Estimation of Earth interior parameters from a Bayesian inversion of very long baseline interferometry nutation time series

Among the variations in the rotation of the Earth, the nutation is the most suitable for studying the Earth's internal structure. The nutation is mainly driven by the gravitational torque of the Moon, the Sun and the planets acting on its equatorial bulge. The Earth response to this external forcing is influenced by its internal structure. Because the gravitational forcing is known to a very good accuracy, the high precision nutation observations, using the very long baseline interferometry (VLBI) technique, allow to estimate Earth interior parameters. The nutational response of the nonrigid Earth to the gravitational forcing has previously been modeled by a semianalytic model which depends on parameters, related to the Earth interior, that are adjusted on the nutation observations. Those parameters are the dynamical ellipticities of the whole Earth and fluid core, compliances describing the deformability of the whole Earth and fluid core, and coupling constants related to the torques generated by the differential rotation of the mantle, fluid core and solid inner core. Most of the nutation models are frequency domain models so that, in previous studies, the time series of observations are processed before the fit in order to get data in the frequency domain. Because the parameters are fit only on the twenty dominant terms in the frequency domain, this fit leads to a loss of information. In this paper, we present a new fit procedure of the nutation model to the observations, which estimates the Earth's parameters directly from the time series of nutation data. This allows to use all the information of the time domain data and to account for the time variable uncertainties on the data (this time variability is due to the improvement of the measurement techniques). Rather than the linearized least squares method used in previous studies, we use a probabilistic (Bayesian) inversion method. This method does not rely on the assumption that the model is linear in its parameters, it is thus particularly well-suited for the highly nonlinear nutation model. In addition, we include an additional parameter to allow for uncertainties in the nutation model itself. This parameter is estimated jointly with the geophysical parameters. As result, we obtain a probability distribution on the parameters. The numerical results are compared with those obtained from previous studies.