Nutation Resonance Research Articles

Time Variations In Gravity And Inferences On The Earth's Structure And Dynamics

This paper reviews how the study of the surface gravity changes is able to provide useful information on the Earth's structure and global dynamics. The spectral range which is observable with superconducting gravimeters is broad and goes from the seismic frequency band to periods longer than one year. We first investigate the seismic and sub-seismic bands with a special attention paid to the gravity detection of core modes in the liquid core and to the Slichter mode of translation of the solid inner core. In the tidal bands, we show how accurate measurements allow us to infer constraints on various phenomena such as mantle (an-)elasticity, as well as ocean and atmospheric loading. The observation of the Free Core Nutation resonance in the diurnal frequency band is reviewed and indirectly suggests an increase in the ellipticity of the core-mantle boundary with respect to its hydrostatic value. A similar resonance is also theoretically predicted in the diurnal band for the rotation of the solid inner core (Free Inner Core Nutation) but we show that its detection is much more difficult because of the small amplitude and lack of a nearby tidal frequency. Oceanic and atmospheric loading mechanisms induce gravity changes over a wide spectral range and we present some recent progress in this field. Finally, because superconducting gravimeters have high calibration stability and small long-term instrumental drift, they can easily measure longperiod gravity variations due to polar motion and hydrogeology.

The structure and electronic state of photoexcited fullerene linked with a nitroxide radical based on an analysis of a two-dimensional electron paramagnetic resonance nutation spectrum

An electron paramagnetic resonance (EPR) study of 3,4-fulleropyrrolidine-2-spiro-4′[2′,2′,6′,6′-tetramethyl]piperidine-1′-oxyl (1) was performed on the photoexcited quartet state in toluene glass. The spectrum of the |S,Ms〉=|3/2,±3/2〉⇔|3/2,±1/2〉 transitions was observed selectively by using a two-dimensional (2D) nutation method and analyzed with a spectral simulation in a randomly oriented system. A position of the nitroxide moiety was determined with respect to the zero-field splitting (zfs) axes of excited triplet fullerene (3C60) by taking into account of the dipolar–dipolar interaction between the radical and 3C60, the hyperfine coupling, the anisotropic g-value of the nitroxide radical, and the zfs of the 3C60 moiety. It was found that none of the zfs axes of the 3C60 moiety coincide with the local C2 axis of the molecule which is defined by the position of addition. A symmetry of the electronic structure in 3C60 is discussed on the basis of the result.

Analytical versus semi-analytical determinations of the Oppolzer terms for a non-rigid Earth

Estimations of the Oppolzer terms for the angular momentum and rotation axes of a non-rigid Earth are obtained from two different approaches and compared. The first approach is an analytical method which relies on the solutions of the Liouville equations for a two-layer Earth model. The Oppolzer terms are evaluated from analytical expressions. The results are then compared to those calculated from Wahr's theory of nutation for a non-rigid Earth, which is the second approach used. Results are obtained for the main nutation frequencies and for the precession case. The differences between the two solutions are generally quite small (the relative error is most of the time under 8%) and are, for a large part, due to successive approximations and truncation effects during their determination. Departures of the results from the two methods are significantly larger for frequencies near the Free Core Nutation (FCN) resonance. This is particularly true for the Oppolzer terms of the angular momentum axis. The Earth model adopted is a little bit different in each case: for the Liouville system solution, we have limited the model to a homogeneous elastic mantle and a homogeneous liquid core. Another source of some of the small differences in the results is the presence of a solid inner core in Wahr's theory. We confirm through the analytical calculation the strong effect of the core on the Oppolzer terms of the angular momentum axis for a non-rigid Earth at the precession frequency. Finally, an application is given in the determination of the axes' position at J2000 for a non-rigid Earth.

Determination of the spectral parameters of nuclear quadrupole resonance from nutation spectra of powdered samples

An analytical expression I(ω) is obtained for a normalized function of the shape of an idealized nuclear quandrupole resonance nutation line of a powdered sample for spins I=3/2 (η≠0). Calculations are made of the initial moments of the nutation spectrum of the powder in the form of functions of ω0=γB1 and the asymmetry parameter η of the electric field gradient tensor. A method is proposed for determining the spectral parameters η and eQqzz from the experimentally measured values of , , , and ω1/2 of the nuclear quadrupole resonance nutation spectrum of the powder.

The response of the Earth to tidal body forces described by second- and third-degree spherical harmonics as derived from a 12 year series of measurements with the superconducting gravimeter GWR/T3 in Brussels

A 12 year tidal gravity registration performed in Brussels with a GWR superconducting gravimeter allows us to separate six tidal components derived from the third-degree lunar potential from those derived from the classical second-degree luni-solar potential (39 components) with which they differ in frequency by the lunar perigee period (8.847 year). Four ter diurnal waves are also separated. Such a separation appears necessary as the results show a non-negligible residue on the third-degree frequency wave M 1 (lunar day period) owing to an amplification of the corresponding oceanic component in the North Atlantic ocean. The other third-degree components also differ slightly from the theoretical model amplitudes. A correct determination of the free core nutation resonance acting on the ψ 1 diurnal solar wave is discussed in relation to atmospheric pressure gravitational effects and climatological disturbances. The zonal fortnightly tide Mf is also deduced with precision but its comparison with the theoretical model raises a problem.

