Direct measurement of diurnal polar motion by ring laser gyroscopes

Schreiber, K. U.; Velikoseltsev, A.; Rothacher, M.; Klügel, Thomas; Stedman, Geoffrey; Wiltshire, David L.

doi:10.1029/2003jb002803

Cited by 87 publications

(57 citation statements)

References 9 publications

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“…2. Utilization of the superfluid interferometer as a geodetic gyroscope requires a more rigid structure placed in a quiet environment 13 . Alternatively, as a device for inertial navigation in a noisy environment, one will need to employ feedback to lock the device at a particular bias point while having a slew rate high enough to track nuisance signals.…”

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confidence: 99%

SuperfluidHe4interferometer operating near2K

2006

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Matter-wave interferometers reveal some of the most fascinating phenomena of the quantum world 1 . Phase shifts due to rotation (the Sagnac effect) for neutrons 2 , free atoms 3 and 4, 5 superfluid 3 He reveal the connection of matter waves to a non-rotating inertial frame. In addition, phase shifts in electron waves due to magnetic vector potentials (the Aharonov-Bohm effect 6 ) show that physical states can be modified in the absence of classical forces. We report here the observation of interference induced by the Earth's rotation in superfluid 4 He at 2 K, a temperature 2000 times higher than previously achieved with 3 He. This interferometer, an analog of a dc-SQUID, employs a recently reported phenomenon wherein superfluid 4 He exhibits quantum oscillations in an array of sub-micron apertures 7,8 . We find that the interference pattern persists not only when the aperture array current-phase relation is a sinusoidal function characteristic of the Josephson effect, but also at lower temperatures where it is linear and oscillations occur by phase slips 9,10 . The modest requirements for the interferometer (2 K cryogenics and fabrication of apertures at the level of 100nm) and its potential resolution suggest that, when engineering challenges such as vibration isolation are met, superfluid 4 He interferometers could become important scientific probes. Superfluid4 He is described by a macroscopic wave function which includes a phase φ that can vary in time and space. Our new interferometer is based on a recently reported phenomenon wherein an array of 4225 (65 2 ) small apertures coupling together two reservoirs of superfluid 4 He exhibits fluid oscillations at the Josephson frequency.The superfluid current I through an aperture array is a function of the fluid phase difference φ Δ between one side of the array and the other. This

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confidence: 99%

SuperfluidHe4interferometer operating near2K

2006

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“…Another reason for variations in δf are changes in the surface normal n of the ringlaser with respect to the rotation axis. These variations may be caused for example by solid Earth tides, ocean loading (Schreiber et al 2009) or diurnal polar motions (Schreiber et al 2004). The third reason for variations in δf are changes in˙ , that is changes in the rotation rate itself.…”

Section: Rotational Motions In Seismologymentioning

confidence: 99%

The influence of crustal scattering on translational and rotational motions in regional and teleseismic coda waves

Gaebler

Sens‐Schönfelder²,

Korn

2015

Geophysical Journal International

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S U M M A R YMonte Carlo solutions to the radiative transfer equations are used to model translational and rotational motion seismogram envelopes in random elastic media with deterministic background structure assuming multiple anisotropic scattering. Observation and modelling of the three additional components of rotational motions can provide independent information about wave propagation in the Earth's structure. Rotational motions around the vertical axis observed in the P-wave coda are of particular interest as they can only be excited by horizontally polarized shear waves and therefore indicate the conversion from P to SH energy by multiple scattering at 3-D heterogeneities. To investigate crustal scattering and attenuation parameters in south-east Germany beneath the Gräfenberg array multicomponent seismogram envelopes of rotational and translational motions are synthesized and compared to seismic data from regional swarm-earthquakes and of deep teleseismic events. In the regional case a nonlinear genetic inversion is used to estimate scattering and attenuation parameters at high frequencies (4-8 Hz). Our preferred model of crustal heterogeneity consists of a medium with random velocity and density fluctuations described by an exponential autocorrelation function with a correlation length of a few hundred metres and fluctuations in the range of 3 per cent. The quality factor for elastic S-waves attenuation Q S i is around 700. In a second, step simulations of teleseismic P-wave arrivals using this estimated set of scattering and attenuation parameters are compared to observed seismogram envelopes from deep events. Simulations of teleseismic events with the parameters found from the regional inversion show good agreement with the measured seismogram envelopes. This includes ringlaser observations of vertical rotations in the teleseismic P-wave coda that naturally result from the proposed model of wave scattering. The model also predicts, that the elastic energy recorded in the teleseismic P coda is not equipartitioned, unlike the coda of regional events, but contains an excess of shear energy. The results confirm that scattering generating the teleseismic P-wave coda mainly occurs in the crustal part of the lithosphere beneath the receiver. Our observations do not require scattering of high frequency waves in the mantle, but weak scattering in the lithospheric mantle cannot be ruled out.

