Publications of the Geomathematics Group

  Publications of the Geomathematics Group

(in reverse chronological order)

2024

• V. Michel: Basics on Geomathematics, online introductory course on youtube, see https://www.youtube.com/@VolkerMichel-Geomathematics, episodes:
  • Polar coordinates - what you need to know about them, https://www.youtube.com/watch?v=jx4uEvfaXdI.
  • Spherical harmonics - a basic introduction, https://www.youtube.com/watch?v=830Wj1pu8DY.
  • Spherical radial basis functions, https://www.youtube.com/watch?v=xNQUQO8KFWY.
• V. Michel: Wozu braucht man eigentlich Mathematik? -  Was Sie zu Routenplanung, Klimawandel, Erdbeben und Quiz-Shows schon immer wissen wollten, aber sich nicht zu fragen trauten, Springer, Berlin, Heidelberg, 2024.
• N. Schneider, V. Michel, K. Sigloch and E. J. Totten, A matching pursuit approach to the geophysical inverse problem of seismic travel time tomography under the ray theory approximation, Geophysical Journal International, 238 (2024), 1546-1581.
• N. Schneider, V. Michel and N. Sneeuw, High-dimensional experiments for the downward continuation using the LRFMP algorithm, preprint available at http://arxiv.org/abs/2308.04167, accepted for publication in: GEM: International Journal on Geomathematics, 2024.

2023

• N. Schneider, (L)IPMP source code for travel time tomography, v3-tt-2023. Zenodo. https://doi.org/10.5281/zenodo.8227888, 2023.
• N. Schneider, (L)IPMP source code for gravitational field modelling, v2-dc-2023. Zenodo. https://doi.org/10.5281/zenodo.8223771, 2023.

2022

• S. Leweke, O. Hauk, V. Michel: Vector-valued spline method for the spherical multiple-shell electro-magnetoencephalography problem, Inverse Problems, 38 (2022), article 085001 (46pp).
• S. Leweke, V. Michel: Regularized functional matching pursuit for the spherical multiple-shell electro-magnetoencephalography problem, Electronic Transactions on Numerical Analysis, 57 (2022), 153-192.
• V. Michel: Geomathematics - Modelling and Solving Mathematical Problems in Geodesy and Geophysics, Cambridge University Press, Cambridge, 2022.
• V. Michel, A. Plattner, K. Seibert: A unified approach to scalar, vector, and tensor Slepian functions on the sphere and their construction by a commuting operator, Analysis and Applications, 20 (2022), 947-988. The preprint is available at arXiv:2103.14650.
• N. Schneider, (L)IPMP source code, v1-2020 (PhD-Thesis), in the collection: (Learning) Inverse Problem Matching Pursuits, publication of software at FoDaSi - research data repository of the University of Siegen, 2022.
• N. Schneider, V. Michel: A dictionary learning add-on for spherical downward continuation, Journal of Geodesy, 96 (2022), article 21 (22pp).

2020

• S. Leweke, V. Michel, A.S. Fokas: Electro-magnetoencephalography for the spherical multiple-shell model: novel integral operators with singular-value decompositions, Inverse Problems, 36 (2020), 035003 (31pp).
• V. Michel, N. Schneider: A first approach to learning a best basis for gravitational field modelling, GEM: International Journal on Geomathematics, 11 (2020), article 9, as part of the topical collection "Mathematical Problems in Medical Imaging and Earth Sciences".

2019

• A. Ishtiaq, V. Michel, H.P. Scheffler: Theory of generalized discrepancies on a ball of arbitrary finite dimensions and algorithms for finding low-discrepancy point sets, GEM: International Journal on Geomathematics, 10 (2019), article 21 (45pp), as part of the topical collection "Mathematical Problems in Medical Imaging and Earth Sciences".
• M. Kontak, V. Michel: The regularized weak functional matching pursuit for linear inverse problems, Journal of Inverse and Ill-Posed Problems, 27 (2019), 317-340.

