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Local Solutions to Inverse Problems in Geodesy

The Impact of the Noise Covariance Structure upon the Accuracy of Estimation

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Abstract

In many geoscientific applications, one needs to recover the quantities of interest from indirect observations blurred by colored noise. Such quantities often correspond to the values of bounded linear functionals acting on the solution of some observation equation. For example, various quantities are derived from harmonic coefficients of the Earth’s gravity potential. Each such coefficient is the value of the corresponding linear functional. The goal of this paper is to discuss new means to use information about the noise covariance structure, which allows order-optimal estimation of the functionals of interest and does not involve a covariance operator directly in the estimation process. It is done on the basis of a balancing principle for the choice of the regularization parameter, which is new in geoscientific applications. A number of tests demonstrate its applicability. In particular, we could find appropriate regularization parameters by knowing a small part of the gravitational field on the Earth’s surface with high precision and reconstructing the rest globally by downward continuation from satellite data.

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Authors and Affiliations

  1. Institute for Mathematical Stochastics, Department of Mathematics, University of Göttingen, Maschmühlenweg 8-10, 37073, Göttingen, Germany

    Frank Bauer

  2. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117, Berlin, Germany

    Peter Mathé

  3. Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstraße 69, 4040, Linz, Austria

    Sergei Pereverzev

Authors
  1. Frank Bauer
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  2. Peter Mathé
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  3. Sergei Pereverzev
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Correspondence to Frank Bauer.

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Bauer, F., Mathé, P. & Pereverzev, S. Local Solutions to Inverse Problems in Geodesy. J Geod 81, 39–51 (2007). https://doi.org/10.1007/s00190-006-0049-5

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  • DOI: https://doi.org/10.1007/s00190-006-0049-5

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