Wavelet analysis for geophysical applications

Reviews of Geophysics

Volumn 35, Issue 4, 1997, Pages 385-412

  Kumar, Praveen ^a   Foufoula Georgiou, Efi ^b  

^a University of Illinois at Urbana Champaign   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATMOSPHERIC TURBULENCE; FRACTALS; GEOPHYSICS; SURFACE TOPOGRAPHY; WAVELET ANALYSIS;

GEOPHYSICAL APPLICATIONS; GEOPHYSICAL PROCESS; MULTI-SCALE FEATURES; MULTIFRACTAL PROCESS; NONSTATIONARY PROCESS; ORTHOGONAL WAVELETS; SEAFLOOR BATHYMETRY; TRANSIENT PHENOMENON;

WAVELET TRANSFORMS;

EID: 0011718060     PISSN: 87551209     EISSN: None     Source Type: Journal    
DOI: 10.1029/97RG00427     Document Type: Article

References (113)

1. Allan, D. W., Statistics of atomic frequency clocks, Proc. IEEE, 31, 221-230, 1966.
2. Antoine, J., P. Carrette, and R. Murenzi, The scale-angle representation in image analysis with 2D wavelet transform, in Signal Processing VI: Theories and Applications, edited by J. Vandewalle et al., pp. 701-704, North-Holland, New York, 1992.
3. Antoine, J., P. Carrette, R. Murenzi, and B. Piette, Image analysis with two dimensional continuous wavelet transform, Signal Process., 31, 241-272, 1993.
4. Arnéodo, A., G. Grasseau, and M. Holschneider, Wavelet transform of multifractals. Phys. Rev. Lett., 61, 2281-2284, 1988.
5. Bell, T. L., and R. Suhasini, Principal modes of variation of rain-rate probability distributions, J. Appl. Meteorol., 33, 1067-1078, 1994.
6. Benedetto, J. J., Frame decompositions, sampling, and uncertainty principle inequalities, in Wavelets: Mathematics and Applications, edited by J. J. Benedetto, and M. W. Frazier, pp. 247-304, CRC Press, Boca Raton, Fla., 1993.
7. Benedetto, J. J., and M. W. Frazier (Eds.), Wavelets: Mathematics and Applications, 575 pp., CRC Press, Boca Raton, Fla., 1993.
8. Benzi, R., and M. Vergassola, Optimal wavelet analysis and its application to two-dimensional turbulence, Fluid Dyn. Res., 8, 117-126, 1991.
9. Benzi, R., L. Biferale, A. Crisanti, G. Paladin. M. Vergassola, and A. Vulpiani, A random process for the construction of multiaffine fields, Physica D, 65, 352-358, 1993.
10. Berkooz, G., J. Elezgaray, and P. Holmes, Coherent structures in random media and wavelets, Physica D, 61, 47-58, 1992.
11. Beylkin, G., R. R. Coifman, I. Daubechies, S. G. Mallat, Y. Meyer, L. A. Raphael, and M. B. Ruskai (Eds.), Wavelets and Their Applications, Jones and Bartlett, Boston, Mass., 1991.
12. Bioschl, G., and M. Sivapalan, Scale issues in hydrological modelling: A review, in Scale Issues in Hydrological Modelling, edited by J. D. Kalma and M. Sivapalan, pp. 9-48, John Wiley, New York, 1995.
13. Brunet, Y., and S. Collineau, Wavelet analysis of diurnal and nocturnal turbulence above a maize crop, in Wavelets in Geophysics, edited by E. Foufoula-Georgiou and P. Kumar, pp. 129-150, Academic, San Diego, Calif., 1994.
14. Chui, C. K., Wavelet Analysis and Its Applications, vol. 1. An Introduction to Wavelets, Academic, San Diego, Calif., 1992a.
15. Chui, C. K., Wavelet Analysis and Its Applications, vol. 2, Wavelets - A Tutorial in Theory and Applications, Academic, San Diego, Calif., 1992b.
