Inverse Gravimetry: Background Material And Multiscale Mollifier Approaches

Keywords

Inverse gravimetry; Mollified spline inversion; Mollifier reduction to singular integrals; Mollifier transfer to reproducing kernel Hilbert space structure; Newton kernel regularization; Newton potential

Abstract

This paper represents an extended version of the publications Freeden (in: Freeden, Nashed, Sonar (eds) Handbook of Geomathematics, 2nd edn, vol 1, Springer, New York, pp 3–78, 2015) and Freeden and Nashed (in: Freeden, Nashed (eds) Handbook of Mathematical Geodesy, Geosystems Mathematics, Birkhäuser, Basel, pp 641–685, 2018c). It deals with the ill-posed problem of transferring input gravitational potential information in the form of Newtonian volume integral values to geological output characteristics of the density contrast function. Some essential properties of the Newton volume integral are recapitulated. Different methodologies of the resolution of the inverse gravimetry problem and their numerical implementations are examined including their dependence on the data source. Three types of input information may be distinguished, namely internal (borehole), terrestrial (surface), and/or external (spaceborne) gravitational data sets. Singular integral theory based inversion of the Newtonian integral equation such as a Haar-type solution is handled in a multiscale framework to decorrelate specific geological signal signatures with respect to inherently given features. Reproducing kernel Hilbert space regularization techniques are studied (together with their transition to certain mollified variants) to provide geological contrast density distributions by “downward continuation” from terrestrial and/or spaceborne data. Numerically, reproducing kernel Hilbert space spline solutions are formulated in terms of Gaussian approximating sums for use of gravimeter data systems.

Publication Date

11-1-2018

Publication Title

GEM - International Journal on Geomathematics

Volume

9

Issue

2

Number of Pages

199-264

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s13137-018-0103-5

Socpus ID

85054490083 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85054490083

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