G41C-0364
Stochastic modeling of Earth's rotation change and polar motion
The rotation of the Earth exhibits relatively small variation in its rate and in the direction of its axis. The short-term changes (variations over days to years) in the rotation rate (or length of day, LOD) and polar motion (PM) are known to be strongly correlated with time-variability in distribution of mass and momentum in the atmosphere and ocean, and these relations can be approximated well as simple stochastic differential equations. Such stochastic equations have been shown useful for estimation and prediction of LOD and PM based on atmospheric and oceanic parameters (e.g., prediction of LOD using numerical forecasts of atmospheric angular momentum). The stochastic model can also be the basis of using the LOD and/or PM as signatures of some atmospheric or oceanic phenomena (e.g., possibility of verifying model-generated deep ocean circulations through ocean angular momentum). In recent years, the accuracy in the measurements of LOD and PM as well as in the numerical circulation models of atmosphere and ocean has undergone steady improvements, motivating a re-examination of the statistical formulations and parameterizations in the differential-equation model. Results of this re-examination will be presented.
G41C-0365
A Six Year Oscillation in Length-of-Day: Signature of an Inner Core Normal Mode
An approximately 6 yr oscillation has been detected in high resolution time series of length-of-day (LOD) that span the last four decades. The LOD time series has been corrected for the effects of angular momentum exchange with the atmosphere and oceans; therefore, the remaining LOD variations can be attributed to interaction between the mantle and the core. Torsional oscillations of the fluid core are well known to be associated with LOD changes on decadal timescales; however, they can not explain the distinct interannual peak observed in the LOD spectrum. The inner core and mantle are gravitational coupled due to their aspherical density distributions. Misalignment of those density fields produces a restoring torque resulting in a normal of oscillation. The period of this mantle-inner core gravitational normal mode depends on the amplitude of density heterogeneity, which is characterised by a coupling constant. The gravitational coupling constant required to match the observed LOD oscillation falls within the range expected from models of mantle flow and can be used to further constrain such models. Detection of the mantle-inner core gravitational coupling normal mode places a lower bound on the viscosity of the inner core. A sufficiently soft inner core would respond by viscous deformation rather than rotation; the observed 6 yr LOD oscillation implies that the characteristic relaxation time of the inner core is on the order of years or longer, corresponding to a viscosity of at least $10^{17}$ N m.
G41C-0366
Time-varying Annual Signals in Geodetic Observation and in Atmospheric and Oceanic Excitations during 1980-2001
The polar motion is composed of two modes: The annual wobble and the Chandler wobble. The Chandler wobble, containing information on the Earth interior, is extracted from the observed polar motion by removing seasonal signals. However, since the seasonal variations are excited by geophysical fluids (e.g. the atmosphere, the oceans, the land water), the seasonal signals show different patterns year by year. In this study, we examined the time-variations of the annual signals in the observed polar motion and in the atmospheric and oceanic excitations (i.e. AAM and OAM functions) over 22 years. We extracted 7-yr data from these time-series in order to estimate the seasonal variations. We calculate the AAM functions from three meteorological reanalysis data sets available today, with IB hypothesis. The OAM values used in this study are downloaded from the website of the IERS Global Geophysical Fluids Center, Special Bureau for the Oceans. We found that the time-variations of the annual AAM+OAM signals have similar patterns to that of the observed annual signals. That means, on the other hand, the annual terms do not show constant amplitude/phase during the period. We will discuss its effects on the retrieved Chandler signals.
G41C-0367
Estimation of Earth Interior Parameters Based on the Nutation Obsservations in Time Series
The nutation response of the non-rigid Earth to the gravitational forcing by the Moon, the Sun, and the planets has been modeled by Mathews et al. 2002 (MHB2000 model). This model is semi-analytic and depends on some unknown Earth interior parameters, of which the numerical values are adjusted on the nutation data, in order to have a model which fits the observations as well as possible. As the external forcing is mainly periodic, nutation observations are first transformed into a series of amplitudes and phases, at the main relevant frequencies, to which the internal parameters are adjusted. We have developed a nutation model similar to MHB2000, but we choose to work with time series rather than frequency series to adjust the Earth interior parameters. The adjustment is done using a Bayesian (or stochastic) inversion method. This direct estimation allows to avoid the extraction of amplitudes and phases of the main frequencies from the nutation data, to account for the time variable quality of the nutation data, and to estimate the precession and obliquity rate consistently with the other geophysical parameters. In the future, it will allow us to include the response of the Earth to non-periodic forcing in the nutation model (such as, for instance, atmospheric effects).
