A method for computation of mean gravity inside the Earth for increasing accuracy of orthometric computations


Department of Surveying and Geomatics Egineering, University of Tehran, P.O. Box 11365-4563


In this paper a method for computation of mean gravity value within the Earth between the computation point and the geoid needed for precise orthometric height computations is presented. The method presented is based on following steps: (1) computation of the global and regional gravity effects using ellipsoidal harmonic expansion to degree and order 360 plus the centrifugal acceleration. (2) Computation of the gravitational effect of terrain masses within the radius of 55km around the computational point applying Newton integral in the equal area map projection. (3) Computation of the gravity at two points on the surface of the Earth and on the geoid using steps 1-2, computing mean and standard deviation of the computed gravity values and increasing the number of points within the Earth to meet the predefined standard deviation for the computation of mean gravity within the Earth. (4) Deriving the mean gravity within the Earth from the steps 1-3. The proposed method for the computation of mean gravity within the Earth is checked against the observed gravity values within the Earth in an exploration borehole. The test computations are made in the following two modes: (a) Computation of gravity values at the observation points in the borehole and comparison of the computed values with the observed values (b) Computing mean gravity within the Earth using the proposed method and the observed gravity values. According to the test computations at a depth of 474.7 m computed gravity differs from the observed gravity by 10.768 mGal and the computed mean gravity from the observed mean gravity by 5.56 mGal.