16. Claasen, T. A. C. M., and W. F. G. Mecklenbrauker, The Wigner distribution - A tool for time-frequency signal analysis, Philips J. Res., 35, 217-250, 1980.
17. Coifman, R., and Y. Meyer, Remarques sur l'analyse de Fourier à fenêtre, C. R. Acad. Sci., Paris, 312, 259-261, 1991.
18. Coifman, R. R., Y. Meyer, and V. Wickerhauser, Wavelet analysis and signal processing, in Wavelets and Their Applications, edited by M. B. Ruskai et al., pp. 153-178, Jones and Bartlett, Boston, Mass., 1992a.
19. Coifman, R. R., Y. Meyer, and V. Wickerhauser, Size properties of wavelet-packets, in Wavelets and Their Applications, edited by M. B. Ruskai, pp. 453-470, Jones and Bartlett, Boston, Mass., 1992b.
20. Collineau, S., and Y. Brunei, Detection of turbulent coherent motions in a forest canopy, I, Wavelet analysis, Boundary Layer Meteorol., 65, 357-379, 1993a.
21. Collineau, S., and Y. Brunet, Detection of turbulent coherent motions in a forest canopy, II, Time-scales and conditional averages, Boundary Layer Meteorol., 66, 49-73, 1993b.
22. Dallard, T., and G. R. Spedding, 2-D wavelet transforms: Generalization on the Hardy space and application to experimental studies, Eur. J. Mech. Fluids, 12(1), 107-134, 1993.
23. Daubechies, I., Orthonormal bases of compactly supported wavelets, Commun. Pure Appl. Math., XLI, 901-996, 1988.
24. Daubechies, I., The wavelet transform, time-frequency localization and signal analysis, IEEE Trans. Inf. Theory, 36(5), 961-1005, 1990.
25. Daubechies, I., Ten Lectures on Wavelets, 357 pp., Soc. for Ind. and Appl. Math., Philadelphia, Pa., 1992.
26. Daubechies, I., Review of Wavelets and Operators by Y. Meyer (Cambridge Univ. Press, New York, 1993) and Wavelets: Algorithms and Applications by Y. Meyer, (Soc. for Ind. and Appl. Math., Philadelphia, 1993) Science, 262, 1589-1591, 1993.
27. Daubechies, I., and J. C. Lagarias, Two-scale difference equations, I, Existence and global regularity of solutions, SIAM J. Math. Anal., 22(5), 1388-1410, 1991.
28. Daubechies, I., and J. C. Lagarias, Two-scale difference equations, II, Local regularity, infinite products of matrices and fractals, SIAM J. Math. Anal., 23(4), 1031-1079, 1992.
29. Daubechies, I., S. Mallat, and A. S. Willsky, Introduction to the special issue on wavelet transforms and multiresolution signal analysis, IEEE Trans. Inf. Theory, 38(2), 529-531, 1992.
30. Davis, G., Adaptive nonlinear approximations, Ph.D. thesis, Dep. of Math., Courant Inst. of Math. Sci., New York Univ., New York, 1994.
31. Donoho, D. L., and I. M. Johnstone, Ideal spatial adaptation via wavelet shrinkage, Biometrika, 81, 425-455, 1994.
32. Everson, R., L. Sirovich, and K. R. Sreenivasan, Wavelet analysis of the turbulent jet, Phys. Lett. A, 146, 314-322, 1990.
33. Fargé, M., Wavelet transforms and their applications to turbulence, Annu. Rev. Fluid Mech., 24, 395-457, 1992a.
34. Fargé, M., The continuous wavelet transform of two-dimensional turbulent flows, in Wavelets and Their Applications, edited by M. B. Ruskai et al., pp. 275-302, Jones and Bartlett, Boston, Mass., 1992b.