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“…For the sake of brevity, we will not engage in an in-depth discussion of the wobble phenomenon and its modeling in this paper. We only mention that today's experimental capabilities allow for its most accurate recording, in particular since the advent of sophisticated surveying techniques, such as GPS and VLBI (Very Long Baseline Interferometry), and refer to the literature for a first introduction [6,7] as well as for more in-depth explanations of the phenomenon [8].…”

Section: Some Historical Background and The Experimental Evidencementioning

confidence: 99%

The spin, the nutation, and the precession of the Earth's axis revisited from a (numerical) mechanics perspective

Müller

2015

Z Angew Math Mech

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Modeling the motion of the Earth's axis, i.e., its spin, nutation and its precession, is a prime example of our ongoing effort to simulate the behavior of complex mechanical systems. In fact, models of increasing complexity of this motion have been presented for more than 400 years leading to an increasingly accurate description. The objective of this paper is twofold namely, first, to provide a review of these efforts and, second, to provide an improved analysis, if possible, based on today's numerical possibilities. Newton himself treated the problem of the precession of the Earth, a.k.a. the precession of the equinoxes, in Liber III, Propositio XXXIX of his Principia [1]. He decomposed the duration of the full precession into a part due to the Sun and another part due to the Moon, which would lead to a total duration of 25,918 years. This agrees fairly well with the experimentally observed value. However, Newton does not really provide a concise rational derivation of his result. This task was left to Chandrasekhar in Chapter 26 of his annotations to Newton's book [2]. He follows an approach suggested by Scarborough [3] starting from Euler's equations for the gyroscope and by calculating the torques due to the Sun and to the Moon on a tilted spheroidal Earth. These differential equations can be solved approximately in an analytic fashion, yielding something close to Newton's more or less fortuitous result. However, the equations can also be treated more properly in a numerical fashion by using a Runge-Kutta approach allowing for a study of their general non-linear behavior. This paper will show how and discuss the outcome of the numerical solution. A comparison to actual measurements will also be attempted. When solving the Euler equations for the aforementioned case numerically it shows that besides the precessional movement of the Earth's axis there is also a nutational one present. However, as we shall show, if Scarborough's procedure is followed, the period of this nutation turns out to be roughly half a year with a very small amplitude whereas the observed (main) nutational period is much longer, namely roughly nineteen years, and much more intense amplitude-wise. The reason for this discrepancy is based on the assumption that the torques of both the Sun and the Moon are due to gravitational actions within the equinoctial plane. Whilst this is true for the Sun, the revolution of the Moon around the Earth occurs in a plane, which is inclined by roughly 5°w.r.t. the equinoctial. Moreover, this plane rotates such that the ascending and descending nodes of the moon precede with a period of roughly 18 years. If all of this is taken into account the analytically predicted nutation period will be of the order of the observed value [4,5]. As in the case of the precession we will provide a more stringent analysis based on a numerical solution of the Euler equations, which leads beyond the results presented in Sect.12.10 of [5].

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Direct measurement of diurnal polar motion by ring laser gyroscopes

Cited by 87 publications

References 9 publications

SuperfluidHe4interferometer operating near2K

SuperfluidHe4interferometer operating near2K

The influence of crustal scattering on translational and rotational motions in regional and teleseismic coda waves

The spin, the nutation, and the precession of the Earth's axis revisited from a (numerical) mechanics perspective

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