메뉴 건너뛰기




Volumn 86, Issue 11, 2006, Pages 856-873

Harmonic spline-wavelets on the 3-dimensional ball and their application to the reconstruction of the Earth's density distribution from gravitational data at arbitrarily shaped satellite orbits

Author keywords

Ball; CHAMP; GOCE satellite missions; GRACE; Inner harmonics; Inverse problem; Multiresolution; Regular surface; Regularization; Sobolev spaces; Spherical harmonics; Spline wavelets

Indexed keywords


EID: 33751393080     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.200510277     Document Type: Article
Times cited : (25)

References (25)
  • 1
    • 0001982999 scopus 로고
    • Global base functions for the mass density in the interior of a massive body (earth)
    • L. Ballani, J. Engels, and E.W. Grafarend, Global Base Functions for the Mass Density in the Interior of a Massive Body (Earth), Manuscripta Geodaetica 18, 99-114 (1993).
    • (1993) Manuscripta Geodaetica , vol.18 , pp. 99-114
    • Ballani, L.1    Engels, J.2    Grafarend, E.W.3
  • 2
  • 3
    • 18744369782 scopus 로고
    • On the structure of uniqueness in linear inverse source problems
    • Theory and Practice of Geophysical Data Inversion, edited by A. Vogel, A. K. M. Sarwar, R. Gorenflo, and O. I. Kounchev (Vieweg Verlag, Braunschweig, Wiesbaden)
    • L. Ballani and D. Stromeyer, On the Structure of Uniqueness in Linear Inverse Source Problems, in: Theory and Practice of Geophysical Data Inversion, Proceedings of the 8th International Mathematical Geophysics Seminar on Model Optimization in Exploration Geophysics, edited by A. Vogel, A. K. M. Sarwar, R. Gorenflo, and O. I. Kounchev (Vieweg Verlag, Braunschweig, Wiesbaden, 1990).
    • (1990) Proceedings of the 8th International Mathematical Geophysics Seminar on Model Optimization in Exploration Geophysics
    • Ballani, L.1    Stromeyer, D.2
  • 4
    • 0345344208 scopus 로고
    • Decomposition principles for linear source problems
    • edited by G. Anger, R. Gorenflo, H. Jochmann, H. Moritz, W. Webers, Mathematical Research, (Akademie-Verlag, Berlin)
    • L. Ballani, D. Stromeyer, and F. Barthelmes, Decomposition Principles for Linear Source Problems, in: Inverse Problems: Principles and Applications in Geophysics, Technology, and Medicine, edited by G. Anger, R. Gorenflo, H. Jochmann, H. Moritz, W. Webers, Mathematical Research, 74 (Akademie-Verlag, Berlin, 1993).
    • (1993) Inverse Problems: Principles and Applications in Geophysics, Technology, and Medicine , vol.74
    • Ballani, L.1    Stromeyer, D.2    Barthelmes, F.3
  • 5
    • 0003699170 scopus 로고
    • Blaisdell Publishing Company, Waltham/Massachusetts, Toronto, London
    • P. J. Davis, Interpolation and Approximation (Blaisdell Publishing Company, Waltham/Massachusetts, Toronto, London, 1963).
    • (1963) Interpolation and Approximation
    • Davis, P.J.1
  • 6
    • 0017149534 scopus 로고
    • On algorithms for the summation of certain special functions
    • P. Deuflhard, On Algorithms for the Summation of Certain Special Functions, Computing 17, 37-48 (1975),
    • (1975) Computing , vol.17 , pp. 37-48
    • Deuflhard, P.1
  • 8
    • 0343569754 scopus 로고
    • On approximation by harmonic splines
    • W. Freeden, On Approximation by Harmonic Splines, Manuscripta Geodaetica 6, 193-244 (1981).
    • (1981) Manuscripta Geodaetica , vol.6 , pp. 193-244
    • Freeden, W.1
  • 12
    • 0036562577 scopus 로고    scopus 로고
    • Satellite-to-satellite tracking and satellite gravity gradiometry (advanced techniques for high-resolution geopotential field determination)
    • W. Freeden, V. Michel, and H. Nutz, Satellite-to-Satellite Tracking and Satellite Gravity Gradiometry (Advanced Techniques for High-Resolution Geopotential Field Determination), Journal of Engineering Mathematics 43, 19-56 (2002).
