Rapid Computation of Gravitational Attraction of Three‐dimensional Bodies of Arbitrary Shape

Abstract

An expression is derived for the gravity anomaly at an external point caused by a horizontal lamina with the boundary of an irregular polygon. This expression is put in a form suitable for computation by a high speed digital computer. By making the number of sides of the polygon sufficiently large, any irregular outline can be closely approximated. Any three dimensional body can be represented by contours. By replacing each contour by a polygonal lamina, the anomaly caused by it can be obtained at any external point. By a system of interpolation between contours combined with a numerical integration the gravity anomaly caused by the three‐dimensional body can be calculated to a high degree of precision. This method may also be used for rapidly computing terrain corrections on a flat earth. By making a small modification it can further be adopted for computing the terrain correction as well as local isostatic compensation on the Airy system up to the external radius of Hayford zone O on a spherical earth. The expression for the anomaly caused by a horizontal polygonal lamina is also obtained for the special case when the sides of the polygon are alternately parallel to the x- and y-axes, that is, the polygonal lamina can be divided into a number of rectangular laminae. A chart is provided for the hand computation of the gravity anomaly in this case.

Magnetic Anomalies Caused by Two-Dimensional Structure: Their Computation by Digital Computers and Their Interpretation

“…Henderson and Zietz (1957) simplify the computation of a total intensity anomaly by projecting a map of a given body in the direction of the earth's field and using a modified Gassmann process for the integration. Talwani and Ewing (1960) calculate the anomaly by dividing the body into parallel and polygonal laminae, similar to the treatment in this report. Their method is put in a form which can be used for digital computers.…”

Geophysical study of the Taharoa ironsand deposit, west coast, North Island, New Zealand

“…Three-dimensional (3-d) modelling was undertaken for the central area of the deposit between Wainui and Mitiwai Streams, where surface and subsurface control was good. The Quaternary sands were modelled using a horizontal, polygonal laminae method modified from Talwani & Ewing (1960). Results of 3-d modelling are also included in Fig.…”

The gravity field and plate boundaries in Venezuela

“…A polygon method (Talwani and Ewing, 1960) for the calculation of gravity due to a two dimensional structure was used in the interpretation of the gravity data. The structure along a profile is represented in two dimensions by a set of polygons each of constant density.…”