35. Fargé, M., The continuous wavelet transform of two-dimensional turbulent flows, in Wavelets and Their Applications, edited by M. Ruskai et al, pp. 275-302, Jones and Bartlett, Boston, Mass., 1992c.
36. Fargé, M., M. Holschneider, and J. F. Colonna, Wavelet analysis of coherent structures in two-dimensional turbulent flows, in Topological Fluid Mechanics, edited by H. K. Moffatt, pp. 765-776, Cambridge Univ. Press, New York, 1990.
37. Fargé, M., E. Goirand, Y. Meyer, F. Pascal, and M. V. Wickerhauser, Improved predictability of two-dimensional turbulent flows using wavelet packet compression, Fluid Dyn. Res., 10(4-6), 229-250, 1992.
38. Fargé, M., J. R. Hunt, and J. C. Vassilicos (Eds.), Wavelets, Fractals and Fourier Transforms: New Developments and New Applications, Oxford Univ. Press, New York, 1993.
39. Fargé, M., N. Kevlahan, V. Perrier, and E. Goirand, Wavelets and turbulence, Proc. IEEE, 84, 639-669, 1996.
40. Flandrin, P., Time-frequency and time-scale, in Proceedings of the 4th Acoustic, Speech and Signal Processing Workshop on Spectrum Estimation Modeling, pp. 77-80, Inst. of Electr. and Electron. Eng., New York, 1988.
41. Flandrin, P., Wavelet analysis and synthesis of fractional Brownian motion, IEEE Trans. Inf. Theory, 38(2), 910-916, 1992.
42. Foufoula-Georgiou, E., and P. Kumar, Wavelets in Geophysics, 384 pp., Academic, San Diego, Calif., 1994.
43. Gamage, N. K. K., and W. Blumen, Comparative analysis of low level cold fronts: Wavelet, Fourier, and empirical orthogonal function decompositions, Mon. Weather Rev., 121, 2867-2878, 1993.
44. Gamage, N. K. K., and C. Hagelberg, Detection and analysis of microfronts and associated coherent events using localized transforms, J. Atmos. Sci., 50(5), 750-756, 1993.
45. Gambis, D., Wavelet transform analysis of the length of the day and the El-Niño/Southern Oscillation variations at intraseasonal and interannual time scales, Ann. Geophys., 10, 331-371, 1992.
46. Gao, W., and B. L. Li, Wavelet analysis of coherent structures at the atmosphere-forest interface, J. Appl. Meteorol., 32, 1717-1725, 1993.
47. Georgakakos, K. P., A. A. Carsteanu, P. L. Sturdevant, and J. A. Cramer, Observation and analysis of midwestern rainrates, J. Appl. Meteorol., 33, 1433-1444, 1994.
48. Glowinski, R., W. M. Lawton, M. Ravachol, and E. Tenenbaum, Wavelet solutions of linear and nonlinear elliptic, parabolic and hyperbolic problems in one space dimension, in Computing Methods in Applied Sciences and Engineering, edited by R. Glowinski and A. Liehnewsky, pp. 55-120, Soc. of Ind. and Appl. Math., Philadelphia, Pa., 1990.
49. Goel, P., and B. Vidakovic, Wavelet transformations as diversity enhancers, Discuss. Pap. 95-08, Inst. of Stat. and Decis. Sci., Duke Univ., Durham, N. C., 1994.
50. Goupillaud, P., A. Grossmann, and J. Morlet, Cycle-octaves and related transforms in seismic signal analysis, Geoexploration, 23, 85-102, 1984.
51. Grossmann, A., and J. Morlet, Decomposition of Hardy functions into square integrable wavelets of constant shape, SIAM J. Math. Anal., 15(4), 723-736, 1984.
52. Grossmann, A., R. Kronland-Martinet, and J. Morlet, Reading and understanding continuous wavelet transforms, in Wavelets: Time-Frequency Methods and Phase Space, edited by J. Combes, A. Grossmann, and P. Tchamitchian, pp. 2-20, Springer-Verlag, New York, 1989.
