The second-order errors of sea-surface gravity measurements

Abstract

An analysis of the effect of a continuous acceleration spectrum on the performance of a sea gravimeter is made. When a continuous rather than a discrete spectrum is assumed, second-order errors due to acceleration product terms become more complex. In particular, the second-order correction which must be applied to the reading of a gimbal-mounted gravimeter is disturbed from the constant value previously found when sinusoidal ship motion was assumed. This disturbance is in the form of very-long-period ‘noise’ which has, in a typical case, a rms value of 1/7 of the constant value. It is shown also that very-long-period ‘noise’ is present in the reading of a vertically stabilized gravimeter owing to a cross-coupling effect and that it occurs whether or not the beam displacement and the horizontal accelerations are correlated. Finally the possibility of errors being caused by nonlinear ship response is discussed. The purpose of the paper is to identify and describe from a statistical standpoint some of the factors determining the reliability of gravity measurements made at sea.