The G-calibration: A new method for an absolute in situ calibration of long-period accelerometers, tested on the Streckeisen instruments of the GEOSCOPE network

1991 ◽  
Vol 81 (4) ◽  
pp. 1360-1372
Author(s):  
P. Bernard ◽  
J.-F. Karczewski ◽  
M. Morand ◽  
B. Dole ◽  
B. Romanowicz
Keyword(s):  
Gravitational Field ◽  
Rotation Axis ◽  
Vertical Component ◽  
Calibration Method ◽  
High Accuracy ◽  
Horizontal Component ◽  
Force Balance ◽  
Absolute Calibration ◽  
Calibration System

Abstract The sensitivity of the Streckeisen's very broadband (VBB) accelerometers is routinely measured on tilt tables by the manufacturer, with an announced accuracy of about 1 per cent. Nevertheless, the transportation of the station or different in situ environmental conditions may modify the sensitivity. As one may expect that a high accuracy in the wave amplitude will be required in the future by seismologists, we developed and tested an in situ absolute calibration method, which does not require the seismometers to be moved. Its principle is simple: A mass is moving in the vicinity of the force-balance accelerometer, and the perturbation of the gravitational field is measured. This calibration method, because it requires the use of G, the gravitational constant, is termed the G-calibration. At a distance of 0.5 m, the gravitational field of a 30 kg mass is 8 × 10−9 m.sec−2, which is 2 order of magnitude greater than the instrumental noise. At the test station of SBB, this acceleration is still 50 times above the seismic noise level for the vertical component, but little above the seismic horizontal noise. The calibration system consists into a small telescope platform (diameter 0.5 m) supporting a horizontal bar of 1 m. Two metallic cylinders of equal mass (about 30 kg) are placed at the two ends of the bar, symmetrically with respect to the vertical rotation axis of the platform. The rotation velocity of the system is controlled with a high accuracy. The accelerometers are located at less than 1 m from the system axis. For the vertical component, we measured the sensitivity at various periods between 2000 and 50 sec, and the result was within 10 per cent of the specified sensitivity; this difference was of the same order as the expected accuracy. For the horizontal component, a slight asymmetry of the two masses with respect to the rotation center and an irregular coupling of the platform to the ground induced a periodic variation of the tilt, dominating over the gravitational signal of the masses at the frequencies of interest, which made the sensitivity measurement less accurate. Nevertheless, the result was still close to the announced sensitivity. We expect that an improved version of our calibration system will allow an accuracy of 1 per cent for the vertical, with a few hours of calibration. This will require an accuracy of a few millimeters in the geometry of the calibration system. Improving the results for the horizontal component will require a careful installation in order to eliminate the tilt perturbation and should lead to an accuracy of a few per cent.

Flows in a rotating spherical shell: the equatorial case

1994 ◽  
Vol 276 ◽  
pp. 233-260 ◽  
Author(s):  
A. Colin de Verdière ◽  
R. Schopp
Keyword(s):  
Angular Momentum ◽  
Rotation Axis ◽  
Dynamic Pressure ◽  
Vertical Component ◽  
Low Frequency ◽  
Zonal Flow ◽  
Horizontal Component ◽  
Meridional Plane ◽  
Earth’S Rotation ◽  
Earth's Rotation

