1st Joint Commission 2 and IGFS Meeting
International Symposium on
Gravity, Geoid and Height Systems 2016

September 19-23, 2016
Thessaloniki, Greece

Fast and accurate evaluation of gravimetric quantities at scattered points in space

20/09/2016 | 11:45 | Session 2: Computational Methods

Author(s):

Kamen Ivanov and Pencho Petrushev

Abstract

The purpose of this talk is to present an algorithm and software for evaluation of gravimetric quantities represented in high degree (>2000) solid spherical or ellipsoidal harmonics at scattered points in the space exterior to the surface of the Earth. To cover well the desired range above the geoid and minimize the computational error the algorithm uses representation of the gravimetric quantities in solid ellipsoidal harmonics. The algorithm is based on approximation using spherical needlets over a number of confocal ellipsoids in the space ranging from -125 m to 540,000 m above the Earth reference ellipsoid. The current version of the software is capable of computing the values of the following gravimetric quantities: the disturbing potential T, the height anomaly, the north-south deflection of the vertical, the east-west deflection of the vertical, and the second radial derivative of the disturbing potential Trr. The values of these quantities are derived from the official NGA Earth Gravitational Model EGM2008. The code computes the values of the gravimetric quantities with guaranteed accuracy (relative error) < 10^{-6} and runs between 427 and 1056 times faster than the software using the standard NGA methods, while using ~ 9.3 GB of memory (RAM).

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