2018

• W. Freeden, V. Michel, F.J. Simons: Spherical harmonics based special function systems and constructive approximation methods, in: Handbook of Mathematical Geodesy (W. Freeden and M.Z. Nashed, eds.), Birkhäuser, Basel, 2018, pp. 753-819.
• S. Gramsch, M. Kontak, V. Michel: Three-dimensional simulation of nonwoven fabrics using a greedy approximation of the distribution of fiber directions, arXiv:1608.01514, 2016; Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM, Journal of Applied Mathematics and Mechanics), 98 (2018), 277-288.
• M. Kontak, V. Michel: A greedy algorithm for non-linear inverse problems with an application to non-linear inverse gravimetry, 2018; local download: this is a post-peer-review, pre-copyedit version of an article published in GEM: International Journal on Geomathematics, 9 (2018), 167-198, as part of the topical collection "Mathematical Problems in Medical Imaging and Earth Sciences". The final authenticated version is available online at: https://link.springer.com/article/10.1007/s13137-018-0110-6.
• S. Leweke, V. Michel, N. Schneider: Vectorial Slepian functions on the ball, Numerical Functional Analysis and Optimization, 39 (2018), 1120-1152; preprint SPG-17, 2017, arXiv 1707.00245.
• S. Leweke, V. Michel, R. Telschow: On the non-uniqueness of gravitational and magnetic field data inversion (survey article), in: Handbook of Mathematical Geodesy (W. Freeden and M.Z. Nashed, eds.), Birkhäuser, Basel, 2018, pp. 883-919.
• V. Michel (ed.): Mathematical Problems in Medical Imaging and Earth Sciences, topical collection, GEM: International Journal on Geomathematics, started in 2018, papers are continuously being collected.
• V. Michel, K. Seibert: A mathematical view on spin-weighted spherical harmonics and their applications in geodesy, in: Handbuch der Geodäsie (W. Freeden und R. Rummel, eds.), Springer Reference Naturwissenschaften, Springer Spektrum, Berlin, Heidelberg, 2018, 113 pages.

2017

• M. Gutting, B. Kretz, V. Michel, R. Telschow: Study on parameter choice methods for the RFMP with respect to downward continuation, Frontiers in Applied Mathematics and Statistics, 3 (2017), article 10, doi: 10.3389/fams.2017.00010.
• A. Ishtiaq, V. Michel: Pseudodifferential operators, cubature and equidistribution on the 3D-ball - an approach based on orthonormal basis systems, Numerical Functional Analysis and Optimization, 38 (2017), 891-910.
• V. Michel, S. Orzlowski: On the convergence theorem for the Regularized Functional Matching Pursuit (RFMP) algorithm, GEM: International Journal on Geomathematics, 8 (2017), 183-190. The article is also available via ShareIt.
• V. Michel, F.J. Simons: A general approach to regularizing inverse problems with regional data using Slepian wavelets, Inverse Problems, 33 (2017), 125016.

2016

• V. Michel, S. Orzlowski: On the null space of a class of Fredholm integral equations of the first kind, Journal of Inverse and Ill-Posed Problems, 24 (2016), 687-710.
• V. Michel, R. Telschow: The regularized orthogonal functional matching pursuit for ill-posed inverse problems, SIAM Journal on Numerical Analysis, 54 (2016), 262-287.

2015

• V. Michel: RFMP - An iterative best basis algorithm for inverse problems in the geosciences, in: Handbook of Geomathematics (W. Freeden, M.Z. Nashed, and T. Sonar, eds.), 2nd edition (new paper), Springer, Berlin, Heidelberg, 2015, pp. 2121-2147.
• 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 of the paper in the 1st edition), Springer, Berlin, Heidelberg, 2015, pp. 2087-2119.

2014

• V. Michel (ed.): Special Issue Dedicated to Willi Freeden's 65th Birthday, International Journal on Geomathematics, 5 (2014), 63-224.
• V. Michel, R. Telschow: A non-linear approximation method on the sphere, International Journal on Geomathematics, 5 (2014), 195-224.
• S. Paul, M.M. Richter, V. Michel: Reaction to hybrid noise in communication, in: Noise Pollution - Sources, Effects on Workplace Productivity and Health Implications (E.R. Nicchi, ed.), Nova, New York, 2014, 41-69.
  

2013

• D. Fischer, V. Michel: Automatic best-basis selection for geophysical tomographic inverse problems,Geophysical Journal International, 193 (2013), 1291-1299.
• D. Fischer, V. Michel: Inverting GRACE gravity data for local climate effects, Journal of Geodetic Science, 3 (2013), 151-162.
• 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.

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: 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).

• 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.

Back to the homepage of the Geomathematics Group

The group does not take responsibility for the sites that are linked (except certainly those which are part of www.geomathematics-siegen.de).