Publications of the Geomathematics Group
(in reverse chronological order)
2013
- D. Fischer, V. Michel: Automatic best-basis selection for geophysical tomographic inverse problems, Geophysical Journal International, 193 (2013), 1291-1299
. - V. Michel: Lectures on Constructive Approximation - Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball, textbook, 326 pages, Birkhäuser Verlag, Boston, 2013.
- V. Michel: Tomography - problems and multiscale solutions, in: Handbook of Geomathematics (W. Freeden, M.Z. Nashed, and T. Sonar, eds.), 2nd edition, completely revised version submitted, 2013.
2012
- N. Akhtar, V. Michel: Reproducing kernel based splines for the regularization of the inverse ellipsoidal gravimetric problem, Applicable Analysis, 91 (2012), 2105-2132 .
- D. Fischer, V. Michel: Inverting GRACE gravity data for local climate effects, Siegen Preprints on Geomathematics, 9
, 2012, accepted for publication in: Journal of Geodetic Science, 2013. - D. Fischer, V. Michel: Sparse regularization of inverse gravimetry – case study: spatial and temporal mass variations in South America, Inverse Problems, 28 (2012), 065012 (34pp) , click here for download.
- A.S. Fokas, O. Hauk, V. Michel: Electro-magneto-encephalography for the
three-shell model: numerical implementation via splines for distributed current in spherical geometry, Inverse Problems, 28 (2012), 035009 (28pp) .
- M. Akram, I. Amina, V. Michel: A study of differential operators for particular complete orthonormal systems on a 3d ball, International Journal of Pure and Applied Mathematics (IJPAM), 73 (2011), 489-506 .
- P. Berkel, D. Fischer, V. Michel: Spline
multiresolution and numerical results for joint gravitation and normal
mode inversion with an outlook on sparse regularisation, International Journal on Geomathematics, 1 (2011), 167-204 .
- V. Michel: Optimally localized
approximate identities on the 2-sphere, Numerical Functional Analysis and Optimization, 32 (2011), 877-903 .
- M. Akram, V. Michel: Locally
supported approximate identities on the unit ball, Revista Matemática Complutense, 23 (2010), 233-249 .
- M. Akram, V. Michel: Regularisation
of the Helmholtz decomposition and its application to geomagnetic field
modelling, International Journal on Geomathematics, 1 (2010), 101-120 .
- P. Berkel, V. Michel: On mathematical aspects of a combined inversion
of gravity and normal mode variations by a spline method, Mathematical Geosciences, 42 (2010), 795-816 .
- V. Michel: Warum Kernwaffentests andere Wellen schlagen als Erdbeben - und was man sonst noch aus Seismogrammen erfährt, Diagonal, 31 (2010), 39-50.
- V. Michel: Tomography - problems and multiscale solutions, in: Handbook of Geomathematics (W. Freeden, M.Z. Nashed, and T. Sonar, eds.), 2010, 949-972.
- A. Amirbekyan, V. Michel: Splines
on the three-dimensional ball and their application to seismic body
wave tomography, Inverse Problems, 24 (2008), 015022 (25pp) .
- A. Amirbekyan, V. Michel, F.J. Simons: Parameterizing surface-wave tomographic
models with harmonic spherical splines, Geophysical Journal International, 174 (2008), 617-628 .
- G. Hebinger, V. Michel, M. Richter, A. Simon: Speech recognition support of assisted living, Schriften zur Funktionalanalysis und Geomathematik, 40 (2008) .
- P. Kammann, V. Michel: Time–dependent
Cauchy–Navier splines and their application to seismic wave front
propagation, Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 88 (2008),155-178 .
- V. Michel, A.S. Fokas: A
unified approach to various techniques
for the
non-uniqueness of the inverse gravimetric problem and wavelet-based
methods, preprint
NI08020 of the Isaac Newton Institute for
Mathematical Sciences, final version published in: Inverse Problems, 24 (2008), 045019 (25pp) .
- V. Michel, K. Wolf: Numerical
aspects of a spline-based multiresolution recovery of the harmonic mass
density out of gravity functionals, Geophysical Journal International, 173 (2008), 1-16 .
- M.J.
Fengler, W.
Freeden, A. Kohlhaas, V. Michel, T. Peters: Wavelet modelling of regional and temporal
variations of the earth's gravitational potential observed by GRACE,
Journal of Geodesy, 81 (2007),5-15 .
- W. Freeden, D. Michel, V. Michel: Product framelet based operator decomposition, Schriften zur Funktionalanalysis und Geomathematik, TU Kaiserslautern, 34 (2007).
- V. Michel: Review of the book
"Mathematical geophysics. An introduction to rotating fluids and the
Navier-Stokes equations", by J.Y. Chemin, B. Desjardins, I. Gallagher,
E. Grenier, Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 87 (2007), p. 246 .
- A.
Chattopadhyay, V. Michel: A model for spherical SH-wave propagation
in self-reinforced linearly elastic media, Archive of
Applied Mechanics, 75 (2006),
113-124 .