G41C-0368
Numerical Modelling of True Polar Wander
Paleomagnetic data have shown that the Earth's rotation axis may have drifted with respect to hotspots (i.e., true polar wander) for large horizontal distance over tens of millions of years. This true polar wander is caused by mantle convection that has redistributed the Earth's mass to cause changes in its principle inertia axes. Changes in the inertia tensor also raises the possibility of "inertial interchange events", in which the rotation axis reorients through ninety degrees, which have been hypothesized as major events in Earth history. We formulate a finite element model of the complete rotational behavior of the Earth when submitted to changes in its inertia tensor. While the basic theory of polar wander is well-established (e.g., Monk & MacDonald, 1960), the general problem is highly nonlinear. Current solutions of the problem have therefore employed approximations requiring either small excursions of the pole from its initial location as done in studies of post-glacial rebound, or requiring a viscous quasi-fluid approximation (for timescales of millions of years). We develop a solution to the problem in a time-stepping finite element code without recourse to these approximations. The solution involves computation of the response of the rotational bulge to an imposed load which perturbs the rotation axis via changes to the inertia tensor. We may then observe the time-dependent evolution of the bulge's relaxation. With the same model we may observe the regimes of both approximations: small polar motion at short timescales and large polar motion at long timescales. We compare our results to previous work in both regimes. We also consider the question of rates of polar motion, and its behavior during inertial interchange events.
G41C-0369
Outer Core Dynamics, Rotational Modes, and Tidal Deformation
We have investigated the influence of the outer core structure on the Earth's rotational modes through the squared Brunt-Väisälä frequency $N^2$. The rotational mode frequencies are all imbedded into the continuous spectrum of inertia-gravity modes, which, in the complex domain, is governed by $N^2$ and the Earth's rotation speed. By solving the equations for the normal modes of a rotating ellipsoidal Earth and varying the $N^2$ parameter, we have shown bifurcations between core mode branches and the four rotational modes. For the FICN, a bifurcation results in two modes sharing similar displacements, i.e. an almost rigid wobble of the inner core and oscillations in the outer core. The corresponding eigenperiods in an inertial frame are separated by a few hundred days. The same kind of interaction occurs between core modes and the Chandler wobble of the mantle, the eigenperiods being now a few days apart in a co-rotating frame. The FCN shows much weaker interactions with core modes. Moreover, beside bifurcations similar to the ones for the FICN and Chandler wobble, the interactions between the FCN and core modes may be such that no mode exists for very narrow $N^2$ ranges. The fourth rotational mode is the Chandler wobble of the inner core. To date, its numerical computation still raises difficulties. We have been able to solve only the case $N^2 = 0$, which shows no interaction with core modes. A consequence of our results is that assuming a Poincaré motion in the outer core does not allow for a complete description of the interaction between the rotational modes and the core dynamics, especially for non-Neutrally stratified models. Given that the core dynamics has possibly a significant influence on the motions of the mantle and inner core, we revisit the forced deformation of the rotating Earth. In particular, we investigate the diurnal and long-period tides. Because of the rotational coupling between displacements of different harmonic degrees, the long-period tides simultaneously involve degree 2 and degree 0 (purely radial) displacements. In this paper, we pay special attention to the long-period variations of $J_2$ that are associated to the degree 2 deformation.