Empirical ocean tide models estimated from TOPEX/POSEIDON altimetry

Three empirical ocean tide models are determined from repeat cycles 10 to 78 of the TOPEX/POSEIDON (T/P) altimeter mission. The three models investigate the effects of the satellite orbit ephemeris on the ocean tides determined from T/P altimetry and the effect of extracting the free core nutation resonance in the definition of the diurnal ocean tide admittance. The altimetric data series use the Joint Gravity Model JGM‐2 geopotential orbit ephemeris and the preliminary JGM‐3 orbit ephemeris computed at the University of Texas, Center for Space Research. The altimetric data from the T/P mission are shown to have the precision necessary to estimate the monthly and fortnightly ocean tides in each bin. Inclusion of existing models of the ocean tides in the polar latitudes not sampled by the altimeter demonstrates the importance of these latitudes on spherical harmonic representations of the ocean tides. The ocean tides are first estimated in bins of size 2.834° in longitude by 1° in latitude and then smoothed to 1° by 1° grids within ±66° latitude. The orthotide response formalism of Groves and Reynolds (1975) is used to represent the diurnal and semidiurnal ocean tides, while a constant admittance is assumed across narrow bandwidths around each of the monthly (Mm), fortnightly (Mf), and termensual (Mt) tidal components. Comparisons of the T/P ocean tide models to tide gauge observations indicate their accuracies to be of the order of 2–3 cm. The T/P‐derived ocean tide models remove approximately 20 cm2 more of the T/P measured sea surface variance than the Cartwright and Ray (1991) tide model and show a 19 cm2 and 15 cm2 improvement over the Schwiderski (1980a, b) and Cartwright and Ray (1991) tide models, respectively, when compared to tide gauge estimates of the ocean tides.

Observation of spin-correlated radical pairs via two-dimensional electron paramagnetic resonance nutation spectroscopy

Two-dimensional (2D) Fourier-transform (FT) electron paramagnetic resonance (EPR) nutation experiments were done in order to verify anomalous flip-angle dependence of a FT–EPR spectrum of a photochemically generated spin-correlated radical pair (SCRP). It was demonstrated by both the experiment and theory that the signals of SCRP have additionally higher and lower nutation frequencies than that of a free radical. This spectroscopy provides a direct spectroscopic evidence of spin-correlation within SCRP, and enables one to partially separate SCRP signals from free radical signals in the 2D EPR spectrum.

Measurement of diurnal and semidiurnal rotational variations and tidal parameters of Earth

We discuss the determination of diurnal and semidiurnal variations in the rotation rate and the direction of rotation axis of Earth from the analysis of 8 years of very long baseline interferometry (VLBI) data. This analysis clearly show that these variations are largely periodic and tidally driven; that is, the periods of the variations correspond to the periods of the largest lunar and solar tides. For rotation rate variations, expressed in terms of changes in universal time (UT), the tidal lines with the largest observed signals are O1 (amplitude 23.5 microseconds in time (μs), period 25.82 solar hours); K1 (18.9 μs, 23.93 hours); M2 (17.9 μs, 12.54 hours); and S2 (8.6 μs, 12.00 hours). For variations in the direction of the rotation axis (polar motion), significant signals exist in the retrograde semidiurnal band at the M2 and S2 tides (amplitudes 265 and 119 microarc seconds (μas), respectively); the prograde diurnal band at the O1, K1, and P1 tides (amplitudes 199,152, and 60 μas, respectively); and the prograde semidiurnal band at the M2 and K2 tides (amplitudes 58 and 39 μas, respectively). Variations in the retrograde diurnal band are represented by corrections to the nutations of Earth's body axes, and our estimates here are consistent with previous estimates except that a previously noted discrepancy in the 13.66‐day nutation (corresponding to the O1 tide) is largely removed in this new analysis. We estimate that the standard deviations of these estimates are 1.0 μs for the UTl variations and 14–16 μas for the polar motion terms. These uncertainties correspond to surface displacements of ∼0.5 mm. From the analysis of atmospheric angular momentum data we conclude that variations in UTl excited by the atmosphere with subdaily periods are small (∼1 μs). We find that the average radial tidal displacements of the VLBI sites in the diurnal band are largely consistent with known deficiencies in current tidal models, i.e., deficiencies of up to 0.9 mm in the treatment of the free core nutation resonance. In the semidiurnal band, our analysis yields estimates of the second‐degree harmonic radial Love number h2 at the M2 tide of 0.604+i0.005±0.002. The most likely explanation for the rotational variations are the effects of ocean tides, but there may also be some contributions from atmospheric tides, the effects of triaxiality of Earth, and the equatorial second‐degree‐harmonic components of the core‐mantle boundary.