Wavelets in geodesy and geodynamics

Wavelets in Geodesy and Geodynamics

Volumn , Issue , 2004, Pages 1-289

  Keller, Wolfgang ^a  

^a NONE

Author keywords

Mathematics; Wavelets

Indexed keywords

EID: 85119109300     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (104)

1. Adam J., K.-P. Schwarz (eds.), Vistas for geodesy in the new millenium. Springer-Verlag, Berlin-Heidelberg-NewYork 2002.
2. Antoniadis, A., G. Oppenheim (eds.), Wavelets and statistics. Springer-Verlag, Berlin-Heidelberg-NewYork 1995.
3. Bacry, E., J. F. Muzy, A. Arneodo, Singularity spectrum of fractal signals: exact results. J. of Stat. Phys. 70, 635-674, 1993.
4. Bayer, M., Geomagnetic field modelling from satellite data by first and second generation avelets. PhD thesis, University of Kaiserlautern, Geomathematics Group, Shaker Verlag, Aachen 2000.
5. Bayer, M., W. Freeden, T. Maier, Wavelet analysis of the geomagnetic field within source regions of ionospheric and magnetospheric currents. Berichte der Arbeitsgruppe Technomathematik, Fachbereich Mathematik, Universität Kaiserslautern Bericht No. 217, 1999.
6. Bayer, M., W. Freeden, T. Maier, A vector wavelet approach in iono- and magnetospheric geomagnetic satellite data. Journal of Atmospheric and Solar- Terrestrial Physics 63, 581-597, 2001.
7. Beth, S., Multiscale approximation by vector radial basis functions on the sphere. PhD thesis, University of Kaiserslautern, Geomathematics Group, Shaker Verlag, Aachen 2000.
8. Beth, S., T. Boos, W. Freeden, On the wavelet determination of scale exponents in energy spectra and structure functions and their application to CCD camera data. In: Schwarz K.-P. (ed.), 221-227, 2000.
9. Bracewell, R., The fourier transform and its application. McGraw-Hill, New York 1965.
10. Burt, P. J., E. H. Andelson, The Laplacian pyramid as a compact image code. IEEE Trans. Commun. 31, 20-51, 1983.
11. Canny, J.,A computational approach to edge detection. IEEE Trans. Patt. Anal. and Mach. Intell. 36, 961-1005, 1986.
12. Cohen, A., I. Daubechies, J. C. Feauveau, Biorthogonal bases of compactly supported wavelets. Comm. Pure Appl. Math. 45, 485-560, 1992.
13. Collatz, L., Funktionalanalysis und Numerische Mathematik. Springer-Verlag, Berlin-Göttingen-Heidelberg 1964.
14. Collin F., R. Warnant, Application of wavelet transform for GPS cycle slip correction and comparison with Kalman filter. manuscripta geodaetica 20, 161-172, 1995.
15. Daubechies I., Ten lectures on wavelets. SIAM, Philadelphia, 1992.
16. Cui, J., W. Freeden, B.Witte, Gleichmässige Approximation mittels sphärischer Finite-Elemente und ihre Anwendung auf die Geodäsie. Zeitschr. f. Vermess. 117, 266-278, 1992.
17. Cui, J., W. Freeden, Equidistribution on the sphere. SIAM J. Sci. Stat. Comput. 18, 595-609, 1999.
18. Dieudonne, J., Grundzüge der modernen Analysis Bd. 1.VEB DeutscherVerlag derWissenschaften, Berlin 1971.
19. Donoho, D. L., Wavelet Shrikage andW.V. D.,A 10-Minute Tour. In: Proceedings of the International Conference on Wavelet and Applications, Toulouse 1992.
20. Donoho, D., I. Johnstone, Ideal spatial adaption via wavelet shrinkage. Biometrika 81, 425-455, 1994.
21. Foufoula-Geourgiou, E., P. Kumar (eds.), Wavelets in geophysics. Academic Press, San Diego 1994.
22. Freeden, W., On the role of (band-limited) harmonic wavelets in Earth's gravitational potential determination. In: Klees R.(ed.), 227-257, 1999.
23. Freeden, W., Multiscale modelling of spaceborne geodata. Teubner Verlag, Stuttgart Leipzig 1999.
24. Freeden, W., Multiscale modelling of GOCE-DATA-products. In: ESAProceedings of the International GOCE User Workshop, ESTEC, Noordwijk, ESAW-188, 111-126, 2001.
25. Freeden, W., O. Glockner, R. Litzenberger, Multiscale modelling from geopotential data. In: Haussman et al. (eds.), 151-174, 1999.
