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Comparative Study of the Spherical Downward Continuation

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Abstract

Downward continuation of the potential data (gravity or magnetic) helps to interpret contributing sources by transforming the physical signal to their neighborhood. This paper applies three continuation approaches (Landweber’s iteration, the direct method and the inverse-matrix approach with Tikhonov’s regularization), based on the Poisson integral equation, and four integration schemes to the second vertical derivative of the anomalous potential \(T_{\rm zz}\) obtained from GOCE data. In the experiments, \(T_{\rm zz}\) was downward continued for 250 km in the area of Central Europe with special attention to edge effects. For the integration schemes, which use prior information outside the region of interest to reduce edge effects, the best agreement with TIM-r4 was achieved by the inverse-matrix approach with Tikhonov’s regularization (RMS = 1.15 eotvos). On the contrary, without prior information the iterative approach performed with RMS = 1.17 eotvos.

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Notes

  1. \(T\) is obtained from \(V\) by subtracting some reference field; we have used GRS80 up to degree 10 (Moritz 1980).

  2. Poisson integral can rigorously be applied to z-derivative of any order in the local frame as long as the term \((R/r)^{i}\) with positive integers \(i\) is constant for two concentric spheres (input and output altitudes), see, e.g., discussion in Hotine (1969, p. 316).

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Acknowledgments

Josef Sebera has been supported by the project EXLIZ—CZ.1.07/2.3.00/30.0013, Martin Pitoňák and Eliška Hamáčková were supported by the project CZ.1.05/1.1.00/02.0090 NTIS—New Technologies for the Information Society. Martin Pitoňák has been supported by the national project APVV-0072-11. We thank Prof. M. Fedi, an anonymous reviewer and an Associate Editor for constructive discussion that helped us to improve the manuscript.

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Authors and Affiliations

  1. Astronomical institute, Academy of Sciences, Ondřejov, Czech Republic

    Josef Sebera

  2. NTIS - New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czech Republic

    Josef Sebera, Martin Pitoňák, Eliška Hamáčková & Pavel Novák

  3. Department of Theoretical Geodesy, Faculty of Civil Engineering, Slovak University of Technology, Radlinskho 11, Bratislava, 813 68, Slovakia

    Martin Pitoňák

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  1. Josef Sebera
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Correspondence to Josef Sebera.

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Sebera, J., Pitoňák, M., Hamáčková, E. et al. Comparative Study of the Spherical Downward Continuation. Surv Geophys 36, 253–267 (2015). https://doi.org/10.1007/s10712-014-9312-0

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