Earth's Rotation Vector Research Articles

Effects of temperature variations in high-sensitivity Sagnac gyroscope

GINGERINO is one of the most sensitive Sagnac laser-gyroscopes based on an heterolithic mechanical structure. It is a prototype for GINGER, the laser gyroscopes array proposed to reconstruct the Earth rotation vector and in this way to measure General Relativity effects. Many factors affect the final sensitivity of laser gyroscopes, in particular, when they are used in long-term measurements, slow varying environmental parameters come into play. To understand the role of different terms allows to design more effective mechanical as well as optical layouts, while a proper model of the dynamics affecting long-term (low frequency) signals would increase the effectiveness of the data analysis for improving the overall sensitivity. In this contribution, we focus our concerns on the effects of room temperature and pressure aiming at further improving mechanical design and long-term stability of the apparatus. Our data are compatible with a local orientation changes of the Gran Sasso site below mu rad as predicted by geodetic models. This value is consistent with the requirements for GINGER and the installation of an high-sensitivity Sagnac gyroscope oriented at the maximum signal, i.e. along the Earth rotation axes.

Reconstruction of the Instantaneous Earth Rotation Vector with Sub-Arcsecond Resolution Using a Large Scale Ring Laser Array.

Absolute rotation rate sensing with extreme sensitivity requires a combination of several large scale gyroscopes in order to obtain the full vector of rotation. We report on the construction and operation of a four-component, tetrahedral laser gyroscope array as large as a five story building and situated in a near surface, underground laboratory. It is demonstrated that reconstruction of the full Earth rotation vector can be achieved with sub-arcsecond resolution over more than six weeks.

Coarse leveling of gyro-free INS

For a stationary system, coarse alignment is used to initially determine the orientation of the INS by utilizing the Earth gravity and rotation vectors. Yet, a gyro-free INS has only accelerometers and hence cannot measure the Earth rotation vector and thus cannot deduce its yaw angle. In this paper, we formulate the coarse-alignment procedure and derive error characteristics for a gyro-free system. In addition, a comparison between different configurations of accelerometers is being conducted.

Cross-equatorial channel flow with zero potential vorticity under the complete Coriolis force

We investigate the cross-equatorial flow of deep ocean currents through a channel along the sea floor using the 1½-layer or equivalent-barotropic shallow water equations. We restrict our attention to flows with zero potential vorticity, motivated by measurements of the deep Atlantic ocean, and focus on the role of the so-called non-traditional components of the Coriolis force due to the locally horizontal component of the Earth's rotation vector. These components are typically neglected in theoretical studies of ocean dynamics. We first obtain steady asymptotic solutions in a straight-walled channel by assuming that the channel half-length is much larger than the intrinsic lengthscale, the equatorial Rossby deformation radius. The leading-order solution describes a current that switches from the western to the eastern side of the channel as it crosses from the southern to the northern hemisphere. Including the non-traditional component of the Coriolis force substantially increases the cross-equatorial transport as long as the flow is everywhere northwards, but substantially decreases the transport if part of the flow retroflects and returns to the southern hemisphere. We compare our steady asymptotic solutions with time-dependent numerical solutions of the non-traditional shallow water equations. We impose the a priori assumption of zero potential vorticity by writing the fluid's absolute angular momentum as the gradient of a scalar potential. The time-average of our numerical solutions converges to our steady asymptotic solutions in the limit of large channel length, with an error of only around 1% even when our asymptotic parameter e is equal to 1. However, our solutions diverge when the layer depth is sufficiently small that portions of the flow become super-critical. The resulting formation of steady shocks prevents the time-dependent solution from approaching the asymptotic solution.

Measuring gravitomagnetic effects by a multi-ring-laser gyroscope

We propose an under-ground experiment to detect the general relativistic effects due to the curvature of space-time around the Earth (de Sitter effect) and to rotation of the planet (dragging of the inertial frames or Lense-Thirring effect). It is based on the comparison between the IERS value of the Earth rotation vector and corresponding measurements obtained by a tri-axial laser detector of rotation. The proposed detector consists of six large ring-lasers arranged along three orthogonal axes. In about two years of data taking, the 1% sensitivity required for the measurement of the Lense-Thirring drag can be reached with square rings of 6 $m$ side, assuming a shot noise limited sensitivity ($ 20 prad/s/\sqrt{Hz}$). The multi-gyros system, composed of rings whose planes are perpendicular to one or the other of three orthogonal axes, can be built in several ways. Here, we consider cubic and octahedron structures. The symmetries of the proposed configurations provide mathematical relations that can be used to study the stability of the scale factors, the relative orientations or the ring-laser planes, very important to get rid of systematics in long-term measurements, which are required in order to determine the relativistic effects.