    • (2002) Journal of Engineering Mathematics , vol.43 , pp. 19-56
    • Freeden, W.1    Michel, V.2    Nutz, H.3
  • 15
    • 33646902105 scopus 로고
    • Splines constructed by pieces of polyharmonic functions
    • edited by P. Laurent et al. (A.K. Peters, Wellesley, MA)
    • O. Kounchev, Splines Constructed by Pieces of Polyharmonic Functions, in: Wavelets, Images, and Surface Fitting, edited by P. Laurent et al. (A.K. Peters, Wellesley, MA, 1994), pp. 319-326.
    • (1994) Wavelets, Images, and Surface Fitting , pp. 319-326
    • Kounchev, O.1
  • 16
    • 0742266761 scopus 로고    scopus 로고
    • Wavelet analysis of cardinal L-splines and construction of multivariate prewavelets
    • Approximation theory X. Wavelets, splines, and applications, edited by C.K. Chui et al., Papers from the 10th international symposium, St. Louis, Mo, USA, March 26-29, (Nashville, TN: Vanderbilt University Press)
    • O. Kounchev and H. Render, Wavelet Analysis of Cardinal L-splines and Construction of Multivariate Prewavelets, in: Approximation theory X. Wavelets, splines, and applications, edited by C.K. Chui et al., Papers from the 10th international symposium, St. Louis, Mo, USA, March 26-29, 2001. (Nashville, TN: Vanderbilt University Press, 2002). Innovations in Applied Mathematics, pp. 333-353,
    • (2001) Innovations in Applied Mathematics , pp. 333-353
    • Kounchev, O.1    Render, H.2
  • 17
    • 0342313992 scopus 로고    scopus 로고
    • A wavelet based method for the gravimetry problem
    • Progress in Geodetic Science, edited by W. Freeden (Shaker Verlag, Aachen)
    • V. Michel, A Wavelet Based Method for the Gravimetry Problem, in: Progress in Geodetic Science, Proceedings of the Geodetic Week 1998, edited by W. Freeden (Shaker Verlag, Aachen, 1998), pp. 283-298.
    • (1998) Proceedings of the Geodetic Week 1998 , pp. 283-298
    • Michel, V.1
  • 19
    • 31244434305 scopus 로고    scopus 로고
    • Scale continuous, scale discretized and scale discrete harmonic wavelets for the outer and the inner space of a sphere and their application to an inverse problem in geomathematics
    • USA
    • V. Michel, Scale Continuous, Scale Discretized and Scale Discrete Harmonic Wavelets for the Outer and the Inner Space of a Sphere and Their Application to an Inverse Problem in Geomathematics, Appl. Comput. Harmon. Anal. (USA) 12, 77-99 (2002).
    • (2002) Appl. Comput. Harmon. Anal. , vol.12 , pp. 77-99
    • Michel, V.1
  • 21
    • 18744366382 scopus 로고    scopus 로고
    • Regularized wavelet-based multiresolution recovery of the harmonic mass density distribution from data of the earth's gravitational field at satellite height
    • V. Michel, Regularized Wavelet-based Multiresolution Recovery of the Harmonic Mass Density Distribution from Data of the Earth's Gravitational Field at Satellite Height, Inverse Problems 21, 997-1025 (2005).
    • (2005) Inverse Problems , vol.21 , pp. 997-1025
    • Michel, V.1
  • 22
    • 0003360039 scopus 로고
    • Spherical harmonics
    • Springer, Berlin, Heidelberg
    • C. Müller, Spherical Harmonics, Lecture Notes in Mathematics, vol. 17 (Springer, Berlin, Heidelberg, 1966).
    • (1966) Lecture Notes in Mathematics , vol.17
    • Müller, C.1
  • 23
    • 18744375347 scopus 로고
    • Mitteilungen aus dem Institut für Theoretische Geodäsie, Universität Bonn
    • N. Weck, Zwei inverse Probleme in der Potentialtheorie. Mitteilungen aus dem Institut für Theoretische Geodäsie, Universität Bonn, 4 27-36 (1972).
    • (1972) Zwei Inverse Probleme in der Potentialtheorie , vol.4 , pp. 27-36
    • Weck, N.1
  • 25
    • 0004021335 scopus 로고
    • Springer, Berlin, Heidelberg, New York
    • K. Yosida, Functional Analysis (Springer, Berlin, Heidelberg, New York, 1980).
    • (1980) Functional Analysis
    • Yosida, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.