26. Freeden, W., O. Glockner, M. Thalhammer, Multiscale gravitational field recovery from GPS-satellite-to-satellite tracking. Studia Geophysica et Geodaetica 43, 229-264, 1999.
27. Freeden, W.,T. Gerven, M. Schreiner, Constructive approximation on the sphere (with applications to geomathematics). Oxford Science Publications, Claredon 1998.
28. Freeden, W., E. Groten, V. Michel, A. Kaboodvand, Geoidal reconstruction, decomposition, fast computation, and noise cancellation by harmonic wavelets. Studia Geophysica et Geodeatica 47, 37-73, 2003.
29. Freeden, W., T. Maier, Spectral and multiscale signal-to-noise thresholding of spherical vector fields. Computational Geosciences 7, 215-250, 2003.
30. Freeden, W., T. Maier, On multiscale denoising of spherical functions: Basic theory and numerical aspects. Electronic Transactions on Numerical Analysis (ETNA) 14, 40-62, 2002.
31. Freeden, W.,V. Michel, Least squares geopotential approximation by windowed Fourier transform and wavelet transform. Berichte d. Arbeitsgruppe Technomathematik, Fachbereich Mathematik, Univ. Kaiserslautern, Bericht No. 216, 1999.
32. Freeden, W., V. Michel, Constructive approximation and numerical methods in geodetic research today - an attempt at a categorization based on an uncertainty principle. Berichte d. Arbeitsgruppe Technomathematik, Fachbereich Mathematik, Univ. Kaiserslautern, Bericht No. 208; also in Journal of Geodesy 73, 452 -465, 1999.
33. Freeden, W., V. Michel, M. Stenger, Multiscale signal-to-noise thresholding. Acta Geodaetica et Geophysica Hungarica 36, 55-86, 2001.
34. Freeden, W., K. Hesse, On the multiscale solution of satellite problems by use of locally supported kernel functions corresponding to equidistributed data on spherical orbits. Studia Scientiarum Mathematicarum Hungarica 39, 37-74, 2002.
35. Freeden, W., F. Schneider, An integrated wavelet concept of physical geodesy. Journal of Geodesy 72, 259-281, 1998.
36. Freeden, W., F. Schneider, Regularization wavelets and multiresolution. Inverse Problems 14, 225-243, 1998.
37. Freeden, W., M. Schreiner, Satellite gradiometry - a new approach. In: Sanso, F. (ed.), 122-139, 1995.
38. Ghil, M., R. Benzi, G. Parisi (eds.), North-Holland, Amsterdam, 1985.
39. Gilbert, A.,Wavelet Lösungen geodätischer Integralgleichungen, Diploma thesis, University Stuttgart, 1997.
40. Gilbert, D., M. Holschneider, J. L. LeMouel,Wavelet Analysis of the Chandler Wobble. JGR, 1998.
41. Gilbert, A., W. Keller, Deconvolution with wavelets and vaguelettes. Journal of Geodesy 74, 306-320, 2000.
42. Grafarend E.W., F.W. Krumm,V. S. Schwarze (eds.), Quo vadis geodesy - The challenge of the 3rd millenium, Springer-Verlag, Berlin 2002.
43. Groupillaud, P., A. Grossmann, J. Morlet, Cycle-octave and related transforms in seismic signal analysis. Geoexploration 23, Elsevier Science Publ., 85-102, 1984/85.
44. Grobmann, Ch., H.-G. Roos, Numerik partieller Differentialgleichungen. B.G. Teubner, Stuttgart 1992.
45. Hackbusch, W., Multi-grid methods and applications. Springer Series in Computational Mathematics, Berlin 1985.
46. Hagelberg, C. R., N. K. K. Gamage, Application of structure preserving wavelet decompositions to intermittence turbulence:A case study. In: Foufoula- Geourgiou, E., P. Kumar (eds.), 45-80, 1994.
47. Haussmann, K. Jetter, M. Reimer (eds.), Advances in multivariate approximation, Mathematical Research, Vol. 107, W.Wiley-VCH, 1999.
48. Jawert, B., W. Sweldens, An overview of wavelet based multiresolution analysises. SIAM Review 36, 3.
49. Katul, G. G., J. D. Albertson, C.,R. Chu, M.,B. Parlange, Intermittency in atmospheric surface layer turbulence: The orthonormal wavelet representation. In: Foufoula-Geourgiou E., P. Kumar (eds.), 81-105, 1994.
