Ohmic and viscous damping of the Earth's Free Core Nutation

<p>The cause for the damping of the Earth's Free Core Nutation (FCN) and the Free Inner Core Nutation (FICN) eigenmodes has been a matter of debate since the earliest reliable estimations from nutation observations were made available. Numerical studies are difficult given the extreme values of some of the parameters associated with the Earth's fluid outer core, where important dissipation processes can take place. We present a linear numerical model for the FCN that includes viscous dissipation and Ohmic heating. We find an asymptotic regime, appropriate for Earth's parameters, where viscous and Ohmic processes contribute equally to the total damping, with the dissipation taking place almost exclusively in the boundary layers. By matching the observed nutational damping we infer an enhanced effective viscosity matching and validating methods from previous studies. We suggest that turbulence caused by the Earth's precession can be a source for the FCN's damping. </p>

Parameters of the Earth’s Free Core Nutation from Diurnal Strain Tides

Earth deformation at the diurnal tidal frequencies includes the resonant tidal-forcing response caused by the Free Core Nutation (FCN), a retrograde mode related to the slight misalignment of the rotation axes of the outer core and mantle. We analyse data from four underground high-sensitivity laser extensometers, whose signal-to-noise ratio in the diurnal tidal band is particularly high, and provide an alternative independent estimate of the FCN complex frequency with respect to more usual techniques (nutation and gravity). Firstly, we differentiate displacements due to diurnal solid tides to obtain extension along any azimuthal direction in terms of three complex parameters (A, S, C) which depend on latitude and frequency. Then, we demonstrate that we can invert the FCN complex frequency and the sensitivity of Im(A) and Re(S) to the resonance from our data. Lastly we obtain the probability distributions of those four parameters. Our results are in full agreement with those from nutation and gravity, as well as with reference IERS (International Earth Rotation and Reference Systems Service) values. Sensitivities of Im(A) and Re(S) to the resonance are estimated here for the first time and are in agreement with values computed using reference Love and Shida numbers from IERS.

Contribution of a joint Bayesian inversion of VLBI and gravimetric data to the estimation of the free inner core nutation and free core nutation resonance parameters

SUMMARY The rotational motions of the internal Earth layers induce resonances in the Earth nutations and tidal gravimetric response to external luni-solar gravitational forcings. The characterization of these resonances is a mean of investigating the deep Earth properties since their amplitudes and frequencies depend on a few fundamental geophysical parameters. In this work, we focus on the determination of the free core nutation and free inner core nutation periods and quality factors from the Bayesian inversion of VLBI and gravimetric data. We make a joint inversion of data from both techniques and show that, even if the results are only slightly different from the inversion of VLBI data alone, such approach may be valuable in the future if the accuracy of gravimetric data increases. We also briefly discuss the polar motion resonance, which is related to the Chandler Wobble as seen from the diurnal frequency band. Our overall estimates of the FCN period and quality factor, TFCN = (−430.2, −429.8) solar days and QFCN = (15 700, 16 700), respectively, are in good agreement with other studies, albeit slightly different for unclear reasons. Despite some concerns about the detection and characterization of the FICN, it seems that we could also successfully estimate its period, TFICN = (+600, +1300) solar days, and give a loose estimate of the upper bound on its quality factor.

Free Core Resonance parameters from diurnal strain tides recorded by the Gran Sasso (Italy) and Canfranc (Spain) underground geodetic interferometers

<p>The Free Core Nutation (FCN) is a retrograde mode related to the slight misalignment of the rotation axis of the fluid outer core and the elastic mantle, with a period of about 430 sidereal days in the celestial frame. In the Earth-fixed reference frame, the (complex) frequency of the Free Core Nutation (FCN) is inside the diurnal tidal band and causes a resonant response (Free Core Resonance, FCR) of some diurnal tidal waves to the tide-generating forces.<br>The FCN is usually investigated through its effects on gravity tides and Earth nutations. Here we analyse about 7 years of discontinuous strain records from two 90-m long laser interferometers (strainmeters) operating under the Gran Sasso (Italy) massif and about 4.6 years of discontinuous strain records from two 70-m-long laser interferometers operating the Central Pyrenees (Spain).<br>Starting from the expressions for the vector displacements due to diurnal and semi-diurnal solid tides, we express  extension along any azimuthal direction in terms of three complex parameters (related to areal strain and the two shear strain components), which are functions of the latitude-dependent Love and Shida numbers. Those three complex parameters are affected by the FCR through three complex resonance strengths.<br>We find that we can infer 4 model parameters from the inversion of our data, i. e. from the comparison between amplitudes and phases of the measured and theoretical diurnal tides close to the resonance: the FCN period, the FCR quality factor, the imaginary part of one of the three resonance strengths, and the real part of another resonance strength. However, local deformation is distorted with respect to regional deformation because of siting effects. Coupling between local extension (measured by the interferometers) and regional deformation can be described by three coupling coefficients per interferometer, thus introducing 12 additional unknown in the inversions.<br>We minimize misfit between amplitudes and phases of the measured and theoretical tidal strain jointly for all the interferometers by sampling the 4D model parameter space, while optimal coupling coefficients for each interferometer are computed through a simple matrix inversion at each sampled point.<br>Theoretical strain tides is corrected for the effects of the water load oscillations caused by ocean tides. We use FES2014 and TPXO9 ocean models, while the appropriate Earth model for different ocean load areas is chosen basing on the widths of the continental shelves nearby the stations and the inversion misfits.<br>Although we analyse records from two stations only and the amount of data is relatively small, our results for the FCN period and (to some extent) the FCR quality factor are robust and comparable to those obtained from gravity tides and  nutations. Moreover, we obtain reliable values of the resonance strengths and robust estimates of the coupling coefficients for all the interferometers.</p>

Frequency dependence of the polar motion resonance

SUMMARY The nutation of the Celestial Intermediate Pole can be considered as a retrograde diurnal polar motion. As the common polar motion, it presents a resonance, but with period TPM and quality factor QPM differing from the ones characterizing the Chandler wobble (TCW = 430.2−431.6 d, QCW in the interval (56 255) according to Nastula & Gross): according to the nutation analysis presented in a separate paper, this period is about TPM = 380 d and the quality factor becomes −10. In this study, we aim to revisit the geophysical interpretation of this result. Two complementary factors account for the observed values: the non-equilibrium response of the ocean to the pole tide potential in the diurnal band, and the resonance of the solid Earth tide at the free core nutation period. This leads to a resonance of TPM in the vicinity of the free core nutation period, confirmed by estimates derived from nutation analysis.