The influence of transverse motion within an atomic gravimeter

Limits on the long-term stability and accuracy of a second generation cold atom gravimeter are investigated. We demonstrate a measurement protocol based on four interleaved measurement configurations, which allows rejection of most of the systematic effects, but not those related to Coriolis acceleration and wave-front distortions. Both are related to the transverse motion of the atomic cloud. Carrying out measurements with opposite orientations with respect to the Earth's rotation vector direction allows us to separate the effects and correct for the Coriolis shift. Finally, measurements at different atomic temperatures are presented and analyzed. In particular, we show the difficulty of extrapolating these measurements to zero temperature, which is required in order to correct for the bias due to wave-front distortions.

Seasonal variations in sea level induced by continental water mass: First results from GRACE

Variations in the Earth's water cycle are commonly quantified by their effect on global mean sea?level. However, the interaction between passive adjustment of the ocean to changes in gravitational attraction due to mass redistribution, the related deformation of the solid Earth and disturbances in the Earth's rotation vector will yield a distribution that is more complicated than a uniform rise or fall of the ocean's surface. In this study, we present the first estimates of seasonal changes in passive sea?level (which we define as the height difference between the sea surface at rest and ocean floor, excluding steric and dynamical effects) based on direct observations of surface mass redistribution, made by the Gravity Recovery and Climate Experiment (GRACE) between 2003 and 2010. We show that this “selfgravitation?effect” causes seasonal variations of the sea?level of up to 1 cm – comparable to the amplitude of the long?period tides – and that inclusion in numerical ocean models results in a better agreement between observed and modelled ocean bottom pressure variations, particularly in coastal zones.

Internal-wave reflection from uniform slopes: higher harmonics and Coriolis effects

Abstract. Weakly nonlinear reflection of internal waves from uniform slopes produces higher harmonics and mean fields; the expressions are here derived for constant stratification and with Coriolis effects fully included, i.e. the horizontal component of the earth rotation vector (referred to as "non-traditional'') is taken into account. Uniformity in one of the horizontal directions is assumed. It is shown that solutions can be as readily derived with as without ; hence there is no need to make the so-called Traditional Approximation. Examples of reflecting internal-wave beams are presented for super-inertial, inertial and sub-inertial frequencies. The problem of resonant and non-resonant forcing of the second harmonic is studied for single plane waves; unlike under the Traditional Approximation, the problem of reflection from a horizontal bottom no longer forms a singular case. Non-traditional effects are favourable to resonant forcing at near-tidal rather than near-inertial frequencies, and generally increase the intensity of the second harmonic. Strong stratification tends to suppress non-traditional effects, but a near-total suppression is only attained for high values of stratification that are characteristic of the seasonal thermocline; in most parts of the ocean, non-traditional effects can therefore be expected to be important.

Non‐traditional reflection of internal waves from a sloping bottom, and the likelihood of critical reflection

The problem of internal inertio‐gravity wave reflection from an arbitrarily orientated uniform slope is solved in a linear setting and with Coriolis effects fully included; that is, the horizontal component () of the Earth rotation vector is taken into account. A new criterion is derived for critical reflection. The presence of creates a specific anisotropy: the criterion depends on the orientation of the bottom slope in the horizontal geographical plane, while it does not depend on the horizontal orientation of the incident wave. Using an empirical‐based bottom‐slope distribution, the probability of critical reflection is calculated for diurnal and semi‐diurnal internal‐tide bands, for a range of latitudes and for various values of stratification. The probability is largest near the inertial latitudes, i.e., when the internal tides are near‐inertial. It is explained how the inclusion of gives significant changes in the probability near these latitudes, especially for weak stratification.

