The equation for the subject title is presented in nondimensional form. The approximation consists of considering a frustum of a vertical cone in which the radii are small relative to the depth to its top. The dependent variable has been taken as being the ratio of the residual gravity (as defined in a previous publication by the author) to the maximum residual gravity. The independent variable was chosen as the ratio of the lateral distance (from the center line of the frustum to a given station) to the depth to the top of the frustum. The two parameters were chosen as being (a) The ratio of depth to the bottom of the frustum to that to its top, (b) The ratio of the bottom radius to that of the top radius. It is then shown that, for special values of the parameters, the equation gives the lateral variation of residual gravity due to cylinders, upright cones, and inverted cones as special cases. Tables of the principal functions, which occur in the equation, are given over practical ranges of values. Graphs of the equation are given. They cover the practical range for each of the variables and each of the parameters. Application of the equation is made to two Gulf Coast salt domes whose dimensions are rather well known from previous drilling. Graphs, showing the degree of correlation, are given. The conclusion is drawn that, despite the approximation involved in the derivation of the equation, and despite the departure of the ratio of the dimensions of the salt domes from that assumed, the correlation with the actual gravity values for two deep salt domes is remarkably close.
An investigation of the Utility of Gulf Coast Salt Domes for the storage or disposal of radioactive wastes
