Direct Harmonic Analysis for the Ellipsoidal Topographic Potential with Global and Local Validation
- PDF / 4,347,316 Bytes
- 18 Pages / 439.37 x 666.142 pts Page_size
- 37 Downloads / 160 Views
Direct Harmonic Analysis for the Ellipsoidal Topographic Potential with Global and Local Validation Hussein A. Abd‑Elmotaal1 · Norbert Kühtreiber2 Received: 18 January 2020 / Accepted: 19 August 2020 © Springer Nature B.V. 2020
Abstract Forward gravity field modelling requires high accurate determination of the topographic potential on the surface of the Earth’s ellipsoid. Since the topography is recently known with high resolution, the determination of the harmonic analysis of the topographic ellipsoidal potential should be carried-out to an ultra-high degree. The paper presents a direct technique to determine the harmonic analysis of the ellipsoidal potential to an ultra-high degree. The detailed derivation of the developed expressions is given. The proposed technique can be used to compute the harmonic analysis of the topographic potential of the whole Earth or for a local/regional window. This has a great advantage when using the proposed technique for local/regional geoid determination within the window remove– restore technique (Abd-Elmotaal and Kühtreiber, Phys Chem Earth Part A 24(1):53–59, 1999, J Geod 77(1–2):77–85, 2003). The developed technique has been compared to existing global solutions for the ellipsoidal topographic potential and it shows quite good agreement. Local tests for the developed technique proved that it works very well. Keywords Forward gravity field modelling · Topographic potential · Ultra-high-degree harmonic analysis · Geoid determination · Gravity reduction · Window remove–restore technique
1 Introduction On the one hand, some global geodetic applications require the forward modelling of the Earth’s gravity field. This necessitates the accurate harmonic analysis of the global topographic (and also isostatic) potential. On the other hand, local and regional geodetic applications employing the window remove–restore technique (Abd-Elmotaal and Kühtreiber 1999, 2003) require the precise ellipsoidal harmonic analysis of the local/regional topographic–isostatic potential. This is needed to get rid of the double consideration of part of * Hussein A. Abd‑Elmotaal [email protected] Norbert Kühtreiber [email protected] 1
Civil Engineering Department, Faculty of Engineering, Minia University, Minia 61111, Egypt
2
Institute of Geodesy, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria
13
Vol.:(0123456789)
Surveys in Geophysics
the topographic–isostatic masses in the neighbourhood of the computational point associated with the traditional remove–restore technique (Forsberg 1984). Both global and local/regional geodetic applications demand the ellipsoidal harmonic analysis of the topographic–isostatic potential to an ultra-high degree to match the high resolution of the topographic models as well as of the Earth’s gravity models available nowadays. Accordingly, the proposed technique is designed to directly compute the ellipsoidal harmonic analysis of the topographic–isostatic potential for local or global applications. The derivation of
Data Loading...
