Tidally induced Sagnac signal in a ring laser

The Earth rotation vector is an integral dynamical quantity of the Earth system, with Earth rotation variations depending on the overall dynamics of the Earth system at all time scales. New observations of Earth rotation variations with a precision better than 10(-9) of the Earth rotation would contribute to the understanding of many geophysical phenomena. High precision short-term observations of the projection of the Earth rotation vector Omega(E) on the area vector A of a ring laser are now possible. Tidally induced Sagnac effects are due to changes in the ring geometry (areal strain and perimeter variations), changes in the normal vector of the ring laser plane (tilt), and the vorticity of the Earth's tidal deformations. Here we estimate the latitude-dependent effect of the Earth's body tide deformations due to vorticity and tilt. At mid-latitudes, the vorticity delta Omega is of the order 8.10(-8)Omega(E), but because it is in the local horizontal plane, it is not detectable by a horizontal ring. The Sagnac effect due to tidal tilt for a horizontal ring at mid-latitudes is of the order of 4.10(-8) of the Earth rotation effect. Thus, the tidal signal is of an order of magnitude where it may be used for validation of existing and future ring lasers.