It is well known that the widely used powerful geostrophic equations that single out the vertical component of the Earth's rotation cease to be valid near the equator. Through a vorticity and an angular momentum analysis on the sphere, we show that if the flow varies on a horizontal scale L smaller than (Ha)1/2 (where H is a vertical scale of motion and a the Earth's radius), then equatorial dynamics must include the effect of the horizontal component of the Earth's rotation. In equatorial regions, where the horizontal plane aligns with the Earth's rotation axis, latitudinal variations of planetary angular momentum over such scales become small and approach the magnitude of its radial variations proscribing, therefore, vertical displacements to be freed from rotational constraints. When the zonal flow is strong compared to the meridional one, we show that the zonal component of the vorticity equation becomes (2Ω.Δ)u1 = g/ρ0)(∂ρ/a∂θ). This equation, where θ is latitude, expresses a balance between the buoyancy torque and the twisting of the full Earth's vorticity by the zonal flow u1. This generalization of the mid-latitude thermal wind relation to the equatorial case shows that u1 may be obtained up to a constant by integrating the ‘observed’ density field along the Earth's rotation axis and not along gravity as in common mid-latitude practice. The simplicity of this result valid in the finite-amplitude regime is not shared however by the other velocity components.Vorticity and momentum equations appropriate to low frequency and predominantly zonal flows are given on the equatorial β-plane. These equatorial results and the mid-latitude geostrophic approximation are shown to stem from an exact generalized relation that relates the variation of dynamic pressure along absolute vortex lines to the buoyancy field. The usual hydrostatic equation follows when the aspect ratio δ = H/L is such that tan θ/δ is much larger than one. Within a boundary-layer region of width (Ha)1/2 and centred at the equator, the analysis shows that the usually neglected Coriolis terms associated with the horizontal component of the Earth's rotation must be kept.Finally, some solutions of zonally homogeneous steady equatorial inertial jets are presented in which the Earth's vorticity is easily turned upside down by the shear flow and the correct angular momentum ‘Ωr2cos2(θ)+u1rCos(θ)’ contour lines close in the vertical–meridional plane.

scholarly journals Volumetric spatial behaviour in rats reveals the anisotropic organisation of navigation

2020 ◽  
Author(s):  
Selim Jedidi-Ayoub ◽  
Karyna Mishchanchuk ◽  
Anyi Liu ◽  
Sophie Renaudineau ◽  
Éléonore Duvelle ◽  
...  
Keyword(s):  
Foraging Behaviour ◽  
Three Dimensional ◽  
Vertical Component ◽  
High Accuracy ◽  
Information Gathering ◽  
Horizontal Component ◽  
Spatial Behaviour ◽  
Horizontal Movement ◽  
Home Base ◽  
Base Formation

Abstract We investigated how access to the vertical dimension influences the natural exploratory and foraging behaviour of rats. Using high-accuracy three-dimensional tracking of position in two- and three-dimensional environments, we sought to determine (i) how rats navigated through the environments with respect to gravity, (ii) where rats chose to form their home bases in volumetric space, and (iii) how they navigated to and from these home bases. To evaluate how horizontal biases may affect these behaviours, we compared a 3D maze where animals preferred to move horizontally to a different 3D configuration where all axes were equally energetically costly to traverse. Additionally, we compared home base formation in two-dimensional arenas with and without walls to the three-dimensional climbing mazes. We report that many behaviours exhibited by rats in horizontal spaces naturally extend to fully volumetric ones, such as home base formation and foraging excursions. We also provide further evidence for the strong differentiation of the horizontal and vertical axes: rats showed a horizontal movement bias, they formed home bases mainly in the bottom layers of both mazes and they generally solved the vertical component of return trajectories before and faster than the horizontal component. We explain the bias towards horizontal movements in terms of energy conservation, while the locations of home bases are explained from an information gathering view as a method for correcting self-localisation.

scholarly journals Contribution to solving the orientation problem for an automatic magnetic observatory

2013 ◽  
Vol 2 (1) ◽  
pp. 1-9 ◽  
Author(s):  
A. Khokhlov ◽  
J. L. Le Mouël ◽  
M. Mandea
Keyword(s):  
Vertical Component ◽  
Calibration Procedure ◽  
High Accuracy ◽  
Absolute Calibration ◽  
Magnetic Observatory ◽  
Time Interval ◽  
Internal Calibration ◽  
Scale Factors ◽  
The Absolute ◽  
Absolute Measurements