- M.J.
Fengler, D. Michel,
V. Michel: 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, Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 86 (2006), 856-873 .
- W.
Freeden, D. Michel,
V. Michel: Local multiscale
approximations of geostrophic oceanic flow: theoretical background and aspects of scientific computing, Marine Geodesy, 28 (2005), 313-329 .
- W.
Freeden, V. Michel: Wavelet
deformation analysis for spherical bodies, International Journal on Wavelets, Multiresolution and Information Processing, 3 (2005), 523-558 .
- 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 (2005), 997-1025 .
- V. Michel: Wavelets on the
3-dimensional ball, Proceedings
in Applied Mathematics and Mechanics (PAMM), 5 (2005), 775-776 .
- M.J.
Fengler, W.
Freeden, V. Michel: The
Kaiserslautern multiscale geopotential model SWITCH03 from orbit
perturbations of the satellite CHAMP and its comparison to EGM96,
UCPH2002_02_0.5, EIGEN-1s, and EIGEN-2,
Geophysical Journal International, 157 (2004), 499-514 .
- W. Freeden, D. Michel, V. Michel: Multiscale modelling of oceanic circulation, in: GOCE, the Geoid and Oceanography, Proceedings of the 2nd International GOCE User Workshop, Frascati, Italy, ESA publications division, Noordwijk, 2004.
- W.
Freeden, V. Michel: Orthogonal zonal, tesseral and sectorial
wavelets on the sphere for the analysis of satellite data,
Advances in Computational Mathematics, 21 (2004), 181-217 .
- W.
Freeden, V. Michel: Multiscale Potential Theory (With Applications
to Geoscience) , Birkhäuser Verlag,
Boston, 2004.
- V. Michel: Multi-scale
approaches for the determination of the earth's Interior - from
gravitational and seismic data, Oberwolfach Workshop Report "Geomathematics", 1 (2004), 1380-1381 .
- W.
Freeden, E. Groten, V. Michel, K. Arfa-Kaboodvand: Geopotential
reconstruction, decomposition, fast computation and noise cancellation
by harmonic wavelets, Studia Geophysica et Geodaetica, 47 (2003), 37-72 .
- W.
Freeden, V. Michel (eds.): Multiscale modelling of CHAMP data,
Schriften zur Funktionalanalysis und Geomathematik, 4 (2003) .
- V. Michel: Theoretical aspects of a multiscale analysis of
the eigenoscillations of the earth,
Revista Matemática Complutense, 16 (2003), 519-554 .
- W.
Freeden, V. Michel, H. Nutz: Satellite-to-satellite tracking and
satellite gravity gradiometry (advanced techniques for high-resolution
geopotential field determination), Journal of Engineering Mathematics, 43 (2002), 19-56 .
- 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, Applied and Computational Harmonic Analysis (ACHA), 12 (2002), 77-99 .
- V. Michel: A Multiscale Approximation for Operator Equations in Separable Hilbert Spaces - Case Study: Reconstruction and Description of the Earth's Interior , habilitation thesis, Shaker Verlag, Aachen,
2002.
- W.
Freeden, V. Michel: Basic aspects of geopotential field
approximation from satellite-to-satellite tracking data,
Mathematical Methods in the Applied Sciences, 24 (2001), 827-846 .
- W.
Freeden, V. Michel, M.
Stenger: Multiscale signal-to-noise thresholding, Acta Geodaetica et Geophysica Hungarica, 36 (2001), 55-86 .
- W.
Freeden, V. Michel: Least-squares geopotential approximation by
windowed Fourier transform and wavelet transform, in: Wavelets in the Geosciences (R. Klees
and
R. Haagmans, eds.), Lecture Notes in Earth Sciences, 90 (2000), 189-241 , Springer Verlag, Berlin, Heidelberg.
- W.
Freeden, V. Michel: Constructive approximation and numerical
methods in geodetic research today - an attempt at a categorization
based on an uncertainty principle, Journal of Geodesy, 73 (1999), 452-465 .
- V. Michel: A Multiscale Method for the Gravimetry Problem: Theoretical and Numerical Aspects of Harmonic and Anharmonic Modelling ,
doctoral thesis,
Geomathematics Group, Department of Mathematics, University of
Kaiserslautern, Shaker Verlag, Aachen, 1999.
- V. Michel: A wavelet based method for the gravimetry problem,
in: Progress in Geodetic Science, Proceedings of the Geodetic Week 1998 (W. Freeden, ed.) , 283-298, Shaker Verlag, Aachen, 1998.
- V. Michel: Singular optimal control - the state of the art, Laboratory of Technomathematics, Geomathematics Group, Department of Mathematics, University of Kaiserslautern, AGTM-Report 169, 1996.
- V. Michel: Singuläre optimale Steuerungen, diploma thesis, University of Kaiserslautern, Department of Mathematics, 1995.
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