The application of the coefficients of the spheric harmonious development in the procedure of the determination functionally anomalic potential

Abstract

In the procedure of the determining functionally anomalic power, in the frame of the method remove-restore the first step presents the elimination of the long wave characteristics of the functionally with the application of the coefficients sphericharmonical development of the power gravity, respectively, to the application global geopotential model(GGM). Over last two decade are developed GGM of the high degree and order, respectively of the degree and order 360, as like what are the models OSU91 (Ohio States University) and EGM96 (Earth Gravity Models). Their application ensures the estimation of the long wave characteristics of the functionally anomalic potential with the acctitude, that is in the case anomalic heights safely less then 1 meter. In this work are presented mathematical models indispensables for theoretical consideration of the models, after wards recurrent expressions to the computation of the Legandres functions high degree and order, and mentioned GGM and practically are applied on the territory of the wider region of the town Belgrade.

U postupku određivanja funkcionala anomalijskog potencijala, u okviru remove-restore metode prvi korak predstavlja eliminacija dugotalasnih karakteristika funkcionala primenom koeficijenata sferno-harmonijskog razvoja potencijala sile Zemljine teže odnosno, primenom globalnog geopotencijalnog modela (GGM). U poslednje dve decenije razvijeni su GGM visokog stepena i reda, odnosno stepena i reda 360, kao što su modeli OSU91 (Ohio States University) i EGM96 (Earth Gravity Models). Njihova primena obezbeđuje ocenu dugotalasne karakteristike funkcionala anomalijskog potencijala sa tačnošću koja je u slučaju anomalijskih visina sigurno ispod 1m. U ovom radu prikazani su matematički modeli neophodni za teorijsko razmatranje modela, zatim rekurzioni izrazi za računanje Ležandrovih funkcija visokog stepena i reda, a pomenuti GGM i praktično su primenjeni za teritoriju šireg područja grada Beograda.