Empirical Earth Rotation Model: a Consistent Way to Evaluate Earth Orientation Parameters
It is customary to perform analysis of the Earth’s rotation in two steps: first, to present results of estimation of the Earth orientation parameters in the form of time series based on a simplified model of variations of the Earth’s rotation for a short period of time, and then to process this time series of adjustmentsby applying smoothing, re-sampling and other numerical algorithms. This approach suffers from self-inconsistency: the total set of Earth orientation parameters depends on a subjective choice of the apriori Earth orientation model, crosscorrelations between points of the time series are lost, and results of an operational analysis per se have a limited use for end users. Here, an alternative approach of direct estimation of the coefficients of expansion of Euler angle perturbations into basis functions is developed. These coefficients describe the Earth’s rotation over the entire period of observations and are evaluated simultaneously with stationpositions, source coordinates and other parameters in a single LSQ solution. In the framework of this approach considerably larger errors in apriori EOP model are tolerated. This approachgives a significant conceptual simplification of representation and estimation of the Earth’s rotation.
The empirical Earth rotation model from VLBI observations
Aims. An alternative to the traditional method for modeling the kinematics of the Earth's rotation is proposed. The purpose of developing the new approach is to provide a self-consistent and simple description of the Earth's rotation in a way that can be estimated directly from observations without using intermediate quantities. Methods. Instead of estimating the time series of pole coordinates, the UT1–TAI angles, their rates, and the daily offsets of nutation, the method for estimating coefficients of the expansion of a small perturbational rotation vector into basis functions is proposed. The resulting transformation from the terrestrial coordinate system to the celestial coordinate system is formulated as the product of the a priori matrix of a finite rotation and an empirical vector of a residual perturbational rotation. In the framework of this approach, the specific choice of the a priori matrix is irrelevant, provided the angles of the residual rotation are small enough to neglect their squares. The coefficients of the expansion into the B -spline and Fourier bases, together with estimates of other nuisance parameters, are evaluated directly from observations of time delay or time range in a single least square solution. Results. This approach was successfully implemented in a computer program for processing VLBI observations. The dataset from 1984 through 2006 was analyzed. The new procedure adequately represents the Earth's rotation, including slowly varying changes in UT1–TAI and polar motion, the forced nutations, the free core nutation, and the high frequency variations of polar motion and UT1.
Geophysical model of the dynamical flattening of the Earth in agreement with the precession constant
SUMMARY The dynamical flattening of the Earth, as observed by geodetic tech#ques, is different by about 1 per cent from the value associated with the PREM,density profile with hydrostatic equilibrium. In this paper, we compute a new dynamical flattening H induced by PREM mean density with hydrostatic equilibrium, to which we add lateral heterogeneities associated with ( 1) seismic velocity variations observed by tomography and (2) internal boundary topographies. First, we compute mantle circulation associated with the density anomalies derived from a tomography model. The flow-induced boundary deformations are then converted into additional mass anomalies which are added to the tomography model for computing the associated perturbation to the Earth’s inertia tensor. Finally, we show that it is possible to obtain a dynamical flattening from the total inertia tensor (i.e. the sum of the PREM inertia tensor and of the perturbation) in agreement with that observed.