G41C-0370
Historical Variations in Inner Core Rotation and Polar Motion at Decade Timescales
Exchanges of angular momentum between the mantle, the fluid core and the solid inner core result in changes in the Earth's rotation. Torques in the axial direction produce changes in amplitude, or changes in length of day, while torques in the equatorial direction lead to changes in orientation of the rotation vector with respect to the mantle, or polar motion. In this work, we explore the possibility that a combination of electromagnetic and gravitational torques on the inner core can reproduce the observed decadal variations in polar motion known as the Markowitz wobble. Torsional oscillations, which involve azimuthal motions in the fluid core with typical periods of decades, entrain the inner core by electromagnetic traction. When the inner core is axially rotated, its surfaces of constant density are no longer aligned with the gravitational potential from mantle density heterogeneities, and this results in a gravitational torque between the two. The axial component of this torque has been previously described and is believed to be partly responsible for decadal changes in length of day. In this work, we show that it has also an equatorial component, which produces a tilt of the inner core and results in polar motion. The polar motion produced by this mechanism depends on the density structure in the mantle, the rheology of the inner core, and the time-history of the angle of axial misalignment between the inner core and the mantle. We reconstruct the latter using a model of torsional oscillations derived from geomagnetic secular variation. From this time-history, and by using published models of mantle density structure, we show that we can reproduce the salient characteristics of the Markowitz wobble: an eccentric decadal polar motion of 30-50 milliarcsecs oriented along a specific longitude. We discuss the implications of this result, noting that a match in both amplitude and phase of the observed Markowitz wobble allows the recovery of the historical rotational variations of the inner core, and also provides constraints on structure, rheology and dynamics of the Earth's deep interior that cannot be observed directly.
G41C-0371
On the Secular Degree 2 Deformation of the Earth
\ Post-glacial rebound (PGR) contributes to global deformation characterized by the degree 2 zonal spherical harmonics. It also moves the Earth_fs principal axis (true polar wander, TPW), resulting in global deformation expressed with the degree 2 tesseral spherical harmonics. Their combined contribution might reach 1 mm/yr (Mitrovica et al., 2001), and could affect estimation of plate motion parameters. Global pattern of mantle convection governs long-wavelength geoid undulation (Hager & Richards, 1989). Antipodal pairs of hot/cold plumes characterize the pattern, and changes in the convection may give rise to degree 2 vertical crustal movements (Gurnis et al., 2000). \ In this study we try to detect degree 2 secular deformation of the Earth from 3-D velocity data of worldwide continuous GPS sites. We looked for vertical velocity field having the shape of zonal, tesseral and sectorial degree 2 spherical harmonics (the latter two have cosine and sine terms), and horizontal velocities proportional to their spatial gradients, using weighted least-squares method. Plate motion parameters (Euler vectors) were estimated simultaneously. With numerical experiments, we confirmed beforehand that the velocity precisions and GPS point distribution are sufficient for the purpose. \ The tesseral and sectorial components were significant with maximum of about 1 mm/year. They are considered real from 3 reasons, i.e. (1) their directions (ratios of cosine and sine terms) were similar for vertical and horizontal fields although estimated separately, (2) the ratios of vertical and horizontal velocity amplitudes (ratio of the secular Love/Shida numbers) were similar for tesseral and sectorial components, and (3) results were robust against tests to split the data set into two. The centers of uplift were, however, located near Indonesia and off the east coast of North America, fairly different from those expected by the current TPW direction. The estimated zonal component was insignificant, which is consistent with the small dJ2/dt from SLR. Correlation between degree 2 parameters and Euler vectors were small; the latter changed little by introducing the former. The pattern of the obtained degree 2 velocity field is somewhat similar to the prediction (Gurnis et al., 2000), but the amplitudes are larger by an order of magnitude.
