On mathematical aspects of a combined inversion of gravity and normal mode variations by a spline method

DOI10.1007/s11004-010-9297-2zbMath1198.86012OpenAlexW2073296778MaRDI QIDQ600862

Paula Berkel, Volker Michel

Publication date: 3 November 2010

Published in: Mathematical Geosciences (Search for Journal in Brave)

Full work available at URL: http://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2038

zbMATH Keywords

splinereproducing kernelsplitting functionregularisationill-posedmass densitynormal modesgravimetryNewton potentialbody wave velocityharmonic densityinverse gravimetric problem

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Inverse problems in geophysics (86A22)

Related Items (6)

Vector-valued spline method for the spherical multiple-shell electro-magnetoencephalography problem ⋮ Spline multiresolution and numerical results for joint gravitation and normal-mode inversion with an outlook on sparse regularisation ⋮ Reproducing-kernel-based splines for the regularization of the inverse ellipsoidal gravimetric problem ⋮ Multi-physics adjoint modeling of Earth structure: combining gravimetric, seismic, and geodynamic inversions ⋮ Convolutions on the sphere: commutation with differential operators ⋮ Spherical Harmonics Based Special Function Systems and Constructive Approximation Methods

Cites Work

• Multiscale potential theory. With applications to geoscience
• 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
• Wavelets on the 3-dimensional Ball
• 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
• On spherical spline interpolation and approximation
• 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
• Isotropic reproducing kernels for the inner of a sphere or spherical shell and their use as density covariance functions
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