Monday 22 August 2005

G4

PM0025
A new methodology for high accuracy orthometric height computations
Ardalan, Alireza¹
1 University Of Tehran, Department of Surveying and Geomatics Eng., Iran
Author email: ardalan@ut.ac.ir
A new methodology for high accuracy orthometric height computations has been developed. This methodology is comprised of two parts: (a) Construction of a high-resolution gravity field model. (b) Application of an iterative method for calculation of the number of points within the Earth needed to compute mean gravity inside the Earth by the high-resolution model to the desired accuracy. The high-resolution gravity field is constructed by combination of (1) centrifugal acceleration, (2) gravitational acceleration due to global to regional masses, (3) gravitational acceleration due to local masses. The gravitational acceleration due to global to regional masses is supplied by the gradient of ellipsoidal harmonic expansion of the Earth's gravitational potential to degree and order "n". The gravitational acceleration due to local masses is represented by Newton integral over the local masses above the reference ellipsoid at the radius r, being determined from the degree "n" of maximum degree and order of expansion of the ellipsoidal harmonics as r=2*104km/n. The closed form of Newton integral in terms of Cartesian coordinates of equal area cylindrical map projection of the reference ellipsoid is used this purpose. For the verification of the accuracy of the proposed method, the gravity observation within the Earth at an exploration borehole at the location longitude=12.1194(deg.) and latitude=49.8164(deg.) is used and the accuracy of "point" and "mean" gravity computations within the Earth by the proposed method is estimated. Based on the numerical results our method is accurate to 10.768(mGal) at a points in depth of 474.7(m) within the Earth, and the mean gravity up to that depth grants the accuracy of 5.56(mGal). Based on error propagation analysis 5.56(mGal) error in mean gravity computations results in 2.78(mm) error in the computation of an orthometric height of 474.7(m). The classical Helmert method resulted in nearly 5 times more error in the computed orthometric height at the same test condition. Considering the tendency of geodetic community to combine orthometric heights with GPS derived height for geoid computations, application of more accurate methods for the orthometric height computations is necessary. The results of this research could be an answer to modern needs of high accuracy orthometric height computations at the GPS era.

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