Abstract. The problem of the absolute calibration of a vectorial (tri-axial) magnetometer is addressed with the objective that the apparatus, once calibrated, gives afterwards, for a few years, the absolute values of the three components of the geomagnetic field (say the Northern geographical component, Eastern component and vertical component) with an accuracy on the order of 1 nT. The calibration procedure comes down to measure the orientation in space of the three physical axes of the sensor or, in other words, the entries of the transfer matrix from the local geographical axes to these physical axes. Absolute calibration follows indeed an internal calibration which provides accurate values of the three scale factors corresponding to the three axes – and in addition their relative angles. The absolute calibration can be achieved through classical absolute measurements made with an independent equipment. It is shown – after an error analysis which is not trivial – that, while it is not possible to get the axes absolute orientations with a high accuracy, the assigned objective (absolute values of the Northern geographical component, Eastern component and vertical component, with an accuracy of the order of 1 nT) is nevertheless reachable; this is because in the time interval of interest the field to measure is not far from the field prevailing during the calibration process.

scholarly journals Solving the orientation problem for an automatic magnetic observatory

2012 ◽  
Vol 2 (1) ◽  
pp. 337-363
Author(s):  
A. Khokhlov ◽  
J. L. Le Mouël ◽  
M. Mandea
Keyword(s):  
Vertical Component ◽  
Calibration Procedure ◽  
High Accuracy ◽  
Absolute Calibration ◽  
Magnetic Observatory ◽  
Time Interval ◽  
Internal Calibration ◽  
Scale Factors ◽  
The Absolute ◽  
Absolute Measurements

Abstract. The problem of the absolute calibration of a vectorial (tri-axial) magnetometer is addressed with the objective that the apparatus, once calibrated, gives afterwards, for a few years, the absolute values of the three components of the geomagnetic field (say the Northern geographical component, Eastern component and vertical component) with an accuracy of the order of 1 nT. The calibration procedure comes down to measure the orientation in space of the three physical axes of the sensor or, in other words, the entries of the transfer matrix from the local geographical axes to these physical axes. Absolute calibration follows indeed an internal calibration which provides accurate values of the three scale factors corresponding to the three axes – and in addition their relative angles. The absolute calibration can be achieved through classical absolute measurements made with an independent equipment. It is shown – after an error analysis which is not trivial – that, while it is not possible to get the axes absolute orientations with a high accuracy, the assigned objective (absolute values of the Northern geographical component, Eastern component and vertical component, with an accuracy of the order of 1 nT) is nevertheless reachable; this is because in the time interval of interest the field to measure are not far from the field prevailing during the calibration process.

Calibrating the 2016 IRIS Wavefields Experiment Nodal Sensors for Amplitude Statics and Orientation Errors

2021 ◽  
Author(s):  
Oluwaseyi J. Bolarinwa ◽  
Charles A. Langston
Keyword(s):  
Signal To Noise Ratio ◽  
Vertical Component ◽  
Calibration Method ◽  
Horizontal Component ◽  
High Signal ◽  
Correction Factors ◽  
Small Aperture ◽  
S Waves ◽  
Amplitude Correction ◽  
Array Calibration

ABSTRACT We used teleseismic P and S waves recorded in the course of the 2016 Incorporated Research Institutions for Seismology (IRIS) community-planned experiment in northern Oklahoma, to estimate amplitude correction factors (ACFs) and orientation correction factors (OCFs) for the gradiometer’s three-component Fairfield nodal sensors and two other gradiometer-styled subarray nodal sensors. These subarrays were embedded in the 13 km aperture nodal array that was also fielded during the 2016 IRIS experiment. The array calibration method we used in this study is based on the premise that a common wavefield should be recorded over a small-aperture array using teleseismic observation. In situ estimates of ACF for the gradiometer vary by 2.3% (standard deviation) for the vertical components and, typically, variability is less than 4.3% for the horizontal components; associated OCFs generally dispersed by 3°. For the two subarrays, the vertical-component ACF usually vary up to 2.4%; their horizontal-component ACFs largely spread up to 3.6%. OCFs for the subarrays generally disperse by 6.5°. ACF and OCF estimates for the gradiometer are seen to be stable across frequency bands having high signal coherence and/or signal-to-noise ratio. Gradiometry analyses of calibrated and uncalibrated gradiometer records from a local event revealed notable improvements in accuracy of attributes obtained from analyzing the calibrated horizontal-component waveforms in the light of catalog epicenter-derived azimuth. The improved waveform relative amplitudes after calibration, coupled with the enhanced wave attribute accuracy, suggests that instrument calibration for amplitude statics and orientation errors should be encouraged prior to doing gradiometry analysis in future studies.

