https://physics.ucf.edu/~britt/Geophysics/Readings/G15-Evolution%20of%20obliquity.pdf

Long term evolution and chaotic diffusion of the insolation quantities of Mars

The Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS) - Achievements, prospects and challenges

The OPERA neutrino experiment at the underground Gran Sasso Laboratory has measured the velocity of neutrinos from the CERN CNGS beam over a baseline of about 730 km with much higher accuracy than previous studies conducted with accelerator neutrinos. The measurement is based on high-statistics data taken by OPERA in the years 2009, 2010 and 2011. Dedicated upgrades of the CNGS timing system and of the OPERA detector, as well as a high precision geodesy campaign for the measurement of the neutrino baseline, allowed reaching comparable systematic and statistical accuracies. An early arrival time of CNGS muon neutrinos with respect to the one computed assuming the speed of light in vacuum of (60.7 \pm 6.9 (stat.) \pm 7.4 (sys.)) ns was measured. This anomaly corresponds to a relative difference of the muon neutrino velocity with respect to the speed of light (v-c)/c = (2.48 \pm 0.28 (stat.) \pm 0.30 (sys.)) \times 10-5.

/pdf/measurement-of-the-neutrino-velocity-with-the-opera-detector-22u2su4sfs.pdf

Measurement of the neutrino velocity with the OPERA detector in the CNGS beam

[1] The analytical formulation of the theories of nutation and wobble reveals the combinations of basic Earth parameters that govern the nutation-wobble response of the Earth to gravitational (tidal) forcing by heavenly bodies and makes it possible to estimate several of them through a least squares fit of the theoretical expressions to the high-precision data now available. This paper presents the essentials of the theoretical framework, the procedure that we used for least squares estimation of basic Earth parameters through a fit of theory to nutation-precession data derived from an up-to-date very long baseline interferometry data set, the results of the estimation and their geophysical interpretation, and the nutation series constructed using the estimated values of the parameters. The theoretical formulation used here differs from earlier ones in the incorporation of anelasticity and ocean tide effects into the basic structure of the dynamical equations of the theory and in the inclusion of electromagnetic couplings of the mantle and the solid inner core to the fluid outer core, though this generalization comes at the cost of making some of the system parameters complex and frequency dependent; it is also more complete, as it takes account of nonlinear terms in these equations, including effects of the time-dependent deformations produced by zonal and sectorial tides, which had been traditionally neglected in nonrigid Earth theories. Among the geophysical results obtained from our fit are estimates for the dynamic ellipticity e of the Earth (e = 0.0032845479 with an uncertainty of 12 in the last digit), for the dynamical ellipticity ef of the fluid core (3.8% higher than its hydrostatic equilibrium value, rather than ∼5% as hitherto), and for the two complex electromagnetic coupling constants. Our best estimates for the RMS radial magnetic fields at the core mantle boundary and at the inner core boundary, based on the estimates for these coupling constants, are ~6.9 and 72 gauss, respectively, when the magnetic field configurations are restricted to certain simple classes. The field strength needed at the inner core boundary could be lower if the density of the core fluid at this boundary or the ellipticity of the solid inner core were lower than that for the Preliminary Reference Earth Model. Our estimate for the resonance frequency of the prograde free core nutation mode, with an uncertainty of ∼10%, constitutes the first firm detection of the resonance associated with this mode; the period found is ∼1025 days, double that with electromagnetic couplings ignored. (Throughout this work, “days,” referring to periods, stands for “mean solar days.”) A new nutation series (MHB2000) is constructed by direct solution of the linearized dynamical equations (with our best fit values adopted for all the estimated Earth parameters) for each forcing frequency, and adding on the contributions from the nonlinear terms and other effects not included in the linearized equations. This series gives a considerably better fit to the nutation data than any of the earlier series based on geophysical theory. In particular, the residuals in the out of phase amplitudes of the retrograde 18.6 year and annual nutations, which had long remained at ∼0.5 milliseconds of arc (mas), are now reduced to the level of the uncertainties in the observational estimates, thanks mainly to the role played by the electromagnetic couplings. The largest remaining discrepancy is that in the out of phase prograde 18.6 year nutation, of ∼72 micorseconds of arc (μas). The frequency dependence of the nutation amplitudes cannot be exactly represented through a resonance formula, nor may the resonance frequencies themselves be interpreted as the eigenfrequencies of free modes because of the presence of complex and frequency-dependent system parameters. Nevertheless, we have constructed a new resonance formula which reproduces our nutation series accurately for almost all nutation frequencies; for the few remaining frequencies, a listing is given of the corrections to be applied in order to reproduce the exact results of the direct solution.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2001JB000390

