Contribution to solving the orientation problem for an automatic magnetic observatory

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

The six-month line in geomagnetic long series

International audienceDaily means of the horizontal components X (north) and Y (east) of the geomagnetic field are available in the form of long series (several tens of years). Nine observatories are used in the present study, whose series are among the longest. The amplitudes of the 6-month and 1-year periodic variations are estimated using a simple but original technique. A remarkably clear result emerges from the complexity of the geomagnetic data: the amplitude of the 6-month line presents, in all observatories, the same large variation (by a factor of 1.7) over the 1920–1990 time span, regular and quasi-sinusoidal. Nothing comparable comes out for the annual line. The 6-month line results from the modulation by an astronomical mechanism of a magnetospheric system of currents. As this latter mechanism is time invariant, the intensity of the system of currents itself must present the large variation observed on the 6-months variation amplitude. This variation presents some similarities with the one displayed by recent curves of reconstructed solar irradiance or the "Earth's temperature". Finally, the same analysis is applied to the aa magnetic index

Scenario-based earthquake hazard and risk assessment for Baku (Azerbaijan)

A rapid growth of population, intensive civil and industrial building, land and water instabilities (e.g. landslides, significant underground water level fluctuations), and the lack of public awareness regarding seismic hazard contribute to the increase of vulnerability of Baku (the capital city of the Republic of Azerbaijan) to earthquakes. In this study, we assess an earthquake risk in the city determined as a convolution of seismic hazard (in terms of the surface peak ground acceleration, PGA), vulnerability (due to building construction fragility, population features, the gross domestic product per capita, and landslide's occurrence), and exposure of infrastructure and critical facilities. The earthquake risk assessment provides useful information to identify the factors influencing the risk. A deterministic seismic hazard for Baku is analysed for four earthquake scenarios: near, far, local, and extreme events. The seismic hazard models demonstrate the level of ground shaking in the city: PGA high values are predicted in the southern coastal and north-eastern parts of the city and in some parts of the downtown. The PGA attains its maximal values for the local and extreme earthquake scenarios. We show that the quality of buildings and the probability of their damage, the distribution of urban population, exposure, and the pattern of peak ground acceleration contribute to the seismic risk, meanwhile the vulnerability factors play a more prominent role for all earthquake scenarios. Our results can allow elaborating strategic countermeasure plans for the earthquake risk mitigation in the Baku city

Scenario-based earthquake hazard and risk assessment for Baku (Azerbaijan)

A rapid growth of population, intensive civil and industrial building, land and water instabilities (e.g. landslides, significant underground water level fluctuations), and the lack of public awareness regarding seismic hazard contribute to the increase of vulnerability of Baku (the capital city of the Republic of Azerbaijan) to earthquakes. In this study, we assess an earthquake risk in the city determined as a convolution of seismic hazard (in terms of the surface peak ground acceleration, PGA), vulnerability (due to building construction fragility, population features, the gross domestic product per capita, and landslide’s occurrence), and exposure of infrastructure and critical facilities. The earthquake risk assessment provides useful information to identify the factors influencing the risk. A deterministic seismic hazard for Baku is analysed for four earthquake scenarios: near, far, local, and extreme events. The seismic hazard models demonstrate the level of ground shaking in the city: PGA high values are predicted in the southern coastal and northeastern parts of the city and in some parts of the downtown. The PGA attains its maximal values for the local and extreme earthquake scenarios. We show that the quality of buildings and the probability of their damage, the distribution of urban population, exposure, and the pattern of peak ground acceleration contribute to the seismic risk, meanwhile the vulnerability factors play a more prominent role for all earthquake scenarios. Our results can allow elaborating strategic countermeasure plans for the earthquake risk mitigation in the Baku city

On the Slow Drift of Solstices: Milankovic Cycles and Mean Global Temperature

The Earth's revolution is modified by changes in inclination of its rotation axis. Despite the fact that the gravity field is central, the Earth's trajectory is not closed and the equinoxes drift. Milankovic (1920) argued that the shortest precession period of solstices is 20,7kyr: the Summer solstice in one hemisphere takes place alternately every 11kyr at perihelion and at aphelion. We have submitted the time series for the Earth's pole of rotation, global mean surface temperature and ephemeris to iterative Singular Spectrum Analysis. iSSA extracts from each a trend, a 1yr and a 60yr component. Both the apparent drift of solstices of Earth around the Sun and the global mean temperature exhibit a strong 60yr oscillation. The "fixed dates" of solstices actually drift. Comparing the time evolution of the Winter and Summer solstices positions of the rotation pole and the first iSSA component (trend) of the temperature allows one to recognize some common features. A basic equation from Milankovic links the derivative of heat received at a given location on Earth to solar insolation, known functions of the location coordinates, solar declination and hour angle, with an inverse square dependence on the Sun-Earth distance. We have translated the drift of solstices as a function of distance to the Sun into the geometrical insolation theory of Milankovic. Shifting the inverse square of the 60yr iSSA drift of solstices by 15 years with respect to the first derivative of the 60yr iSSA trend of temperature, that is exactly a quadrature in time, puts the two curves in quasi-exact superimposition. The probability of a chance coincidence appears very low. Correlation does not imply causality when there is no accompanying model. Here Milankovic's equation can be considered as a model that is widely accepted. This paper identifies a case of agreement between observations and a mathematical formulation

