Spline multiresolution and numerical results for joint gravitation and normal-mode inversion with an outlook on sparse regularisation

DOI10.1007/s13137-010-0007-5zbMath1301.86012OpenAlexW2000920411MaRDI QIDQ476207

Volker Michel, Doreen Fischer, Paula Berkel

Publication date: 28 November 2014

Published in: GEM - International Journal on Geomathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13137-010-0007-5

zbMATH Keywords

inverse problemsplinereproducing kerneltomographyregularisationmantlecrustinverse gravimetrynormal-modessparse regularisation

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Inverse problems in geophysics (86A22) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Numerical methods for inverse problems for integral equations (65R32)

Related Items

A Slepian framework for the inverse problem of equivalent gravitational potential generated by discrete point masses, Vector-valued spline method for the spherical multiple-shell electro-magnetoencephalography problem, A non-linear approximation method on the sphere, Vectorial Slepian Functions on the Ball, Reproducing-kernel-based splines for the regularization of the inverse ellipsoidal gravimetric problem, A greedy algorithm for nonlinear inverse problems with an application to nonlinear inverse gravimetry, Moment discretization for ill-posed problems with discrete weakly bounded noise, The Regularized Orthogonal Functional Matching Pursuit for Ill-Posed Inverse Problems, A first approach to learning a best basis for gravitational field modelling, Inverse Gravimetry as an Ill-Posed Problem in Mathematical Geodesy, Spherical Harmonics Based Special Function Systems and Constructive Approximation Methods, Regularized functional matching pursuit for the spherical multiple-shell electro-magnetoencephalography problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On mathematical aspects of a combined inversion of gravity and normal mode variations by a spline method
• Multiscale potential theory. With applications to geoscience
• On algorithms for the summation of certain special functions
• Satellite-to-satellite tracking and satellite gravity gradiometry (Advanced techniques for high-resolution geopotential field determination)
• 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
• A unified approach to various techniques for the non-uniqueness of the inverse gravimetric problem and wavelet-based methods
• Vector spherical spline interpolation—basic theory and computational aspects
• The unique determination of neuronal currents in the brain via magnetoencephalography
• Inversion method for magnetoencephalography
• Electro-magneto-encephalography for the three-shell model: numerical implementation via splines for distributed current in spherical geometry
• Time‐dependent Cauchy‐Navier splines and their application to seismic wave front propagation
• Splines on the three-dimensional ball and their application to seismic body wave tomography
• Regularized wavelet-based multiresolution recovery of the harmonic mass density distribution from data of the Earth's gravitational field at satellite height
• Kernel matching pursuit