G41C-0372
Description of Earth Orientation Parameters Using an Approach Based on Stochastic Processes
The International Terrestrial Reference Frame (ITRF) is a key product for scientific users in the field of Geodesy, Astronomy and Geophysics. The last issue (namely ITRF2004) which will be available before the end of 2005 will be the opportunity to introduce Earth Orientation Parameters (EOPs) in addition to the set of station positions and velocities that was currently derived so far. EOP observations are treated in a consistent way with the terrestrial frame by the analysis centers of the various Space Geodesy techniques. Therefore, the intrinsic nature of these parameters is the same as the one of station coordinates. It becomes now classical to adopt a time-series description of station positions, an approach which is already adopted for EOPs. Nevertheless, EOPs are usually combined together with sets of stations coordinates for terrestrial frame computation as if they were not correlated in time, which is certainly not the case. The dynamic equations that connect one parameter at one epoch to the next one are investigated here with the prospective objective of introducing this information while combining sets of station coordinates and EOPs for ITRF computation. Although this link is of stochastic nature, it is however based on physical principles (such as variable components of Liouville equation due for example to atmospheric excitation). These physical principles are also investigated.
G41C-0373
Recent Advancements in the Determination of Earth Orientation Combination Solutions and Predictions
The Earth's orientation is described using five parameters. The longitude and obliquity of the celestial ephemeris pole define the orientation of the Celestial Ephemeris Pole (CEP) with respect to the celestial reference frame. The orientation of the CEP with respect to the terrestrial reference frame is described by the polar motion (PM) parameters x and y, while the measure of the angle about the rotation axis through which the solid Earth has rotated is defined as universal time (UT1). In addition to several practical applications such as navigational correction, Earth Orientation Parameter (EOP) solutions are useful in studying the interaction of the solid Earth with its fluid envelope as well as climate change. Therefore, many users need accurate near-real time EOP solutions with predictions. The International Earth Rotation and Reference Systems Service (IERS) Rapid Service/Prediction Center (RS/PC), located at the U.S. Naval Observatory, combines over 2700 EOP observations produced from space geodetic technique observations, such as Satellite Laser Ranging (SLR), Global Positioning System (GPS), and Very Long Baseline Interferometry (VLBI), to produce a daily EOP solution with predictions. Since the beginning of the IERS combination pilot project, minimally constrained intra-technique combinations are regularly available from all geodetic technique services. Because of the need for more accurate predictions, the RS/PC is constantly looking for better approaches and observations to meet these new requirements. This study examines the RS/PC's recent efforts to improve the daily and weekly IERS Bulletin A EOP solutions and predictions produced using these intra-technique combinations from the International Laser Ranging Service (ILRS), International GNSS Service (IGS), International VLBI Service (IVS), and the International DORIS Service (IDS). Future modifications to the methodology used by the RS/PC for combination and prediction are discussed. These new EOP solutions are compared to the currently available IERS EOP series and the excitation functions computed from atmospheric and oceanic angular momentum estimates from global numerical models.
G41C-0374
Geocenter : notion, definition and realization
Comparison between the geophysical theoretical variations of the geocenter and the ones observed by spatial geodesy is not trivial:the geodetic community works in a reference frame not centered to the center of mass and the initial reference sphere used by the geophysicists is not realistic. Within the frame of the french research group AGRET (Astrometrie, Geodynamique et Systemes de Reference), the geodetic, geophysical and astronomical communities worked together in order to propose a definition of the geocenter and to establish the relations between measurements and geophysical reference frame. We present in this paper the mean conclusions of this working group and we propose some recommendations.
G41C-0375
Comparison of Implementation Strategies of the 2nd-order Ionosphere Correction in GPS Data Processing
The 2nd-order ionospheric delay of the GPS signal has been shown to be a contributing factor to both static and seasonal errors of GPS station positions. Caused by Faraday rotation of the GPS electromagnetic waves traveling through the ionosphere in the presence of the Earth's magnetic field, the effect was demonstrated to contribute a latitude-dependent southward bias of the order of several millimeters to the station position, and a similar size error to the vertical component. Since this 2nd-order error is proportional to the Total Electron Content (TEC) along the signal propagation path, it also displays a semi-annual cycle, which corresponds to seasonal fluctuations of the ionosphere. These seasonal variations mimic similar variations in the uncorrected GPS station position time series. Two approaches to implement the corrections have been proposed in the literature. The first approach is equivalent to applying a time varying epoch-by-epoch linear combination of the L1 and L2 signals, which eliminates higher-order terms. The second approach is based on a calculation of the TEC and a correction to the LC range measurement. We implemented the two methods in the GIPSY-OASIS software package, and compared their accuracy and practicality of their implementation in routine GPS data processing. We have found that although harder to implement, the TEC approach is more precise. The time-dependent method "leaks" about 10% of the correction into a phase bias error, which may also affect the quality of bias fixing. Both methods give rise to latitude dependent seasonal and long term corrections, which may be misinterpreted as geocenter fluctuations if not accounted for.
