Relative Determination of the Density of Surface Rocks and the Mean Density of the Earth From Vertical Gravity Measurements*

Abstract

The 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, Us 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 (I~ and (r 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 grJcm3. 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 u 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 easrth computed from the average density of the rock samples, was very close to the accepted standard value of 5.52 gr./cms. 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 fol!owed a line parallel to a fault, the other a line crossing this fault. The results differed appreciably from the standard value of (I llz, 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.

Estimation of Bouguer correction density based on underground and surface gravity measurements and precise modelling of topographic effects – two case studies from Slovakia

“…There is a reason why we could consider the density determination by underground gravity measurements as superior to other methods. As Hammer (1950) and Domzalski (1955) mentioned, the average (integrated) bulk density of the rocks is exactly what we need in gravity prospecting. In addition, such density can generally differ from the densities obtained from the measurements on rock samples.…”

“…The gravity difference between a station at the surface and a vertically offset underground station depends on the mean density of the Earth, as well as on the density of the rock layer between the stations (e.g. Domzalski, 1955). Knowing one of these densities the other one can be determined, while the determination of the average rock layer density is generally more reliable.…”

The comparison of different methods of determining the rock density from gravity data

“…If there are more underground points along the local vertical, the commonly used term for the output density estimates is the interval density between the respective underground measurement points (e.g., Domzalski, 1955;Madej, 2017). On the other hand, if there are only two measuring points along vertical, namely the underground one and the surface one, Zahorec and Papčo (2018) use exclusively the term correction density.…”

Mass properties of sedimentary rocks and gravimetric effects of petroleum and natural-gas reservoirs

“…In that year, Airy (1856) first attempted to determine the mean density of the earth by measuring with a pendulum the vertical gradient of gravity between the top and bottom of a vertical shaft sunk through sedimentary rocks, the average density of which was estimated from laboratory measurements of bulk density of hand samples. Although there have been subsequent attempts to repeat Airy's experiment (Miller and Innes, 1953;Domzalski, 1955) most mine shaft and borehole gravimeter measurements have had an op· posiite aim: to determine, from measurements of the vertical gradient of gravity underground, the densities of the rocks surrounding the shaft or borehole. The author (McCulloh, 1965) has recently reviewed most of the papers reporting the results of gravimetric de· terminations of rock density in situ in mine shafts, tunnels, quarries, and borehdles in North America, western Europe, and European Russia, as well as the literature describing experimental borehole gravime· ters that actually have been constructed and tested.…”