Some Theoretical Considerations in the Measurement of Gravity at Sea

Abstract

summary The theory of operation of spring gravity meters on a stabilized platform in the presence of horizontal and vertical accelerations is considered in the first section of this paper. It is shown that levelling errors with the same period as the horizontal accelerations are very important. The amplitude of such levelling errors should not exceed about 8 seconds of arc when the amplitude of the horizontal accelerations is 5oooomgal. A second effect, which is present even on a perfectly stabilized platform, has been named the “cross-coupling” effect. It is produced by coupling between the vertical and horizontal accelerations and may, for a typical gravity meter, cause an error in excess of 100mgal when the horizontal and vertical accelerations both have amplitudes of 50000 mgal. The second part of the paper is devoted to a discussion of a gravity meter free to swing in gimbals. An expression for the second-order correction is derived taking into account free and forced oscillations of the gimbal system. This expression takes an especially simple form ½gθ2 (θ is the deflection of the gimbal system from the true vertical) when the gravity sensing element is positioned at the correct distance below the gimbal axis.