53. Hagelberg, C., and N. K. K. Gamage, Application of structure preserving wavelet decomposition to intermittent turbulence: A case study, in Wavelets in Geophysics, edited by E. Foufoula-Georgiou and P. Kumar, pp. 45-80, Academic, San Diego, Calif., 1994.
54. Holschneider, M., Localization properties of wavelet transforms, J. Math. Phys., 34(7), 3227-3244, 1993.
55. Holschneider, M., Wavelets: An Analysis Tool, 423 pp., Oxford Sci., New York, 1995.
56. Howell, J. F., and L. Mahrt, An adaptive decomposition: Application to turbulence, in Wavelets in Geophysics, edited by E. Foufoula-Georgiou and P. Kumar, pp. 107-128, Academic, San Diego, Calif., 1994.
57. Hubbard, B. B., The World According to Wavelets, 264 pp., A. K. Peters, Wellesley, Mass., 1996.
58. Hudgins, L. H., C. A. Friehe, and M. E. Mayer, Fourier and wavelet analysis of atmospheric turbulence, in Progress in Wavelet Analysis and Applications, edited by Y. Meyer and S. Roques, pp. 491-498, Frontiers, Gif-sur-Yvette, France, 1993a.
59. Hudgins, L. H., C. A. Friehe, and M. E. Mayer, Wavelet transform and atmospheric turbulence, Phys. Rev. Lett., 71, 3279-3282, 1993b.
60. Katul, G. G., and B. Vidakovic, The partitioning of attached and detached eddy motion in the atmospheric surface layer using Lorentz wavelet filtering, Boundary Layer Meteorol., 77, 153-172, 1996.
61. Katul, G. G., J. D. Albertson, C. R. Chu, and M. B. Parlange, Intermittency in atmospheric turbulence using orthonormal wavelets, in Wavelets in Geophysics, edited by E. FoufoulaGeorgiou and P. Kumar, pp. 81-105, Academic, San Diego, Calif., 1994.
62. Kumar, P., A wavelet-based methodology for scale-space anisotropic analysis, Geophys. Res. Lett., 22(20), 2777-2780, 1995.
63. Kumar, P., Role of coherent structures in the stochastic-dynamic variability of precipitation, J. Geophys. Res., 101(D21), 26,393-26,404, 1996.
64. Kumar, P., and E. Foufoula-Georgiou, A multicomponent decomposition of spatial rainfall fields, 1, Segregation of large- and small-scale features using wavelet transforms, Water Resour. Res., 29(8), 2515-2532, 1993a.
65. Kumar, P., and E. Foufoula-Georgiou, A multicomponent decomposition of spatial rainfall fields, 2, Self-similarity in fluctuations, Water Resour. Res., 29(8), 2533-2544, 1993b.
66. Kumar, P., and E. Foufoula-Georgiou, A new look at rainfall fluctuations and scaling properties of spatial rainfall using orthogonal wavelets, J. Appl. Meteorol., 32, 209-222, 1993c.
67. Kumar, P., and E. Foufoula-Georgiou, Wavelet analysis in geophysics: An introduction, in Wavelets in Geophysics, edited by E. Foufoula-Georgiou and P. Kumar, pp. 1-43, Academic, San Diego, Calif., 1994.
68. Liu, P., Wavelet spectrum analysis and ocean wind waves, in Wavelets in Geophysics, edited by E. Foufoula-Georgiou and P. Kumar, pp. 151-166, Academic, San Diego, Calif., 1994.
69. Mallat, S., A theory for multiresolution signal decomposition: The wavelet representation, IEEE Trans. Pattern Anal. Mach. Intel., 11(7), 674-693, 1989a.
70. Mallat, S., Multifrequency channel decomposition of images and wavelet models, IEEE Trans. Acoust. Speech Signal Anal., 37(12), 2091-2110, 1989b.
