Explicit construction of the modified spherical harmonic series for the gravity gradients and analysis of their characteristics

• Autorzy: Petrovskaya M. S. , Vershkov A. N.

Identyfikatory

DOI

10.2478/v10018-009-0001-z

• Języki publikacji: EN

Abstrakty

EN

The present paper complements the research carried out in PV2008 (Petrovskaya and Vershkov, 2008), concerning the expansion of the gravity gradients in the local northoriented reference frame in orthogonal series of modified spherical harmonics. In PV2008 procedures are developed for recovering the orthogonal bases of these series. Then an idea is briefly described how the spectral relations can be obtained between the gravity gradients and the geopotential. However no explicit procedures are demonstrated for their derivation. In the present paper successive transformations are described for each derivative which convert the initial non-orthogonal expansion into the orthogonal series. The resulting spectral relations are applied for evaluating the harmonic coefficients of these series at different altitudes, on the basis of the geopotential model EGM2008. The corresponding degree variances are estimated. The new simple expressions for the gravity gradients are convenient for various applications. In the present paper they are implemented for constructing digital colored maps for Fennoscandia region which attracts much attention of geophysicists. These maps visually demonstrate an anomalous behavior of the gravity gradients in this area.

Słowa kluczowe

EN

gravity gradients; modified spherical harmonic expansions; spectral coefficients; degree variances; digital maps for gravity gradients; Fennoscandia region

• Wydawca: Centrum Badań Kosmicznych PAN ; De Gruyter
• Czasopismo: Artificial Satellites : Journal of Planetary Geodesy
• Rocznik: 2007
• Tom: Vol. 42, No. 4
• Strony: 185--214
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Petrovskaya M. S.

• Central (Pulkovo) Astronomical Observatory of the Russian Academy of Sciences Pulkovskoe Shosse 65/1, St. Petersburg, 196140, Russia

autor

Vershkov A. N.

• Central (Pulkovo) Astronomical Observatory of the Russian Academy of Sciences Pulkovskoe Shosse 65/1, St. Petersburg, 196140, Russia

Bibliografia

• CE (2005) Catalog of earthquakes in Northern Europe 1375-2005. The Institute of Seismology of the University of Helsinki. http://www.seismo.helsinki.fi/bulletin/list/catalog/Scandia_clean.html
• Claessens SJ New relations among associated Legendre functions and spherical harmonics. Journal of Geodesy, vol 79: 398-406.
• ETOPO2v2 (2006) 2-minute Gridded Global Data. U.S. Department of Commerce, National Oceanic and Atmospheric Administration, National Geophysical Data Center. http://www.ngdc.noaa.gov/mgg/fliers/06mgg01.html
• Grafarend E. W., Voosoghi B. (2003) Intrinsic deformation analysis of the Earth’s surface based on displacement fields derived from the space geodetic measurements. Case studies: present-day deformation patterns of Europe and of the Mediterranean area (ITRF data sets). Journal of Geodesy, Vol. 77, No. 5-6, pp. 303-326.
• Heiskanen W. A., Moritz H. (1979) Physical Geodesy. Institute of Physical Geodesy, Technical University, Graz, Austria.
• Holmes S. A., Featherstone W. E. (2002) A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalized associated Legendre functions. Journal of Geodesy, Vol. 76, No. 5, pp. 279-299.
• Ilk KH (1983) Ein Beitrag zur Dynamik ausgedehnter Körper - Gravitationswechselwirkung. Deutsche Geodätische Kommission, Reihe C, Heft Nr 288, München.
• Moritz H (1980) Geodetic Reference System 1980. Bull Géod 54 (4): 395-405.
• Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2008) An Earth Gravitational Model to Degree 2160: EGM2008, presented at the 2008 General Assembly of the European Geosciences Union, Vienna, Austria, April 13-18.
• Petrovskaya M. S., Vershkov A. N. (2006) Non-singular expressions of the gravity gradients in the local north-oriented and orbital reference frames. Journal of Geodesy, Vol. 80, No. 3, pp. 117-127.
• Petrovskaya M.S., Vershkov A. N. (2008) Development of the local north-oriented second order derivatives of the Earth potential in orthogonal series of modified spherical harmonics. Journal of Geodesy, Vol. 82, No. 12, pp. 929-944, DOI: 10.1007/s00190- 008-0223-z.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).