Development of an in situ calibration method for current-to-voltage converters for high-accuracy SI-traceable low dc current measurements

Metrologia ◽  
2013 ◽  
Vol 50 (5) ◽  
pp. 509-517 ◽  
Author(s):  
George P Eppeldauer ◽  
Howard W Yoon ◽  
Dean G Jarrett ◽  
Thomas C Larason
Keyword(s):  
Calibration Method ◽  
High Accuracy ◽  
In Situ Calibration ◽  
Dc Current

scholarly journals An On-Orbit Dynamic Calibration Method for an MHD Micro-Angular Vibration Sensor Using a Laser Interferometer

Sensors ◽  
2019 ◽  
Vol 19 (19) ◽  
pp. 4291
Author(s):  
Yingjie Wu ◽  
Xingfei Li ◽  
Fan Liu ◽  
Ganming Xia
Keyword(s):  
Laser Interferometer ◽  
Calibration Method ◽  
Vibration Sensor ◽  
Absolute Calibration ◽  
Dynamic Calibration ◽  
Calibration System ◽  
Angular Vibration ◽  
Lift Off ◽  
Orbit Dynamic ◽  
Dynamic Calibration Method

The magnetohydrodynamic (MHD) micro-angular vibration sensor is a significant component of the MHD Inertial Reference Unit (MIRU) and measures micro-amplitude and wide frequency angular vibration. The MHD micro-angular vibration sensor must be calibrated in orbit since the ground calibration parameters may change after lift-off. An on-orbit dynamic calibration method for the MHD micro-angular vibration sensor is proposed to calibrate the complex sensitivity of the sensor in high frequency. An absolute calibration method that combines a homodyne laser interferometer and an angular retroreflector was developed. The sinusoidal approximation method was applied, and the calibration system was established and tested using a manufactured MHD sensor. Furthermore, the measurement principle and installation errors were analyzed, including the eccentric installation error of the retroreflector, the tilt installation error of the retroreflector, and the optical path tilt error. This method can be realized within a rotation range of ± 3 ∘ and effectively avoid the installation error caused by mechanical errors. The results indicate that the calibratable angular vibration frequency range is 25–800 Hz, and the angular velocity range is 0 . 076 –7590 mrad/s. The expanded uncertainties of the sensitivity amplitude and phase shift of the calibration system for the MHD micro-angular sensor are 0 . 04 % and 1 . 2 ∘ ( k = 2 ) .

Galilean Relativity

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Inertial Frame ◽  
Vertical Component ◽  
Horizontal Component ◽  
The Other ◽  
One Dimension ◽  
Everyday Experience ◽  
Low Speed ◽  
Principle Of Relativity ◽  
Galilean Relativity ◽  
Laws Of Motion

Galilean relativity is a useful description of nature at low speed. Galileo found that the vertical component of a projectile’s velocity evolves independently of its horizontal component. In a frame that moves horizontally along with the projectile, for example, the projectile appears to go straight up and down exactly as if it had been launched vertically. The laws of motion in one dimension are independent of any motion in the other dimensions. This leads to the idea that the laws of motion (and all other laws of physics) are equally valid in any inertial frame: the principle of relativity. This principle implies that no inertial frame can be considered “really stationary” or “really moving.” There is no absolute standard of velocity (contrast this with acceleration where Newton’s first law provides an absolute standard). We discuss some apparent counterexamples in everyday experience, and show how everyday experience can be misleading.

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