Angular Velocity Of Earth Research Articles

GINGER data analysis for seismology

Since several years, the ring laser gyroscope GINGERINO is operative inside the underground Gran Sasso laboratory. It monitors on a continuous basis the local Earth angular velocity in the horizontal plane. It provides unique information for geophysics in general, being one of the few top sensitivity angular velocity sensors. The present paper describes the analysis procedure developed for the data uploaded on the EIDA data base, suitable for seismological investigation in the frequency window 100 s up to 100 Hz. Typical errors and data quality will be discussed. This work is part of the data analysis tools under development for the GINGER project, a ring laser array, part of the UGSS (Underground Gran Sasso Seismology) multi components array at present in construction inside the Gran Sasso laboratory.

Effects of Coriolis Force on the Nonlinear Interactions of Acoustic-Gravity Waves in the Atmosphere

The nonlinear theory of acoustic-gravity waves ( AGWs ) in the atmosphere is revisited with the effects of the Coriolis force. Previous theory in the literature [Phys. Scr . 90 (2015) 055001] is advanced. Starting from a set of fluid equations modified by the Coriolis force, a general linear dispersion relation is derived which manifests the coupling of the high-frequency acoustic-gravity waves ( AGWs ) and the low-frequency inertial gravity waves ( IGWs ). The frequency of IGWs is enhanced by the Earth's angular velocity. The latter also significantly modifies the nonlinear coupling of AGWs and IGWs whose evolutions are described by the Zakharov approach as well as the Wigner- Moyal formalism. The consequences of the two equivalent evolution equations modified by the Coriolis force are briefly discussed.

High Precision Fiber-Optic Gyroscope Resolution Test Method Based on Low Precision Turntable

Aiming at the inability of low precision ordinary turntable to effectively measure the resolution of the high-precision fiber-optic gyroscope (FOG), this paper proposes a method for a high-precision FOG resolution test based on a low-performance turntable with the earth's angular velocity as the input value. Taking a two-axis turntable with 1 arc-minute angular precision as an example, the Two-Degrees-Of-Freedom (2-DOF) theoretical angle range is obtained, through stationary gyro biaxial angular position error incremental output analysis. The method can be used for high-precision FOG including, 0.001 deg/h, 0.0001 deg/h, 0.00001 deg/h (three typical accuracies) resolution measurements. The detailed test steps are presented. Simulation results show that traditional test methods fail under the same working conditions, while the proposed method can effectively measure the high-resolution gyro resolution effective coverage within the theoretical angle range of the corresponding two-axis turntable. Experimental results demonstrate that the two-axis turntable based on with 1 arc-minute angular precision can effectively perform a high-precision FOG resolution of 0.005 deg/h.

Kalman Filter Cascade for Attitude Estimation on Rotating Earth

This article presents a discrete-time attitude estimation solution based on a cascade of two linear time-varying Kalman filters (KFs). Under mild assumptions, the cascade's first KF resorts to body-fixed measurements of angular velocity and of a constant inertial vector to yield an estimate of Earth's angular velocity. The latter, in addition to all previous measurements, is fed to the second KF to obtain an estimate of the rotation matrix. Although topological constructions are lifted, a last-step projection operator is employed that maps the final rotation matrix estimate onto $SO(3)$ . Briefly, two linear time-varying systems are designed, with no linearizations whatsoever, that are shown to be uniformly completely observable, thus rendering the overall solution globally exponentially stable. Simulation results are presented that allow to assess the performance of the cascaded KF duo. A set of experimental results is also presented that validates the efficiency of the proposed solution and deems it a suitable attitude estimation choice for applications where only one body-vector measurement is available.

Attitude estimation using high-grade gyroscopes

This paper addresses the problem of attitude estimation using the angular velocity of Earth as a reference vector. A nonlinear observer is proposed that evolves on the special orthogonal group and is aided by angular velocity readings containing implicit measurements of the Earth’s spin. Additionally, the observer resorts to body-fixed measurements of one constant inertial reference vector. The observer’s sole tuning parameter, shaped as a matrix gain, is computed from a time-varying Kalman filter strategically applied to a uniformly observable linear time-invariant system, which is obtained from the linearized rotation matrix error dynamics. The nonlinear observer is proved to be locally exponentially stable but, most noticeably, in spite of this local-based inception, a Monte Carlo simulation analysis demonstrates the good properties of the observer in terms of convergence rate, tuning capability, and large basin of attraction. Furthermore, extensive experimental results confirm the properties of the proposed technique and validate its usage in real world applications.

