Geodesy [G]

G31A
MCC:3005
Wednesday

Earth Rotation and Geocenter I

G31A-01 INVITED

Geocenter Motions From Satellite Geodesy; A Unified Observation Model

Changes in the displacement vector between the Center of Mass (CM) of the Earth system and the Center of the Earth's geometrical Figure (CF) is commonly called geocenter motion and is observable using geodetic techniques. Estimates of this geocenter motion have been at various levels of agreement both between and within different geodetic techniques. Cross-technique differences can be partly explained by a broad spectrum of technique specific errors and different tracking networks. Geocenter motions on the intra-annual scale are caused by global scale surface mass re-distribution which causes elastic deformation of the solid Earth and displaces the center of the geodetic tracking network (and hence CF) from CM. Given this underlying physical process we can unify expected changes in both deformation and gravity through an elastic Earth model and build a much stronger framework for estimating geocenter motions than via deformational or empirical approaches alone. Using such a unified approach allows a contribution to be made by techniques that are not directly sensitive to station displacements (such as satellite gravity measurements) or alternatively allows techniques that are not sensitive to gravitational aspects of frame definition (i.e. the origin) to contribute via observations of relative site motion. This is particularly pertinent for GPS which can exploit good spatial coverage and provide low inter-site estimation precision but has a less precise determination of the center of mass and hence the origin of the frame. We demonstrate how a unified model can be applied to geocenter motion estimation using GPS solutions from the IGS analysis centers. Through a combination of error propagation and simulation we show how a model that unifies both the shift and inter-site motion is conceptually stronger for GPS than one based on either alone, or a "common-mode" filter approach. We further investigate the contribution to be made by adding observations of the temporal gravity field from SLR such that different techniques have complementary input.

G31A-02

Measurement of Geocenter Variations With GNSS

The position of the geocenter can only be measured with satellite-geodetic methods. Time series of geocenter coordinates are produced by all three techniques, SLR, DORIS, and GNSS. Geocenter variations, in particular in the axial direction, are affected by orbit models used to represent the satellite trajectories. In particular for the large satellites operated in GNSS constellations the impact of radiation pressure models is significant. The presentation shows the effects and illustrates the underlying mechanisms.

G31A-03 INVITED

Comments On The Ability Of Satellite-Geodetic Techniques To Measure Geocenter Motions.

The accuracy of the Earth's geocenter motion estimates is one of the challenges of the global analysis of geodetic satellite measurements. The geocenter motions are ascribed to time varying mass distribution in the atmosphere, the oceans and ground waters. The motion of the Earth's center of mass (geocenter) with respect to a terrestrial reference frame attached to the crust is usually described by time series of the coordinates of the origin of the individual data sets derived from SLR, DORIS or GPS. The intercomparison of space geodetic time series and their comparison with geophysical predictions at the seasonal, interannual and long term frequencies are used to evaluate the space geodetic reference frame results in terms of accuracy and stability. The ability to detect motions induced by the global geophysical fluids is evaluated.

G31A-04

Atmospheric Delay Modelling in GPS Analysis and its Influence on Geocenter and Earth Rotation

A three-parameter continued fraction of the form 1/sin(elevation) is usually used in the analyses of GPS data as an analytic expression for mapping the atmospheric zenith delay to the line-of-sight. The coefficients 'a' of this continued fraction form are either simple functions of day of year and station coordinates (Niell Mapping Functions (NMF) or Global Mapping Functions (GMF)) or they are determined from numerical weather models (Isobaric Mapping Functions (IMF) or Vienna Mapping Functions (VMF)). Biases and other systematic differences between the mapping functions cause systematic changes of the station coordinates and influence in particular the station heights. As these biases are different in various regions of the Earth, apparent effects like geocenter motion, flattening of the Earth and variations in x- and y-pole can be created when using obsolete mapping functions. These effects especially occur at annual periods. The influence of the differences between the mapping functions mentioned above is simulated by using ERA40 data (40 years Re-Analysis data from the European Centre of Medium-Range Weather Forecasts). These simulations are compared with results from one year of GPS analysis with the GAMIT/GLOBK software.

G31A-05 INVITED

The Impact of Source Structure on VLBI Measurements

The current limitation of vlbi data analysis is caused predominantly by troposphere and instrumental errors, but also at some level by the extended brightness distribution of the observed radio sources, which are only imperfect fiducial points in the sky at the milliarcsecond scale. Such radio structures give rise to ''structural'' effects in the VLBI measurements, which vary with the length and orientation of the VLBI baselines relative to the source brightness distribution, causing extra ''noise'' for the more extended sources. Temporal evolution of these structures may also result in apparent source position shifts over time when combining observations at several epochs. While these effects have a direct impact on the celestial frame, they also affect at some level Earth rotation and geodetic measurements. This paper will discuss the magnitude of these effects for the sources that are part the International Celestial Reference Frame, especially for those that are routinely used in Earth rotation measurements. It will also review the progress made so far in reducing such errors by including models of source structure in the VLBI data analysis process.