On the semiannual and annual variations of geomagnetic activity and components

International audienceThe semiannual and annual lines in a long series of magnetic observatories daily values, as well as in the aa-activity index series, are investigated. For both periods, amplitudes and phases of the lines corresponding to the different series present grossly common variations on decadal time scales; relative phases and amplitude ratios between the observatories change with the same time constants. The results are briefly discussed with regards to commonly received theories of the semiannual variation of magnetic activity, and some possible mechanisms for the observed geographical variability are suggested

Is the Earth's magnetic field a constant ? a legacy of Poisson

In the report he submitted to the Acad\'emie des Sciences, Poisson imagined a set of concentric spheres at the origin of the Earth's magnetic field. It may come as a surprise to many that Poisson as well as Gauss both considered the magnetic field to be constant. We propose in this study to test this surprising assertion for the first time evoked by Poisson (1826). First, we will present a development of Maxwell's equations in the framework of a static electric field and a static magnetic field in order to draw the necessary consequences for the Poisson hypothesis. In a second step, we will see if the observations can be in agreement with Poisson (1826). To do so, we have chosen to compare 1) the polar motion drift and the secular variation of the Earth's magnetic field, 2) the seasonal pseudo-cycles of day length together with those of the sea level recorded by different tide gauges around the globe and those of the Earth's magnetic field recorded in different magnetic observatories. We then propose a mechanism, in the spirit of Poisson, to explain the presence of the 11-year in the magnetic field. We test this mechanism with observations and finally we study closely the evolution of the g10 coefficient of the IGFR over time

On variations of global mean surface temperature: When Laplace meets Milankovi\'c

In his mathematical theory, Milankovic finds a link between the heat received by the Earth surface per unit time as a function of the solar ephemerids and derives a model of climate changes at periods longer than a few thousand years and more. In this paper, we investigate the potential connections of global temperature and Earth rotation at much shorter periods, in the complementary range of one to a few hundred years. For temperature, we select the HadCrut05. For Earth rotation, defined by pole coordinates and length of day, we use the IERS data sets. Using iterative Singular Spectrum Analysis (iSSA), we extract the trend and quasi-periodic components of these time series. The first quasi-periodic components (period ~80-90 years) are expressions of the Gleissberg cycle and are identical (at the level of uncertainty of the data). Taken together, the trend and Gleissberg components allow one to reconstruct 87% of the variance of the data for lod and 48% for temperature. The next four iSSA components, with periods ~40, 22, 15 and 9 years. The Lagrange and Laplace theories imply that the derivative of pole motion should be identical to lod variations: this strong check is passed by the trend + Gleissberg reconstructions. The annual oscillations of pole motion and lod are linked to annual variations in Sun-Earth distance, in agreement with an astronomical, but not a climatic origin. The results obtained in this paper for the observed temperature/rotation couple add to the growing list of evidence of solar and planetary forcings of gravitational nature on a number of geophysical processes (including sea-level, sea-level pressure, sea-ice extent, oceanic climate indices).Comment: 13 pages, 13 figure

A description of the neutralino observables in terms of projectors

Applying Jarlskog's treatment of the CKM matrix, to the neutralino mass matrix in MSSM for real soft gaugino SUSY breaking and $\mu$-parameters, we construct explicit analytical expressions for the four projectors which acting on any neutralino state project out the mass eigenstates. Analytical expressions for the neutralino mass eigenvalues in terms of the various SUSY parameters, are also given. It is shown that these projectors and mass eigenvalues are sufficient to describe any physical observable involving neutralinos, to any order of perturbation theory. As an example, the $e^-e^+ \to \tilde \chi^0_i \tilde \chi^0_j$ cross section at tree level is given in terms of these projectors. The expected magnitude of their various matrix elements in plausible SUSY scenarios is also discussed.Comment: 14 pages, no figures. Version to appear in Phys. Rev. D. e-mail: [email protected]