50. Kantorovich, L. V., G. P. Akilov, Functional analysis. Pergamon Press, Oxford 1982.
51. Keller, W., Local geoid determination by wavelet-vaguelette decomposition. Phys. Chem. Earth 21, 147-150, 1996.
52. Keller, W., A wavelet-vaguelette analysis of geodetic integral formulae. In: Segawa, J., H. Fujimoto, S. Okubo (eds.), 557-565, 1997.
53. Keller, W., Collocation in reproducing kernel Hilbert spaces of a multiscale analysis. Phys. Chem. Earth 23, 25-29, 1998.
54. Keller, W.,A wavelet approach to non-stationary collocation In: Schwarz, K.-P. (ed.), 208-214, 2000.
55. Keller, W.,Awavelet solution to1Dnon-stationary collocation with an extension to 2D. In: Sideris M. G. (ed.), 79-85, 2002.
56. Keller, W., A wavelet approach for the construction of multi-grid solvers for large linear systems. In: Adam, J., K.-P. Schwarz (eds.), 265-271, 2002.
57. Kenney, J. F., E. S. Keeping, Mathematics of statistics, Part 1. Van Norstrand, Princeton NJ 1962.
58. Klees, R. (ed.), Wavelets in the geosciences. Springer-Verlag, Berlin-Heidelberg- NewYork, 1999.
59. Kolmogorov, A. N., The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 4, 299-303, 1941.
60. Kolmogorov, A. N., S. Fomin, Reelle Funktionen und Funktionalanalysis.VEB Deutscher Verlag derWissenschaften, Berlin 1975.
61. Kronland-Martinet, R., J. Morlet, A. Grossmann, Analysis of sound patterns through wavelet transforms. Int. Journ. of Pattern Recogn. and Artific. Intell. 1, 273-301, 1987.
62. Kusche, J., Implementation of multi-grid solvers for satellite gravity anomaly recovery. Journal of Geodesy 74, 773-782, 2001.
63. Kusche, J., S. Rudolph, Satellite gravity anomaly recovery using multi-grid methods. In: Sideris M. G. (ed.), 91-97, 2001.
64. Little, S. A., P. H. Carter, D. K., Smith.Wavelet analysis of a bathymetric profile reveals anomalous crust. Geophys. Res. Letts. 20, 1915-1918, 1993.
65. Li, D., J. Shao.Thewavelet and its application in image detection. ISPRS Journal of Photogrammetry and Remote Sensing 49, 4-11, 1994.
66. Li, Q., K. Vasudevan, F. A. Cook, Seismic skeletonization: A new approach to interpretation of seismic reflection data. J. Geophys. Research 102, 8427-8445, 1997.
67. Little, S. A.,Wavelet analysis of seafloor bathymetry:An example. In: Foufoula- Geourgiou E., P. Kumar (eds.), 167-182, 1994.
68. Louis, A.K., P. Maab, A. Rieder,Wavelets. B.G. TeubnerVerlag, Stuttgart 1994.
69. Maier, T., Multiscale geomagnetic field modelling from satellite data: Theoretical aspects and numerical applications. PhD thesis, Universität Kaiserslautern, 2002.
70. Maier, T., C. Mayer, Multiscale downward continuation of CHAMP FGM-data for crustal field modelling. Mathematische Geologie Band 5, C-Press Verlag, Dresden 2002.
71. Mallat, S., W. L. Hwang, Singularity detection and processing with wavelets. IEEEE Trans INFO. Theory 38, 617-643, 1992.
72. Mallat, S., A wavelet tour of signal processing. Academic Press San Diego, 1999.
73. Meyer,Y.,Wavelets and operators. Cambridge University Press, 1992.
74. Mayer, C., T. Maier, Multiscale determination of radial current distribution from CHAMP FGM-data. Mathematische Geologie Band 5, C-PressVerlag Dresden, 2002.
75. Neumann J. v., Mathematische Grundlagen der Quantenmechanik. Grundlehren der Mathematischen Wissenschaften, Band 38, Springer-Verlag, Heidelberg 1968.
76. Obuchov, A. M., Statistische Beschreibung stetiger Felder. (Translation from Russian). Sammelband zur statistischen Theorie der Turbulenz, Akademie- Verlag, Berlin 1958.
77. Parisi, G., U. Frisch,Turbulence and predictability in geophysical fluid dynamics and climate dynamics. In: Ghil, M., R. Benzi, G. Parisi (eds.), 71-88, 1985.