Effects of zonal deformations and the Earth's rotation rate variations on precession-nutation

Because of their importance in the accurate modeling of the Earth's orientation in space, some non-negligible predictable effects on precession-nutation are investigated. This paper considers the coupling effects between the axial and the equatorial components of the Earth's rotation vector in the dynamical equations, and the effects of the second order lunisolar torque due to the Earth's zonal deformations. Firstly, the coupling effects are shown to contribute for less than 0.1 μ as and are therefore negligible. Secondly, we demonstrate that the 0.7 mas contribution of the rotation rate variations due to zonal tides to the nutation in obliquity deduced by Bretagnon et al. ([CITE], Proc. IAU Coll., 180, 230; [CITE], Celest. Mech. Dyn. Astr., 80, 177) is an artefact which comes from an incomplete way of taking into account the effect of the rotation rate variations. The net contribution is shown to be negligibly small. Thirdly, for an Earth model with an elastic mantle and decoupled liquid core, the contribution of the second-order lunisolar torque due to the Earth's zonal deformations is shown to be 207.9 μ as and –9.7 μ as on the 18.6-year nutation respectively in longitude and in obliquity, and a correction of –4925.9 μ as/century on the precession in longitude.

INFLUENCE OF THE ATMOSPHERE ON EARTH ROTATION: WHAT NEW CAN BE LEARNED FROM THE RECENT ATMOSPHERIC ANGULAR MOMENTUM ESTIMATES?

The interaction between the atmosphere and the underlying solid mantle is one of the most important sources of changes in all three components of the Earth's rotation vector on different time scales. In this paper the NCEP/NCAR reanalysis time series of four times daily atmospheric effective angular momentum (EAM) estimates is used to investigate some selected aspects of the atmospheric influence on Earth rotation. Emphasis is placed on the controversial features which were difficult or impossible to study using the operational EAM data, such as excitation of the free oscillations in polar motion, the Chandler wobble (CW) and the free core nutation (FCN), or the roles of diurnal and semidiurnal atmospheric tides and atmospheric normal modes in the rotational dynamics of the Earth.

Sea‐level change and true polar wander during the Late Cretaceous

We demonstrate that rapid changes in the Earth's rotation vector can drive relative sea‐level (RSL) variations in excess of 100 m in as little as 1 m.y. Stratigraphic constraints on sea‐level change can thus be used as an independent test of true polar wander (TPW) events proposed on the basis of paleomagnetic evidence. Recent estimates of Late Cretaceous TPW include a period of rapid motion, however a corresponding period of large and rapid sea‐level change is not consistently evident in our preliminary examination of the geological record. This suggests that the magnitude of Late Cretaceous TPW may have been overestimated, although a definitive conclusion requires a comprehensive study of high‐resolution Late Cretaceous sea‐level records. (Index Terms: 1239, 1527, 4556, 8159).

Tides and Earth Rotation

A short general explanation of tidal forces and tidal effects is given. The influences of Earth tides and ocean tides on the Earth's rotation vector are presented. Today, the theoretical models for periodic variations in the Earth's rotation and in polar motion can be compared with precise measurements done by modern space techniques. Secular changes of the Earth's rotation due to interactions within the Earth-Moon-system are also discussed.

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 ΩE 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 δΩ is of the order 8 · 10−8ΩE, 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.

Numerical studies of open ocean deep convection

Open ocean deep convection is examined with a nonhydrostatic model based on primitive equations. Strong cooling on the surface of the ocean enforces vertical motion which takes place in the narrow regions of convective cells. Different equations of state are considered, and it is shown that a linear equation of state with a constant thermal expansion coefficient cannot represent the buoyancy field and fluxes properly. The inclusion of thermobaric effects leads to additional vertical acceleration in the whole water column. The parametrization of the convective fluxes by a convective adjustment algorithm represents the horizontal mean temperature quite well but suppresses the entire vertical mass transport within the convective cells. This mass transport may be important for the transport of other tracers. Investigation of an energy cycle of the convective motion sorts out sources and sinks and reveals the conversion between different forms of energy during convective events. Both the vertical and the horizontal component of the Earth rotation vector contribute to the time mean energy balance with the same order of magnitude, but the instantaneous amplitudes of the distinct terms may differ substantially. A sensitivity study with respect to eddy and thermal diffusion coefficients distinguishes two regions; at high values of the diffusivities the velocities and tracer distributions show that a strong dependence on this values occurs, while for sufficiently small coefficients, only a weak dependence is observed.