71. Mallat, S. G., and Z. Zhang, Matching pursuits with timefrequency dictionaries, IEEE Trans. Signal Process., 41(12), 3397-3415, 1993.
72. Mandelbrot, B., and J. Van Ness, Fractional Brownian motions, fractional noises and applications, SIAM Rev., 10(4), 422-437, 1968.
73. Marr, D., Vision, 397 pp., W. H. Freeman, New York, 1982.
74. Meneveau, C., Analysis of turbulence in the orthonormal wavelet representation, J. Fluid Mech., 232, 469-520, 1991a.
75. Meneveau, C., Dual spectra and mixed energy cascade of turbulence in the wavelet representation, Phys. Rev. Lett., 11, 1450-1453, 1991b.
76. Meyer, Y., Wavelets and Operators, Cambridge Univ. Press, New York, 1992.
77. Meyer, Y., Review of An Introduction to Wavelets by C. K. Chui and Ten Lectures on Wavelets by I. Daubechies, Bull. Am. Math. Soc., 28(2), 350-360, 1993a.
78. Meyer, Y., Wavelets: Algorithms and Applications, Soc. of Ind. and Appl. Math., Philadelphia, Pa., 1993b.
79. Meyer, Y., and S. Roques, Progress in Wavelet Analysis and Applications, Frontiéres, Gif-sur-Yvette, France, 1993.
80. Morlet, J., G. Arens, E. Fourgeau, and D. Giard, Wave propogation and sampling theory, 1, Complex signal and scattering in multilayered media, Geophysics, 47(2), 203-221, 1982a.
81. Morlet, J., G. Arens, E. Fourgeau, and D. Giard, Wave propagation and sampling theory, 2, Sampling theory and complex waves, Geophysics, 47(2), 222-236, 1982b.
82. Papoulis, A., The Fourier Integral and Its Applications, 318 pp., McGraw-Hill, New York, 1962.
83. Percival, D. B., and P. Guttorp, Long-memory processes, the Allan variance and wavelets, in Wavelets in Geophysics, edited by E. Foufoula-Georgiou and P. Kumar, pp. 325-344, Academic, San Diego, Calif., 1994.
84. Perica, S., and E. Foufoula-Georgiou, Linkage of scaling and thermodynamic parameters of rainfall: Results from midlatitude mesoscale convective systems, J. Geophys. Res., 101(D3), 7431-7448, 1996a.
85. Perica, S., and E. Foufoula-Georgiou, Model for multiscale disaggregation of spatial rainfall based on coupling meteorological and scaling descriptions, J. Geophys. Res., 101(D21), 26,347-26,361, 1996b.
86. Perrier, V., Towards a method for solving partial differential equations using wavelet bases, in Wavelets: Time-Frequency Methods and Phase-Space, edited by J. M. Combes et al., pp. 269-283, Springer-Verlag, New York, 1990.
87. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 994 pp., Cambridge Univ. Press, New York, 1992.
88. Qian, S., and J. Weiss, Wavelets and the numerical solution of partial differential equations, J. Comput. Phys., 106, 155-175, 1993.
89. Ramanathan, J., and O. Zeitouni, On the wavelet transform of fractional Brownian motion, IEEE Trans. Inf. Theory, 37(4), 1156-1158, 1991.
90. Rioul, O., A discrete time multiresolution theory, IEEE Trans. Signal Process., 41(10), 2591-2606, 1993.
91. Rioul, O., and M. Vetterli, Wavelets and signal processing, IEEE Signal Process. Mag., 8(4), 14-38, 1991.
92. Robinson, S. K., Coherent motion in turbulent boundary layer, Annu. Rev. Fluid Mech., 23, 601-639, 1991.
93. Ruskai, M. B., G. Beylkin, R. Coifman, I. Daubechies, S. Mallat, Y. Meyers, and L. Raphael (Eds.), Wavelets and Their Applications, Jones and Bartlett, Boston, Mass., 1992.