G41C-0376
First and Second Degree Gravitational Variations From Satellite Laser Ranging
Satellite Laser Ranging (SLR) is a key ingredient for the definition of the Terrestrial Reference System (TRF). SLR defines uniquely the origin and in part the scale of the TRF. Driven by numerous geophysical processes, continuous mass redistribution within the Earth system causes concomitant changes in the Stokes coefficients describing the terrestrial gravity field. Seasonal changes in these coefficients have been closely correlated with mass transfer in the atmosphere, hydrosphere and oceans and they are now routinely monitored from dedicated space missions (e.g. GRACE). The stability, integrity and applicability of the TRF are directly related to the accuracy and fidelity with which such motions can be observed or modeled during the position determination of the defining sites. Variations in the very low degree and order harmonics, produce geometric effects that are manifested as changes in the origin and orientation relationship between the instantaneous and the mean reference frame, as well as the orientation of the axes of figure. SLR has contributed the most accurate weekly observations of these effects yet, demonstrating millimeter level accuracy. Our multi-year TRF definition is done incrementally, adding every week, the new weekly data set, thereby extending the validity of the TRF and thus allowing the accurate observation of several significant geophysical events, recent and in the past, involving mass motion in the hydrosphere and the solid Earth. We now have a new series of weekly results, consistent with the IERS Conventions 2003, using the latest improvements in modeling SLR observations. We will present our results from several years of LAGEOS and ETALON SLR data, assess their accuracy, compare them the previous series, to geophysical signals, and to the monthly series from the GRACE project.
G41C-0377
Development of a New VLBI Sampler Unit Dedicated to e-VLBI for Near Real-Time Monitoring of Earth Rotation
National Institute of Information and Communications Technology (NICT) has developed three models of VLBI samplers, ADS1000, ADS2000 and K5/VSSP, dedicated to near real-time VLBI observation (e-VLBI) through a high-speed network connection for monitoring earth orientation parameters. Among these three models, the K5/VSSP, which is designed to be a PCI bus board mountable on a general purpose PC, has broadened the base for VLBI users, i.e., any PC equipped with the K5/VSSP PCI-bus board can be a VLBI recorder, and the data transfer through the Internet is easily realized. With the advent of K5/VSSP the development of software correlator also greatly progressed. Recently we have developed a new VLBI sampler named K5/VSSP32 as a successor to the K5/VSSP. Maximum sampling frequency is increased up to 32MHz. When the number of quantization bit is limited to one, the sampling frequency of 64MHz is possible. Moreover USB 2.0 (Universal Serial Bus specification revision 2.0) is adopted as an interface to connect the sampler with a host PC. It is hence possible to use note book PCs for VLBI observations if it is desired. Specifications are summarized in Table 1. We will report the results of some test observations using K5/VSSP32 at the meeting. begin{center} Table1. Specifications of VLBI samplers end{center} begin{tabular}{ccccc} hline model & ADS1000 & ADS2000 & K5/VSSP & K5/VSSP32 hline # of CH & 1 & 16 & 4 & 4 per unit & & & & Max & & & & sampling & 1024MHz & 64MHz & 16MHz & 32MHz frequency & & & & # of & 1,2 & 2 & 1,2,4,8 & 1,2,4,8 AD bits & & & & Max data rate & 2048Mbps & 2048Mbps & 64Mbps & 256Mbps per unit & & & & Output & VSI-H & VSI-H & PCI-bus & USB 2.0 hline end{tabular}