A LINE‐INTEGRAL METHOD OF COMPUTING THE GRAVIMETRIC EFFECTS OF TWO‐DIMENSIONAL MASSES

Abstract

Many computing schemes have been devised for determining the gravity anomalies produced by two‐dimensional masses. Most of these are based upon the evaluation of an areal integral and require specially constructed templates or tables. In the present paper it is shown that the gravity anomaly Δg at the origin of coordinates, produced by a two‐dimensional mass of constant density contrast Δρ, may be obtained quite simply by means of either of the line integrals [Formula: see text] where z is the vertical coordinate, and θ the polar coordinate expressed in radians of a point on the periphery of the mass in a plane normal to its axis and passing through the origin. The line integrals are evaluated around the periphery of the mass and are of opposite sign if taken in the same direction of traverse, or are of the same sign if taken in opposite directions. For use of these integrals no special equipment is required other than a simple template consisting of radial lines, θ=const., and horizontal lines, z=const., which can be constructed in a few minutes with protractor and scale. This can be constructed either for 1:1 or for an exaggerated vertical‐to‐horizontal scale.