Correction and update to ‘The earth's C21and S21gravity coefficients and the rotation of the core’

Wahr (1987) used satellite constraints on C21 and S21 (the spherical harmonic coefficients of the earth's external gravitational potential) to infer certain properties of the core and core/mantle boundary. It is shown here, contrary to the claim by Wahr, that it is not possible to use C21 and S21 to placed bounds on the core's products of inertia. As a result, Wahr's constraints on the l = 2, m = 1 components of the core/mantle boundary topography and on the angular orientation of the inner core with respect to the earth's rotation vector are not justified. On the other hand, Wahr's conclusions about the time-averaged torque between the core and mantle and the resulting implications for the l = 2, m = 1 components of fluid pressure at the top of the core can be strengthened. Wahr's conclusions about the mean rotational flow in the core are unaltered.

Anomalous curvature of equipotential surfaces due to variations in the Earth's rotation

The anomalies of the Gaussian curvature of geopotential equipotential surfaces due to variations in the Earth's rotation vector have been derived theoretically.

Comparison of Earth rotation as inferred from radio interferometric, laser ranging and astrometric observations

New techniques are being developed to improve the spatial and temporal resolutions achievable in measurements of the rotation vector of the Earth. Such improvements are expected to expose fine details of this rotation and to aid in understanding their physical causes. Although not yet fully developed, two of these techniques are now in routine use: radio interferometry and laser ranging. In the former technique, antennas up to thousands of kilometres apart are used to observe compact extragalactic radio sources. The differences in arrival time of the signals propagating from each source to the antennas, measured by the method of very-long-baseline interferometry (VLBI), are sensitive to variations in each of the components of the Earth's rotation vector. In the latter technique, lasers are used to measure the distance (range) to artificial Earth satellites (satellite laser ranging, SLR) and to optical retroreflectors on the Moon (lunar laser ranging, LLR). To assess the accuracy being achieved in the measurement of Earth rotation it is useful to compare results obtained with these different techniques. National programmes and international cooperation, exemplified by the International Astronomical Union/International Union of Geodesy and Geophysics project MERIT1,2, are encouraging the collection of data suitable for accurate intercomparisons. Here we compare results for a 400-day period from late September 1980 to December 1981, for which data from all three types of measurements are available. We also compare corresponding results from classical astrometric observations which demonstrate the degree of improvement in accuracy afforded by the new techniques.

Secular‐invariant relationships among internal geomagnetic field coefficients

Some features of the secular variation of the geomagnetic field are examined. Contours encircling constant magnetic flux (third adiabatic invariant), corresponding to a “shell” of field lines in secular motion, reveal a general westward drift that is longitude and latitude dependent (with minima in the north Pacific and south Atlantic areas). Some invariant relationships appear among the field coefficients in the tilted, centered dipole (geomagnetic) coordinate system. The quadrupole phases ϕ2¹ and ϕ2², with a westward drift of 0.38 degrees per year, seem to bear a constant phase difference of 45° physically this corresponds to a n=2, m=1 current system that is tilted with respect to the geomagnetic equator. The octupole phases, particularly ϕ3², appear to be locked to the earth's rotation vector (no drift at all in the tilted dipole system). In our present epoch, the energy contained in the quadrupole and octupole field outside the core is increasing at a rate roughly equal to that of decrease of main dipole field energy. The hexadecapole terms show a mixture of westward and eastward drifts. On the average, the total hexadecapole current system does not reveal any notable drift in the original (geographic) frame of reference.

Sampling and Quantization Errors in a Digitally Mechanized Inertial Navigator

This paper investigates the effects of sampling and quantization in a digitally mechanized inertial navigator. A constant altitude, meridian plane, pure Schuler tuned inertial navigator model on a nonrotating earth is used for analysis. Insofar as sampling and quantization effects are concerned, nothing significant is lost by this restriction since the cross-coupling effects are small, and the earth rotation vector components on the platform axes are slowly varying. On the other hand, the analysis is greatly simplified by these restrictions. Time and frequency domain analysis of the sampled-data system is presented and the effects of quantization present at the digital computer input and output are evaluated. It is concluded that root-mean-square position errors can be held to a few thousand feet for a two hour mission, using a sampling rate of the order of one second and a gyro impulse torquer quantization level of about one arc second.