78. Pike, J. C., Analysis of high resolution marine seismic data using the wavelet Transform. In: Foufoula-Geourgiou E., P. Kumar (eds.), 183-211, 1994.
79. Polya, G., G. Szegö, Aufgaben und Lehrsätze der Analysis. Vol. II, Springer- Verlag, Berlin 1971.
80. Rosenfeld, A., M. Thurston, Edge and curve detection for visual scene analysis. IEEE Trans. Comput. C 29, 1971.
81. Sanso, F. (ed.), International Association of Geodesy Symposia 114, Springer- Verlag, Berlin-Heidelberg-NewYork 1995.
82. Sanso, F., M. G. Sideris, On the similarities and differences between system theory and least-squares collocation in physical geodesy. Bolletino di Geodesia e Science Affini LVI, 173-206, 1997.
83. Schmidt, M.,Wavelet analysis of stochatic signals. IERS Technical Note No 28, 65-71, 1997.
84. Schmidt, M., Ein Beitrag zur zweidimensionalenWavelet-Analyse von Zufallsprozessen, Zeitschr. f. Vermess. 126, 270-275, 2001.
85. Schmidt, M., H. Schuh,Wavelet-Analyse der mit VLBI beobachteten Nutationsreihen, Zeitschr. f. Vermess. 124, 24-30, 1999.
86. Schmidt, M., H. Schuh, Abilities of wavelet analysis for investigating shortperiod variations of Earth Rotation. IERS Technical Note No 28, 73-80, 2000.
87. Schmidt, M., Ein Beitrag zur zweidimensionalenWavelet-Analyse von Zufallsprozessen, Zeitschr. f. Vermess. 126, 270-275, 2001.
88. Schmidt, M., Grundprinzipien der Wavelet-Analyse und Anwendungen in der Geodäsie, Shaker-Verlag, Reihe Geodäsie Band 9, Aachen 2001.
89. Schmidt, M., H. Schuh, Wavelet-Analyse von Erdrotationsschwankungen, Zeitschr. f. Vermess. 126, 94-100, 2001.
90. Schmitz-Hübsch, H.,Wavelet-Analysen der Erdrotationsparameter im hochfrequenten Bereich. Schriftenreihe der Deutschen Geodätischen Kommission, Reihe, Heft A 118, München 2002.
91. Schmitz-Hübsch, H., H. Schuh, Seasonal and short-period fluctuations of Earth Rotation investigated byWavelet Analysis. In: Grafarend E.W., F.W. Krumm, V. S. Schwarze (eds.), 125-135, 2002.
92. Schröder, P., W. Sweldens, Pherical wavelets: texture processing. Tech. Rep. 4. Industrial Mathematics Initiative, Department of Mathematics, University of South Carolina 1995.
93. Schwarz, K. P. (ed.), Geodesy Beyond 2000. The Challenge of the First Decade. International Association of Geodesy Symposia Vol. 121, Springer-Verlag, Berlin-Heidelberg 2000.
94. Schwarz, K. P., Sideris M.G., R. Forsberg: The use of FFT techniques in physical geodesy. Geophys. J. Int. 100, 485-514, 1990.
95. Segawa, J., H. Fujimoto, S. Okubo (eds.), Gravity, geoid and marine geodesy. Springer-Verlag, Berlin-Heidelberg-NewYork 1997.
96. Sideris, M. G., A fast Fourier transform method for computing terrain corrections, manuscr. geod. 10, 66-73, 1985.
97. Sideris M. G. (ed.), Gravity, geoid and geodynamics 2000, Springer-Verlag, Berlin-Heidelberg-NewYork 2002.
98. Sideris, M. G., K. P. Schwarz, Recent advances in the numerical solution of the linear Molodensky problem. Bull Geod. 62, 521-540, 1988.
99. Sideris, M. G., I. N. Tziavos, FFT-evaluation and application of gravity field convolution integrals with mean and point data. Bull. Geod. 62, 540-561, 1988.
100. Sweldens W., The lifting scheme: A custom-design construction of biorthogonal wavelets. Tech. Rep. 7. Industrial Mathematics Initiative, Department of Mathematics, University of South Carolina 1994.
101. Tsay, J. R.,Wavelets für das Facetten-Stereosehen. Veröff. DKG, Reihe C, Nr. 454, München 1996.
102. Vasudevan, K., F. A. Cook, Empirical mode skeletonization of deep crustal seismic data: Theory and applications. J. Geophys. Research 105, 7845-7855, 2000.
103. Valdimirov,V. S., Obobcennye fukcii v matematiceskoij fysike. Izdanye Nauka, Moskva 1976.
104. Wallace, G. K., The JPEG still picture compression standard. Communications of the ACM, 34, 30-44,1991.