Indirect perturbation influence of planets on the variation of the instantaneous angular velocity of the rigid Earth in the lunar-solar gravitational field

The differential equation and its solution for indirect influence of the planetary perturbation on the variation of the rotational angular velocity of the rigid Earth in the lunar-solar gravitational field are obtained by using Euler’s dynamic equations. The theoretical results show that the angular velocity of the Earth varies with the periodic and mixed periodic variation under the lunar and solar gravitational field due to the planetary perturbation on the Earth orbit. The numerical results for the amplitudes of the periodic terms and the coefficient of the mixed periodic terms are presented.

The GINGER project and status of the GINGERino prototype at LNGS

GINGER (Gyroscopes IN GEneral Relativity) is a proposal for measuring in a ground-based laboratory the Lense-Thirring effect, known also as inertial frame dragging, that is predicted by General Relativity, and is induced by the rotation of a massive source. GINGER will consist in an array of at least three square ring lasers, mutually orthogonal, with about 6-10 m side, and located in a deep underground site, possibly the INFN - National Laboratories of Gran Sasso. The tri-axial design will provide a complete estimation of the laboratory frame angular velocity, to be compared with the Earths rotation estimate provided by IERS with respect the fixed stars frame. Large-size ring lasers have already reached a very high sensitivity, allowing for relevant geodetic measurements. The accuracy required for Lense-Thirring effect measurement is higher than 10-14 rad/s and therefore Earth angular velocity must be measured within one part in 10-9. A 3.6 m side, square ring laser, called GINGERino, has been recently installed inside the Gran Sasso underground laboratories in order to qualify the site for a future installation of GINGER. We discuss the current status of the experimental work, and in particular of the GINGERino prototype.

Earth's spin and volcanic eruptions: evidence for mutual cause‐and‐effect interactions?

AbstractThe angular velocity of Earth's rotation shows decadal oscillations due to the lunisolar gravitational torque, as well as inter‐ or intra‐annual changes arising from the angular momentum exchange between the atmosphere and the solid Earth. The energies involved in the Length of Day (LOD) variations may affect the crustal deformation rate and seismic energy release on a global scale. We found significant correlation between the occurrences of major volcanic eruptions and the LOD pattern since AD 1750. On a multiyear scale, eruption frequency worldwide increases with LOD changes. Moreover, the injection of sulphur gases into the atmosphere during major eruptions is accompanied by significant inter‐annual LOD variations. This provides evidence of complex mutual cause‐and‐effect interactions: stress changes induced by multiyear variations in Earth's spin may affect climactic volcanic activity; also, the atmosphere's dynamic response to volcanic plumes may result in global changes of wind circulation and climate, with consequent LOD variations.

Enhanced ring lasers: a new measurement tool for Earth sciences

We report the progress in the technology of fabrication of large ring lasers that has resulted in an increase in instrumental rotation sensitivity by as much as a factor of 3, to δΩ = 1.2 × 10-11 rad s-1 Hz-1/2, which makes the domain of changes in the angular velocity of Earth's rotation, ΔΩ/Ω ≈ 10-9, accessible to a local rotation sensor. New studies show that the largest contribution to the observed deviation in sensor performance with respect to the computed shot noise limit is caused by the micro-seismic background activity of the Earth. Our efforts have been concentrated on the improvement of sensor stability, including correction of drift effects, which are caused by the aging of the laser gas, fixing scale factor instabilities induced by atmospheric pressure variations, and minimising the temperature variations resulting from corresponding adiabatic expansion and compression of the local air around the instrument. To achieve this, we have recently introduced a pressure-stabilising vessel with dimensions slightly larger than the ring laser apparatus, such that it encloses the entire structure. By monitoring the optical frequency in the ring laser cavity continuously and stabilising the scale factor in a closed loop system with the pressure-stabilising vessel, it has become possible to extend the range of sensor stability from the short term (1 — 3 days) to well into the mid-term regime (>40 days), and possibly even well beyond that. Once a sufficiently long timeseries of the ring laser data has been recorded, we will be able to define the range of temporal stability in more detail. The extension of the regime of stability gives access to geophysical signals at frequencies substantially lower than previously observable with ring lasers.

Research on Independent Coarse Alignment of Aircraft Carriers SINS

Carrier-based Aircraft closely watched as the aircraft carrier weapons, storms and other factors affect the generated carrier swing to sway.This will enable the gyro measurement to the Earth's rotation angular velocity signal to noise ratio dropped significantly, giving the aircraft carrier's initialaligned to bring difficulties. To solve this problem, the Earth gravity acceleration in the inertial space the SINS independent coarse alignment, and gives the process of acceleration due to gravity points vector of analytic coarse alignment and fine alignment algorithm. Theoretical analysis and simulation results show that the moving base SINS alignment method can effectively solve the initial alignment of the aircraft carrier in the state of the ship mooring.

