A GENERALIZED FORM OF NETTLETON'S DENSITY DETERMINATION*

Abstract

ABSTRACTThe formula for the Bouguer anomaly contains the density of the masses above the datum plane. If we use a wrong value for the density we obtain on the Bouguer map additional anomalies which coincide with the topographic features.If we do not know the Bouguer density we can compute several Bouguer maps based on different arbitrary densities. Then we select that map which shows the least correlation with the topography and obtain in this way a reasonable value for the density. This method has been found by Nettleton.Several authors have formulated this process mathematically and have elaborated numerical methods. This paper will present such a method. It differs from the former methods by the following: A general formula for the Bouguer density is presented, using a non‐specified linear operator. By choosing special definition for this operator, we can obtain the formulae of several of the known methods. It is shown that the determination of the density by “Nettleton Profiles” gives less reliable results than the statistical investigation of the whole area covered by the gravity survey. The known methods do not consider the variations of the vertical gradient. It is shown that in areas with a regional gravity anomaly or an extended topographic feature the known methods yield poor results. It is shown that the vertical gradient of gravity used as operator gives a most exact and simple formula. It is shown how the electronic computer—after reading the Bouguer values based on an arbitrary initial density—can compute the residuals, derivatives etc., which are based on the corrected Bouguer density.