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APPROXIMATION OF THE GRAVITATIONAL ATTRACTION OF GEOLOGICAL BODIES*

1971; Wiley; Volume: 19; Issue: 2 Linguagem: Inglês

10.1111/j.1365-2478.1971.tb00594.x

1365-2478

Radu Botezatu, M. Visarion, F. SCURTU, G. CUCU,

Reservoir Engineering and Simulation Methods

A bstract The gravitational attraction produced by a geological body of irregular shape can be easily determined by dividing it into cubes of small size. The exact expression of the effect of a cube is very complicated, but it can be calculated by using an electronic computer. 4851 values of the gravitational attraction were determined for different positions of a cube with the side of 2 l and the center in M ( x 0 , y 0 , z 0 ), for x 0 ∈[0;20], y 0 ∈[0;20] and z 0 ∈[0;10]. Using these values, templates in double logarithmic representation were drawn, with x 0 and z 0 as parameters and y 0 as abscissa, and with x 0 and y 0 as parameters and z 0 in abscissa; this double set of templates permits a good interpolation for all cubes in the considered domain of M. The use of templates was tested to approximate the effect produced by a theoretical model of spherical shape and in a real case of a three‐dimensional salt body of known shape based on a large number of boreholes. In both cases very good results were obtained.