Local Solutions to Inverse Problems in Geodesy |
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| Authors: | Frank Bauer Peter Mathé Sergei Pereverzev |
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| Institution: | 1.Institute for Mathematical Stochastics, Department of Mathematics,University of G?ttingen,G?ttingen,Germany;2.Weierstrass Institute for Applied Analysis and Stochastics,Berlin,Germany;3.Johann Radon Institute for Computational and Applied Mathematics (RICAM),Austrian Academy of Sciences,Linz,Austria |
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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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| Keywords: | Regularization by local data Ill-posed inverse problems Gaussian random noise Satellite gravity gradiometry |
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