Lunar perturbations in variations of earth angular velocity and atmospheric pressure

The analysis of the contribution of lunar declination variations to the total variance of air pressure anomalies at meteorological stations of the global network is carried out on the basis of the data of daily observations. It is demonstrated that the changes in the declination of the Moon while moving around the Earth is accompanied by nonrandom variations of atmospheric pressure. Their manifestation depends significantly on the season and geographic latitude. The contribution of the lunar effect to the total variance of pressure anomalies is spatially inhomogeneous and amounts to 40% and more in the basic centers. The maximum effect is reached in the late spring or early summer in the corresponding hemisphere: in May and June in the Northern Hemisphere and in October and November in the Southern Hemisphere.

A laser gyroscope system to detect the gravito-magnetic effect on Earth

Ring lasers are inertial sensors for angular velocity based on the Sagnac effect. In recent years they have reached a very high sensitivity and accuracy; the best performing one, the ring Laser G in Wettzell (Germany), a square ring with 16 m perimeter, has reached a sensitivity of 12prad/s very close to the shot noise limit inferred from ring-down time measurements. On this basis it is expected that an array of six square ring lasers of 36 m perimeter, can perform a 1% accuracy test for the measurement of the Lense-Thirring frame dragging after 2 years of integration time. Essential for this measurement is the comparison between the Earth angular velocity and orientation in space measured with the ring array and compared to the measurement series maintained by the International Earth Rotation and Reference System Service (IERS), which measures Earth Rotation and pole position with respect to remote quasars. It has been shown that the accuracy of G in Wettzell is limited by the low frequency motion of the near surface laboratory, which is of the order of several prad/s, roughly 100 times larger than the Lense-Thirring contribution. For this reason the entire experiment should be placed in a quite underground laboratory, where these perturbations are reduced. The feasibility to properly place such a device inside the GranSasso INFN National Laboratory has been investigated.

Anticyclogenesis of surface pressure field in winter season, blocking, and variability of the Earth angular velocity

Analyzed are the anomalies of monthly mean values of surface pressure over Eurasia in winter seasons of 1901–2010. It is noted that the centers of large monthly positive pressure anomalies (16–24 hPa) are usually located within the 60°–70°N latitude zone. The Siberian high is well developed but the pressure anomalies in its center amount to 3–8 hPa only. The large monthly pressure anomalies at the isobaric surface of 500 hPa in the first natural synoptic area are mainly accompanied by the E-type of circulation (according to G.Ya. Vangengeim). The number of days with the western (W) type of circulation is extremely small and is practically absent when the anomalies in the center exceed 20 hPa (blocking process). The time periods of increase (decrease) in the annual number of days with W-circulation are well agreed with the periods of the Earth rotation acceleration (deceleration). The positive pressure anomalies were four or five times more frequent in the periods of the Earth angular velocity decrease: in 1933–1972 and after 2004.

Rossby–Khantadze electromagnetic planetary vortical motions in the ionospheric E-layer

AbstractIt is shown that in the earth's conductive ionospheric E-region, large-scale ultra low-frequency Rossby and Khantadze electromagnetic waves can propagate. Along with the prevalent effect of Hall conductivity for these waves, the latitudinal inhomogeneity of both the earth's angular velocity and the geomagnetic field becomes essential. Action of these effects leads to the coupled propagation of electromagnetic Rossby and Khantadze modes. Linear propagation properties of these waves are given in detail. It is shown that the waves lose the dispersing property for large values of wave numbers. Corresponding nonlinear solitary vortical structures are constructed. Conditions for such self-organization are given. It is shown that nonlinear large-scale vortices generate the stronger pulses of the geomagnetic field than the corresponding linear waves. Previous investigations are revised.

On the 60-year signal from the core

The decadal variation in the length of day and in the Earth's magnetic field is analyzed by empirical mode decomposition (EMD). The existence of a periodicity of about 60-years in the Earth's angular velocity has often been inferred and is confirmed here, with a new estimate of approximately 62 years. The existence of a similar periodicity in the geomagnetic field has been controversial. From the time series analyses presented here of the magnetic declination at 10 observatories, it is concluded that a geomagnetic periodicity of about 62 ± 3 years does exist. A similar analysis of the magnetic inclination at five observatories gives a period of 58 ± 5 years. The declination data from four observatories is found to correlate with the length of day signal, with a correlation coefficient of approximately 0.6.