G31A-06

Operational numerical simulations of short-term atmospheric and oceanic induced variations of Earth's rotation and coordinates of the geocenter

Circulation and tidal induced mass redistributions in the atmosphere-ocean system affect the Earth's rotational parameters and the geocenter on timescales from hours to decades. While seasonal to interannual signals in atmosphere and oceans are mainly attributed to the general circulation, subdaily to fortnightly mass redistributions are dominated by gravitational as well as pressure induced tidal effects. In contrast to the oceans, gravitational tides in the atmosphere can almost be neglected, but pressure variations principally caused by the combined effects of sunlight absorption of water vapor and ozone heating can be observed down to the Earth's surface, which cause in turn additional oceanic tides due to pressure loading. Since atmospheric conditions are typically described by 6-hourly analysis fields, semidiurnal pressure variations cannot be properly resolved. Therefore, ECMWF's 3-hourly short-range forecasts are combined with corresponding analyses to describe atmospheric variability down to subdiurnal timescales. The resulting atmospheric fields are used as forcing conditions for simulations with the Ocean Model for Circulation and Tides (OMCT) in order to estimate the oceanic response and, thus, short-term mass redistributions in the atmosphere-ocean system and corresponding influences on nutation, polar motion, length-of-day, and coordinates of the geocenter. Since operational atmospheric data are available within a few days only, atmospheric and oceanic mass variations as presented here can be provided on an operational basis relevant, e.g., for high-resolution Earth rotation parameters and a separation of gravitationally and pressure induced oceanic tides.

G31A-07 INVITED

Viscous and Electromagnetic Coupling at the Core Mantle Boundary

Differential rotation between the liquid core and the solid mantle generates a thin layer at the top of the core where the Lorentz and viscous forces may balance the Coriolis forces and play a major role. We solve the induction and the momentum equation to compute the velocity and the magnetic field in boundary layer. Different regimes are possible. On a hand, when the difference of conductivity between the mantle and the core is small, a pure magnetic case may take place where induced electrical currents are produced in a skin layer and loop into a conductive solid layer in the mantle. On an other hand, given that the fluid in the outer core is likely to be subject to turbulence, we can assume an Ekman layer based on eddy viscosity of $10^{-1} m^2/s$, such a pure viscous case where an Ekman layer generate a viscous skin at the base of the mantle is possible as well. A visco-magnetic regime where both, viscous and magnetic torques work together to balance the change in angular momentum and influence the Earth's axis of rotation is also investigated. A study of the effects of the small scales of the imposed magnetic field on the magnetic torque is done. It shows that for this non-linear model, the contribution of the unknown part of the magnetic spectra is weak even with the hypothesis of high energy for degrees above 13. Results are compared with previous approaches, in particular with the weak magnetic field approximation (Buffett et al, 1992). Using the result of the nutation theory (Mathews et al, 2002) we show that in order to retrieve VLBI (Very Long Baseline Interferometry) data, the presence of a viscous boundary layer in the electromagnetic skin layer at the CMB, with its additional dissipative torques is necessary. An apparent Ekman number at the top of the core between $3$ and $5\;10^{-11}$ is inferred depending on the electrical conductivity of the mantle. Moreover, the magnetic field at the C.M.B is comparbale to the observed one, smaller than the value find by previous authors with an inviscid analysis (Buffett et al, 2002).

G31A-08

Mantle Dynamics and the Long-Term Rotational Stability of the Earth

The long term (10-100 Ma) rotational stability of a dynamic, evolving Earth is a classic problem in geophysics framed by a series of seminal studies (e.g., Gold, 1955; Goldreich and Toomre, 1969). Gold (1955), for example, considered the stability of a hydrostatic planet subject to an imperfectly compensated (internal or external) load. In this case, the hydrostatic bulge provides no long-term rotational stability and the reorientation of the pole, or so-called true polar wander (TPW), would be governed solely by the location of the load. In particular, a mass excess of any size (indeed, as small as Gold's beetle) would drive a TPW that would eventually reorient the load to the equator. Gold's (1955) arguments were extended by Goldreich and Toomre (1969) who demonstrated that a group of anomalous masses moving randomly on the surface (the classic set of scurrying beetles) could drive rapid (relative to the speed of the masses) reorientation of the rotation pole. This inherent instability of the rotation axis appears to be at odds with observational evidence for a relatively stable rotation axis over the last 200 Ma. Previous studies have attempted to explain this stability through some combination of a high viscosity (sluggish) lower mantle and/or a relatively fortuitous distribution of mantle heterogeneity. We will present a new set of predictions of long term TPW based on a suite of three-dimensional convection simulations initiated using seismically-inferred mantle heterogeneity. These simulations, which are constrained by recent estimates of the radial profile of mantle viscosity (Mitrovica and Forte, 2004) and which also incorporate the stabilizing influence of a heterogeneous lithosphere, yield a suite of simple conditions governing rotational stability in the post-Jurassic Earth.