Modeling of nutation and precession: New nutation series for nonrigid Earth and insights into the Earth's interior

Mars Orbiter Laser Altimeter (MOLA) topography and gravity models from 5 years of Mars Global Surveyor (MGS) spacecraft tracking provide a window into the structure of the Martian crust and upper mantle. We apply a finite-amplitude terrain correction assuming uniform crustal density and additional corrections for the anomalous densities of the polar caps, the major volcanos, and the hydrostatic flattening of the core. A nonlinear inversion for Moho relief yields a crustal thickness model that obeys a plausible power law and resolves features as small as 300 km wavelength. On the basis of petrological and geophysical constraints, we invoke a mantle density contrast of 600 kg m-3; with this assumption, the Isidis and Hellas gravity anomalies constrain the global mean crustal thickness to be >45 km. The crust is characterized by a degree 1 structure that is several times larger than any higher degree harmonic component, representing the geophysical manifestation of the planet's hemispheric dichotomy. It corresponds to a distinction between modal crustal thicknesses of 32 km and 58 km in the northern and southern hemispheres, respectively. The Tharsis rise and Hellas annulus represent the strongest components in the degree 2 crustal thickness structure. A uniform highland crustal thickness suggests a single mechanism for its formation, with subsequent modification by the Hellas impact, erosion, and the volcanic construction of Tharsis. The largest surviving lowland impact, Utopia, post-dated formation of the crustal dichotomy. Its crustal structure is preserved, making it unlikely that the northern crust was subsequently thinned by internal processes.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2004JE002262

Crustal structure of Mars from gravity and topography

In this paper we give values of the tidal gravimetric factor as well as of the Love numbers for the tidal surface displacement and for the tidal mass redistribution potential that are consistent with the presently adopted definitions. We present analytical expressions for these quantities and compute numerical values for two rotating, nonspherical Earth models. In the first model the Earth is everywhere in hydrostatic equilibrium, and the inner core and mantle are both elastic. In the second model the Earth is ellipsoidal with an inelastic mantle and with a nonhydrostatic initial state for which the effects of mantle convection and its associated boundary deformations are considered. This latter model is constrained to reproduce the observed free core nutation period and global Earth dynamical flattening.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1998JB900051

Tides for a convective Earth

The classical time transfer method used to realize International Atomic Time (TAI) is based on the common view technique, with GPS observations collected by C/A code receivers. The resulting clock offsets between the laboratory clock and GPS time are obtained from a fixed procedure defined by the Consultative Committee for Time and Frequency (CCTF). A similar procedure can be applied to the Receiver INdependent EXchange (RINEX) observation files produced by geodetic receivers driven by a stable external frequency. If the link between the receiver clock and the external clock is stable and precisely determined, the geodetic receivers can then be used for time transfer to TAI. In that case, we propose some modifications to the CCTF procedure to adapt it for the links between geodetic receivers, in order to take advantage of the P codes available on L1 and L2. This new procedure forms the ionosphere-free combination of the P1 and P2 codes as given by the 30 s RINEX observation files, the standard of the International GPS Service. The procedure is tested using the Ashtech Z-XII3T geodetic receivers and the results are compared with those obtained with the classical CCTF procedure based on the C/A code by computing the fractional frequency stability (Allan deviation) of the time links. Over short baselines, the two techniques are equivalent, while the new technique provides a factor 2 improvement for a transatlantic time link. For time links between a time receiver and a geodetic receiver, the differential satellite delays (P1-C/A or P2-C/A) must additionally be introduced. We show here that these biases do not, however, alter the long-term (>3 days) stability of the time transfer results. The corrections associated with tidal station displacement are also investigated, and the results indicate that they do not significantly improve the results at the present level of precision.