94. Saito, N., Simultaneous noise suppression and signal compression using a library of orthonormal bases and the minimum description length criteria, in Wavelets in Geophysics, edited by E. Foufoula-Georgiou and P. Kumar, pp. 299-324, Academic, San Diego, Calif., 1994.
95. Schultz, R. L., and H. W. Wyld, Using wavelets to solve the Burgers equation - A comparative study, Phys. Rev. A, 46(12), 7953-7958, 1992.
96. Sellers, P. J., F. G. Hall, G. Asrar, D. E. Strebel, and R. E. Murphy, An overview of the First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE), J. Geophys. Res., 97(D17), 18,345-18,371, 1992.
97. Shensa, M. J., An inverse DWT for nonorthogonal wavelets, Tech. Rep. TR 1621, Nav. Command and Ocean Surveillance Cent., San Diego, Calif., July 1993.
98. Steiner, M., R. A. Houze Jr., and S. E. Yuter, Climatological characterization of three-dimensional storm structure from operational and raingage data, J. Appl. Meteorol., 34, 1978-2007, 1995.
99. Teti, J. G., and H. N. Kritikos, SAR ocean image representation using wavelets, IEEE Trans. Geosci. Remote Sens., 30(5), 1089-1094, 1992.
100. Tewfik, A. H., and M. Kim, Correlation structure of the discrete wavelet coefficients of fractional Brownian motion, IEEE Trans. Inf. Theory, 38(2), 904-909, 1992.
101. Tokay, A., and D. Short, Evidence from tropical raindrop spectra of the origin of rain from stratiform versus convective clouds, J. Appl. Meteorol., 35, 355-371, 1996.
102. Tukey, J. W., Exploratory Data Analysis, 688 pp., Addison-Wesley, Reading, Mass., 1977.
103. Turner, B. J., M. Y. Leclerc, M. Gauthier, K. E. Moore, and D. R. Fitzjarrald, Identification of turbulence structures above a forest canopy using a wavelet transform, J. Geophys. Res., 99(D1), 1919-1926, 1994.
104. Venugopal, V., and E. Foufoula-Georgiou, Time-frequency-scale analysis of high resolution temporal rainfall using wavelet packets, J. Hydrol., 187, 3-27, 1996.
105. Vetterli, M., and C. Herley, Wavelets and filter banks: Theory and design. IEEE Trans. Signal Process., 40(9), 2207-2232, 1992.
106. Wickerhauser, M. V., Acoustic signal compression with wavelet packets, in Wavelets - A Tutorial in Theory and Applications, edited by C. K. Chui, pp. 679-700. Academic, San Diego, Calif., 1992.
107. Wickerhauser, M. V., Adapted Wavelet Analysis From Theory to Software, 486 pp., A. K. Peters, Wellesley, Mass., 1994.
108. Wornell, G. W., A Karhunen-Loève-like expansion for 1/f-processes via wavelets, IEEE Trans. Inf. Theory, 36(4), 859-861, 1990.
109. Wornell, G. W., Signal Processing With Fractals: A Wavelet-Based Approach, Prentice-Hall, Englewood Cliffs, N. J., 1995.
110. Xu, J.-C., and W.-C. Shann, Galerkin-wavelet methods for two-point boundary-value-problems, Numer. Math., 63(1), 123-144, 1992.
111. Yamada, M., and K. Ohkitani, Orthonormal wavelet expansion and its application to turbulence, Prog. Theor. Phys., 83(5), 819-823, 1990.
112. Yamada, M., and K. Ohkitani, Orthonormal wavelet analysis of turbulence, Fluid Dyn. Res., 8, 101-115, 1991a.
113. Yamada, M., and K. Ohkitani, An identification of energy cascade in turbulence by orthonormal wavelet analysis, Prog. Theor. Phys., 86(4), 799-815, 1991b.