Analysis of very long baseline interferometry data indicates that systematic errors in prior estimatesof baseline length, of order 5 cm for • 8000-km baselines, were due primarily to mismodeling of the electrical path length of the troposphere and mesosphere ("atmospheric delay"). Here we discuss observational evidence for the existence of such errors in the previously used models for the atmospheric delay and develop a new "mapping" function for the elevation angle dependence of this delay. The delay predicted by this new mapping function differs from ray trace results by less than • 5 ram, at all elevations down to 5 ø elevation, and introduces errors into the estimates of baseline length of •< 1 cm, for the multistation intercontinental experiment analyzed here.

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Gravitational and pressure couplings between the solid inner core and the rest of the Earth give rise to torques through which the inner core influences the nutational motions of the Earth. In view of the very small magnitude of the moment of inertia of the inner core relative to that of the the Earth as a whole, one expects from physical considerations that inclusion of the inner core in the dynamics should lead to a new nutational normal mode with a natural frequency not too far from that of the free core nutation, and to an associated weak resonance in the amplitude of forced nutations. We present here a treatment of the nutation problem for an oceanless, elastic, spheroidally stratified Earth, with the dynamical role of the inner core explicitly included in the formulation. As a preliminary to the setting‐up of dynamical equations, we devote some attention to a careful definition of a suitable coordinate system and of certain basic dynamical variables. We use the approach of Sasao et al. (1980), with their system of dynamical equations enlarged by the inclusion of two additional equations which are needed to describe the rotational motion of the inner core. An extension and sharpening of a line of reasoning employed by them enables us to derive expressions for the torques which couple the mantle and the fluid outer core to the solid inner core. Solving the enlarged system of equations, we show that a new nearly diurnal eigenfrequency does emerge; a rough estimate places it not very far from the prograde annual tidal excitation frequency, so that possible resonance effects on nutation amplitudes need careful consideration. Another eigenfrequency, attributable to a wobble of the inner core, is also found; its value is estimated to be a few times smaller than the wobble frequency that the inner core would have in the absence of couplings to the rest of the Earth. Considering an expansion, in terms of resonance contributions, of the amplitude of forced nutations normalized relative to that for a corresponding rigid Earth model, we indicate how the coefficients in the expansion are related to those in expansions of the type used by Wahr (1981b). Finally, we discuss the problem of comparing observed nutation amplitudes with those computed on the basis of Earth models generated from seismological data, with special reference to the fact that the dynamical ellipticity of the Earth, as computed from published Earth models which assume the condition of hydrostatic equilibrium, differs significantly from that determined from the precession constant. Numerical results, corrections for unmodeled effects, and comparison with observational results will be dealt with in accompanying papers.

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We apply the theory developed in Paper 1 (Mathews et al., this issue), which includes the solid inner core explicitly in the dynamical equations, to obtain the eigenfrequencies and other characteristics of the Earth's nutational normal modes as well as the amplitudes of forced nutations at various tidal frequencies, for two commonly used Earth models, 1066A and the Preliminary Reference Earth Model (PREM). We also make an evaluation of various procedures for taking account of known deviations of the Earth from models, notably in the dynamical ellipticity e for which the two models yield values which are over 1% smaller than the value e* deduced from the precession constant. On adopting the procedure of simply replacing e by e* in the equations of our theory, the values obtained for some of the nutation amplitudes for model 1066A differ significantly from the corresponding results of Wahr (1981b). The largest of the differences, which occur in the prograde semiannual, retrograde 18.6 year, and retrograde annual nutation terms, amount to −0.59, 0.35, and −0.25 milliarcseconds (mas), respectively, while the standard errors in the very long baseline interferometry (VLBI) determinations are now only about 0.04 mas except in the long period terms. The difference in the procedures used to take account of the discrepancy between e and e* contributes −0.56, 0.81, and −0.17 mas, respectively, to the above‐noted differences. For the purpose of comparison with VLBI‐observed data, we use the results for a “modified PREM,” defined by a set of Earth model parameters which differ from those of PREM only in having e* for the dynamical ellipticity of the Earth as a whole and a modified value for the dynamical ellipticity eƒ of the fluid outer core. The amplitudes computed for this model, with corrections applied for the effects of ocean tides and mantle anelasticity, are in generally satisfactory agreement with observed values, when the modified eƒ is determined by matching the theoretical and observed values for the retrograde annual term. (The modified eƒ is 0.002665, about 4.6% higher than in PREM, equivalent to an increase, relative to PREM, of about 430 meters in the difference between the equatorial and the polar radii of the core‐mantle boundary. We find that contributions from inner‐core dynamics to the prograde semiannual and annual, and the retrograde 18.6 year and annual terms, recomputed for modified PREM, amount to −0.09, 0.03, −0.36, and −0.09 mas, respectively.) The largest residual remaining, other than in the long‐period terms which still have an uncertainty of about 1 mas, is −0.25 mas in the prograde fortnightly amplitude. Consideration of possible sources of the discrepancies is facilitated by a resonance expansion of the amplitude of forced nutations, as a function of frequency, normalized relative to that for a rigid Earth model. We also provide tables which exhibit the sensitivities of various relevant quantities (the eigenfrequencies and the coefficients which appear in the resonance expansion, as well as t...

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We discuss the application of Kalman filtering techniques to the analysis of very long baseline interferometry (VLBI) data. The VLBI observables are geometrically related to the geodetic and astrometric parameters which can be determined from them. However, contributions to the observables from the clocks at, and the atmospheres above, the VLBI sites must be accounted for if reliable estimates of geodetic and astrometric parameters are to be obtained. Here an implementation of a Kaiman filter to account for stochastic behavior on those parameters which vary during the course of a VLBI experiment is discussed. Both the nature of the stochastic processes which should be used in the model for the VLBI data and the implementation of the Kaiman filter estimator are considered. From the results obtained, we conclude that the Kaiman filter is appropriate for analyzing VLBI data. The choice of stochastic model does not unduly affect the estimates of the geodetic parameters and the quality of these estimates is higher than that for conventional weighted least squares estimators.