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  4. Reduction of the gravity vertical gradients to a spherical surface

Reduction of the gravity vertical gradients to a spherical surface

ISTCGCAP.
2014;
Volume 79, Number 79
: pp. 48 - 53
Received: February 21, 2014
Accepted: March 24, 2014
Authors:
  1. Alexander N. Marchenko
  2. Yu. O. Lukyanchenko
1
Department of Geodesy, Institute of Geodesy, Lviv Polytechnic National University
2
Lviv Polytechnic National University

The GOCE mission has produced gravity gradient data during 2009–2013 years. Various data sets were obtained, such as: tensor of second derivatives in different systems, satellite orbit parameters, the models of the gravitational field of the Earth. In contrast to the direct approach, space-wise-approach, and time-wise approach the construction of the spherical grid of gradients were orthogonality relationships are carry out, was developed via upward/downward continuation to sphere. This paper considers the vertical gravity gradients zz V (EGG TRF2 [Gruber Th., 2010]) in particular. The data sets are oriented in LNOF (Local North Oriented Frame) along the satellites track. On the following step the gravity gradients are reduced to the spherical surface and regular grid a built for for further processing. Reduction of gradients to the sphere is very important step in processing of these data. For example gravity anomalies, also, are related to the sphere. This paper considers way of reduction of gradients, using a Taylor’s series. The article performs experimental calculating and illustrated the corresponding results. The advantages of reduced gradients are demonstrated. Paper gives some recommendations in the application of EGM2008 for calculating of necessary corrections.

reduction
vertical gravity gradient
GOCE mission
satellite gradiometry
  1. Bouman J., Fiorot S., Fuchs M., Gruber T., Schrama E., Tscherning C., Veicherts M., Visser P. GOCE gravitational gradients along the orbit. J Geod (2011) 85:791–805.
  2. Fano U., Racah G. Irreducible Tensorial Sets. Academic Press. New York, 1959. Goldberg J.N. Spin-s Spherical Harmonics and Edth. Goldberg J.N. et al. J. Math. Phys., Vol. 8, pp. 2155–61, 1967.
  3. Gruber Th., Rummel R., Abrikosov O., R. van Hees. GOCE High Level Processing Facility GOCE Level 2 Product Data Handbook, ч, 2010, The European GOCE Gravity Consortium EGG-C, 77 p.
  4. Haagmans R, Prijatna K, Omang O. An Alternative Concept for Validation of GOCE Gradiometry Results Based on Regional Gravity, In: Gravity and Geoid, 2002, 3rd Meeting of the IGGC. Tziavos (ed.), Gravity and Geoid 2002, pp 281-286, Ziti Editions, 2003.
  5. Heck B. Zur lokalen Geoidbestimmung aus terrestrischen Messungen Vertikaler Schweregradienten. Dissertationen Reihe C 259. Deutsche Geodätische Kommission, München, 1979.
  6. Heiskanen W., Moritz H. Physical Geodesy, Freeman and Co. San Francisco and London, 1967.
  7. Novak P., Sebera; J., Val'ko M., Baur O. On the downward continuation of gravitational gradients(GOCE-GDC project). 2012, GGHS, Venice, Italy.
  8. Pail R. GOCE gravity models. Institute of Astronomical and Physical GeodesyTU München.
  9. Pail R., Plank G. Assessment of three numerical solution strategies for gravity field recovery from GOCE satellite gravity radiometry implemented on a parallel platform. Journal of Geodesy (2002) 76: 462–474.
  10. Rummel R., Gravity Gradiometry: From Loránd Eötvös to Modern Space Age. Acta Geod. Geoph. Hung., Vol. 37(4), pp. 435–444, 2002.
  11. Srivastava H.M, Gupta L.C. Some Families of Generating Functions for the Jacobi Polynomials. Comp. Math. Appl., Vol. 29, no.4, pp. 29–35, 1995.
  12. Tóth Gy. The Eötvös spherical horizontal gradiometric boundary value problem – gravity anomalies from gravity gradients of the torsion balance. In: Gravity and Geoid 2002, Tóth Gy, 3rd Meeting of the IGGC. Tziavos (ed.), Gravity and Geoid 2002, pp. 102–107, Ziti Editions, 2003.