https://iopscience.iop.org/article/10.1088/0026-1394/40/4/307/pdf

Time transfer to TAI using geodetic receivers

When neglecting calibration issues, the accuracy of GPS-based time and frequency transfer using a combined analysis of code and carrier phase measurements highly depends on the noise of the GPS codes. In particular, the pseudorange noise is responsible for day-boundary discontinuities which can reach more than 1 ns in the time transfer results obtained from geodetic analysis. These discontinuities are caused by the fact that the data are analyzed in daily data batches where the absolute clock offset is determined by the mean code value during the daily data batch. This pseudorange noise is not a white noise, in particular due to multipath and variations of instrumental delays. In this paper, the pseudorange noise behavior is characterized in order to improve the understanding of the origin of the large day-boundary discontinuities in the geodetic time transfer results. In a first step, the effect of short-term noise and multipath is estimated, and shown to be responsible for only a maximum of 150 ps (picoseconds) of the day-boundary jumps, with only one exception at NRC1 where the correction provides a jump reduction of 300 ps. In a second step, a combination of time transfer results obtained with pseudoranges only and geodetic time transfer results is used to characterize the long-term evolution of pseudorange errors. It demonstrates that the day-boundary jumps, especially those of large amplitude, can be explained by an instrumental effect imposing a common behavior on all the satellite pseudoranges. Using known influences as temperature variations at ALGO or cable damages at HOB2, it is shown that the approach developed in this study can be used to look for the origin of the day-boundary discontinuities in other stations.

On the link between GPS pseudorange noise and day-boundary discontinuities in geodetic time transfer solutions

The standard for GNSS time transfer was first defined in 1984, associated to the use of GPS signals, which were at that time degraded by the Selective Availability. It was updated at a few instances to follow the evolution of GPS, of the receivers, and the inclusion of GLONASS. With the emergence of additional navigation systems like Galileo, BeiDou, QZSS, the standard has to be further adapted. This paper prepared by the CCTF Working Group on GNSS Time Transfer details the associated extended standard, named CGGTTS for Common GNSS Generic Time Transfer Standard, and the corresponding Version 2E of the format.Full paperThe full paper is available online at: http://metrologia.bipm.org/guides-stds-conventions/2015/G1.pdf

https://iopscience.iop.org/article/10.1088/0026-1394/52/6/G1/pdf

CGGTTS-Version 2E : an extended standard for GNSS Time Transfer

The resonance due to the nearly diurnal free wobble, observed in the diurnal tesseral tides and in the associated nutations, is used to determine the frequency and the damping of this wobble. The data are stacked to provide a least squares estimation of the resonance parameters: frequency, quality factor, and complex strengths. Some previous papers presented the same kind of analysis using either tidal or nutation data sets; in both cases, the frequency was about −(1 + 1/435) cycle/sidereal day, but the quality factor was larger for nutation data than for tidal data. In this paper we analyze simultaneously both sets of data, and we focus our attention on the determination of the free core nutation period and quality factor. We have analyzed a series of tidal data sets provided by the International Center for Earth Tides (ICET), and nutation data sets gathered from published matter. Our final result is obtained from a global stacking using four independent nutation data sets and three superconducting gravimeter data sets together. The values of the fitted parameters are found to be λFCN = −(1 + 1/(434.1 ± 0.9)) cycle/sidereal day and Q ≃ 54,000 (36,000; 109,000).

Pascale Defraigne

Papers

Tides for a convective Earth

Time transfer to TAI using geodetic receivers

On the link between GPS pseudorange noise and day-boundary discontinuities in geodetic time transfer solutions

CGGTTS-Version 2E : an extended standard for GNSS Time Transfer

Stacking gravity tide measurements and nutation observations in order to determine the complex eigenfrequency of the nearly diurnal free wobble