Comments on “The Roles of the Horizontal Component of the Earth's Angular Velocity in Nonhydrostatic Linear Models”

Comments on “The Roles of the Horizontal Component of the Earth's Angular Velocity in Nonhydrostatic Linear Models”

COUPLED OSCILLATIONS IN THE EARTH-MOON SYSTEM AND GEOPHYSICAL PROCESSES

In the Earth-Moon system, oscillations of close frequencies can be transformed as a result of the degree of coupling. The observed extended period of the Chandler oscillations can be explained by coupling of the oscillations. The problem of amplitude and period variations of the main oscillations of the Earth poles is treated on the basis of parametric excitement. For the first instability region an equation is obtained to determine the amplitudes of possible steady-state solutions. The variation limits of Chandler period oscillations and the relation between amplitudes of a possible steady-state solution for two periodic polar motion components are computed. The possible influence of energy exchange in coupled Earth-Moon oscillations on excitement and self-excitement in geophysical processes is discussed. As an illustration the interaction between the Earth's angular velocity variations and variations in the Siberian anticyclone parameters are considered.

The Roles of the Horizontal Component of the Earth's Angular Velocity in Nonhydrostatic Linear Models

Abstract Roles of the horizontal component of the earth's rotation, which is neglected traditionally in atmospheric and oceanographic models, are studied through the normal mode analysis of a compressible and stratified model on a tangent plane in the domain that is periodic in the zonal and meridional directions but bounded at the top and bottom. As expected, there exist two distinct kinds of acoustic and buoyancy oscillations that are modified by the earth's rotation. When the cos(latitude) Coriolis terms are included, there exists another kind of wave oscillation whose frequencies are very close to the inertial frequency, 2Ω sin(latitude), where Ω is the earth's angular velocity. The objective of this article is to clarify the circumstance in which a distinct kind of wave oscillation emerges whose frequencies are very close to the inertial frequency. Because this particular kind of normal mode appears only due to the presence of boundary conditions in the vertical, it may be appropriate to call these w...

Pattern formation in the marginally unstable Ekman layer

We consider the spatio-temporal evolution of patterns in the marginally unstable Ekman layer driven by an applied shear stress. Both the normal and tangential components of the Earth's angular velocity are included in a tangent plane approximation of the oceanic boundary layer at latitude λ. The fluid motion in a layer of finite depth as well as one of infinite depth is considered. The linear instability in the infinite depth case is known to depend on the direction of the applied stress for λ ¬= 90°, but this dependence is weak for the stress-driven Ekman layer. By contrast, the weakly nonlinear motion exhibits for finite and infinite depths qualitatively different dynamics for different stress directions. The problem is treated by the method of multiple scales. In the case of finite depth, this leads to the Davey-Hocking--Stewartson equation, an amplitude equation of complex Ginzburg-Landau type coupled to a Poisson equation. In the case of infinite depth, it leads to the anisotropic complex Ginzburg-Landau equation for the amplitude of the roll motion. Motions in both finite and infinite depth basins are explored by numerical simulation, and are shown to lead to chaotic dynamics for the modulation envelope in most cases. The statistics and the nature of the patterns produced in this motion are discussed.

On the Nonhydrostatic Atmospheric Models with Inclusion of the Horizontal Component of the Earth's Angular Velocity

Two nonhydrostatic effects that have been neglected traditionally in the hydrostatic primitiveequation models are studied in this article. One such effect is due to the vertical acceleration in the vertical equation of motion. The other is due to a Coriolis term involving 2Ω cos (latitude), where Ω is the rate of earth’s rotation, and is referred to here as a cos (latitude) Coriolis term. Cos (latitude) Coriolis terms appear in the vertical and zonal equations of motion. The questions to be investigated are: (1) what are the dynamical consequences of these two nonhydrostatic effects, (2) how the roles of cos (latitude) Coriolis terms can be compared with sin (latitude) Coriolis terms, (3) which nonhydrostatic effect is likely more important, and (4) should these effects be included in atmospheric modeling for describing what kind of motions? These questions are studied quantitatively through a normal mode analysis of compressible, and stratified atmosphere with rotation on a tangent plane in a three-dimensional space that is open horizontally, but bounded by two rigid horizontal planes in the vertical. Numerical results are presented for an isothermal model. Considering the current trend of numerical modeling in permitting to use finer resolutions and to extend the top of model atmosphere higher, it is prudent to include both nonhydrostatic effects in the dynamical core of next generation atmospheric models for all scales of motions.