Off-level corrections for gravity meters

Gravity meters must be aligned with the local gravity at any location on the surface of the earth in order to measure the full amplitude of the gravity vector. The gravitational force on the sensitive component of the gravity meter decreases by the cosine of the angle between the measurement axis and the local gravity vector. Most gravity meters incorporate two horizontal orthogonal levels to orient the gravity meter for a maximum gravity reading. In order to calculate a gravity correction it is often necessary to estimate the overall angular deviation between the gravity meter and the local gravity vector using two measured horizontal tilt meters. Typically this is done assuming that the two horizontal angles are independent and that the product of the cosines of the horizontal tilts is equivalent to the cosine of the overall deviation. These approximations, however, break down at large angles. This paper derives analytic formulae to transform angles measured by two orthogonal tilt meters into the vertical deviation of the third orthogonal axis. The equations can be used to calibrate the tilt sensors attached to the gravity meter or provide a correction for a gravity meter used in an off-of-level condition.