RAPID COMPUTATION OF THE GRAVITATION ATTRACTION OF TOPOGRAPHY ON A SPHERICAL EARTH*

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Abstract
A brief review of the existing methods of gravity reduction is given and a new method suitable for use on high speed digital computers is described. The method is based on the formula for the gravitational attraction of a frustum of a cone. The topographic contours are represented by polygons and the x and y coordinates of corners of the polygons constitute the input to the computer. The vertical component of the gravitational attraction is calculated by evaluating the cone formula for a number of vertical sections of the topography. Each vertical section is simplified by adopting a procedure of grouping and averaging for the distant points of the section. The effect of the earth's sphericity is taken into account by lowering the distant points of the sections by amounts determined by the curvature. The computations include the area close to the point at which the attraction is required and may be limited to an area defined by a circle centered at this point. The method is therefore compatible with the conventional zone chart methods.As an illustration of the method the gravitational attraction of Caryn Seamount in the Atlantic Ocean is computed. The total Bouguer correction and the Terrain correction are also computed for an area in northwestern South America and comparisons are made with hand computations by a zone chart method. As an example, for work at sea, the Bouguer corrections for an area near the Island of Mauritius in the Indian Ocean are computed and the effects of sphericity and three‐dimensionality are calculated.The gravitational attraction of two‐dimensional bodies can be computed in a very similar manner. The attraction of the Puerto Rico Trench model is computed and the results are compared with other methods. The effects of sphericity and assumptions involved in extending the models to infinity are discussed.