RELATIVE DETERMINATION OF THE DENSITY OF SURFACE ROCKS AND THE MEAN DENSITY OF THE EARTH FROM VERTICAL GRAVITY MEASUREMENTS*

Abstract

AbstractThe gravity difference between two stations, one at the surface and the other underground vertically below the former and at a given distance from it, depends on the mean density of the earth, σm as well as on the density of the layer of rock contained between the two stations. When one of these densities is known, the other can be computed from this gravity difference. The reliability of this determination depends on the relative accuracies with which σm and σ can be obtained.These accuracies are discussed in the paper. The mean density of. the earth has been determined with an accuracy of approximately 0.01 gr/cm3. The determination of the density of a layer of rock depends on density determinations of rock samples which are not representative of the layer as a whole. Thus the accuracy of the value of σ based on a number of sample determinations will depend on many factors, including the method of averaging the density values obtained from the samples and the degree of uniformity in the geology.To investigate the problem discussed above, three sets of gravity measurements were made under differing conditions. In each instance a number of pairs of stations vertically above each other were occupied on the surface and underground. The results computed from the data on each pair of stations in a set of measurements were considered as repeated measurements of the same quantity, and the most probable value was calculated.The results demonstrated that the accuracy varied with the conditions prevailing in the area where the observations were made. In Godstone Quarries the dip of the strata was negligible, the rocks fairly uniform and structural conditions undisturbed. Consequently, although the rock layer between the surface and underground stations was only of the order of a hundred feet, the mean density of the earth computed from the average density of the rock samples, was very close to the accepted standard value of 5.52 gr./cm3. This agreement, however, was easily upset when only one random sample density was assumed as representative of a given formation.In a different locality in Cumberland the observations were made in a mine and on the surface. The rock layer between the surface and the underground stations was approximately a thousand feet thick. One set of measurements followed a line parallel to a fault, the other a line crossing this fault. The results differed appreciably from the standard value of σm, particularly in the latter case.It is concluded that the gravity difference between a surface and an underground station can be used satisfactorily to determine the average density of a rock layer in situ and en bloc, using the standard value for the mean Earth density.