, Phys. Rev., 83(1951)1193
[49] N.Sherman, Phys. Rev., 89(1953)25
[50] C. P. Barret et al., Phys. Rev., 95(1954)1571
[51] T. E. Cranshaw & W. Galbraith, Phil. Mag., 45(1954) 1109
[52] Amenomori M, Ayabe S, Cao P Yet al: Observation of Multi-TeV Gamma Rays from the Crab Nebula Using the Tibet Air Shower Array. Astrophys. J., 1999,525:L93
[53] XU Xian Wu, DING Lin Kai, CAO Pei Yuan. Search for TeV Gamma Rays from the Crab Nebula with Tibet Ⅱ/HD AS Array. High Energy Phys. And Nucl. Phys., 2000,24:473(in Chinese)(徐贤武，丁林垲，曹培圆等．Tibet Ⅱ／HD阵列寻找来自蟹壮星云的TeVγ射线．高能物理与核物理，2000，24：473)
[54] L. Myssowsky & L.Tuwin, Z. Phys.,39:No. 2-3(1926)146
[55] A. H. Compton et al., Rev. Sci. Instrum., 5:No.12(1934)415
[56] W. Galbraith, Extensive Air Showers, Butterworths Seie. Publi., (1958)123
[57] L.I. Dorman, Cosmic Rays Variations. and Space Explorations, North Holland Publi. Comp., (1974) 106
[58] 贾焕玉等，高能物理与核物理，18(1994)788
[59] H. P.William, Numerical Recipes in C, Cambridge Univ.Pre.,Second Edi.