Simultaneous determination of terrain correction and local average topographic density

Abstract

Nettleton’s method is based on the elevation dependence of the surface free-air gravity anomalies and widely used to obtain an optimal average density value by applying e.g. L2 norm model inversion. Its accuracy, however, strongly depends on how efficiently the regional trends and very local (terrain) effects are removed from the gravity anomalies processed. If the geometry of the topography is fixed then the terrain correction term at the evaluation point P is a linear function of the unknown average topographical density. Therefore it can also be included in the equation system to be solved by inversion and an estimation of the density can be obtained in one step, without iteration. The results of this simple refinement of Nettleton’s method as well as the distorting effect of the regional trend are demonstrated by a local example. It reviews the gravity survey of a loess bluff and its surrounding on the bank of the river Danube. The derived density values increase from $ρ_t$=1163±543 kg/m3 to $ρ_t$=1764±113 kg/m3 as the gravity anomalies are gradually reduced by regional and local (terrain) effects during data processing. The lab determination of surface loess samples from the area having only 3.5% water content gives 1610±100 kg/m3