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Spectral combination of spherical gravitational curvature boundary-value problems
University of West Bohemia, NTIS—New Technologies for the Information Society, Faculty of Applied Sciences, Technicka´ 8, 306 14 Plzen, Czech Republic.
University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.ORCID iD: 0000-0003-0067-8631
University of Newcastle, School of Engineering, Faculty of Engineering and Built Environment, Callaghan, NSW 2308, Australia.
The Hong Kong Polytechnic University, Department of Land Surveying and Geo-informatics, 181 Chatham Road South, Hung Hom, 999077 Kowloon, Hong Kong.
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2018 (English)In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 214, no 2, p. 773-791Article in journal (Refereed) Published
Abstract [en]

Four solutions of the spherical gravitational curvature boundary-value problems can be exploited for the determination of the Earth’s gravitational potential. In this paper we discuss the combination of simulated satellite gravitational curvatures, that is, components of the third-order gravitational tensor, by merging these solutions using the spectral combination method. For this purpose, integral estimators of biased-and unbiased-types are derived. In numerical studies, we investigate the performance of the developed mathematical models for the gravitational field modelling in the area of Central Europe based on simulated satellite measurements. First, we verify the correctness of the integral estimators for the spectral downward continuation by a closed-loop test. Estimated errors of the combined solution are about eight orders smaller than those from the individual solutions. Second, we perform a numerical experiment by considering the Gaussian noise with the standard deviation of 6.5 x 10(-17) m(-1) s(-2) in the input data at the satellite altitude of 250 km above the mean Earth sphere. This value of standard deviation is equivalent to a signal-to-noise ratio of 10. Superior results with respect to the global geopotential model TIM-r5 (Brockmann et al. 2014) are obtained by the spectral downward continuation of the vertical-vertical-vertical component with the standard deviation of 2.104 m(2) s(-2), but the root mean square error is the largest and reaches 9.734 m(2) s(-2). Using the spectral combination of all gravitational curvatures the root mean square error is more than 400 times smaller but the standard deviation reaches 17.234 m(2) s(-2). The combination of more components decreases the root mean square error of the corresponding solutions while the standard deviations of the combined solutions do not improve as compared to the solution from the vertical-vertical-vertical component. The presented method represents a weight mean in the spectral domain that minimizes the root mean square error of the combined solutions and improves standard deviation of the solution based only on the least accurate components.

Place, publisher, year, edition, pages
2018. Vol. 214, no 2, p. 773-791
Keywords [en]
Geopotential theory; Inverse theory; Satellite geodesy
National Category
Geophysics
Research subject
ENGINEERING, Geodesy
Identifiers
URN: urn:nbn:se:hv:diva-13107DOI: 10.1093/gji/ggy147ISI: 000448238600002Scopus ID: 2-s2.0-85048579755OAI: oai:DiVA.org:hv-13107DiVA, id: diva2:1261755
Note

Funders:  Czech Science Foundation, 18-06943S

Available from: 2018-11-08 Created: 2018-11-08 Last updated: 2019-10-22Bibliographically approved

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Eshagh, Mehdi

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