Sensitivity analysis of the non-linear Liouville equation

Abstract

The non-linear gyroscopic model DyMEG has been developed at DGFI in order to study the interactions between geophysically and gravitationally induced polar motion and the Earth’s free wobbles, in particular the Chandler oscillation. The model is based on a biaxial ellipsoid of inertia. It does not need any explicit information concerning amplitude, phase, and period of the Chandler oscillation. The characteristics of the Earth’s free polar motion are reproduced by the model from rheological and geometrical parameters. Therefore, the traditional analytical solution is not applicable, and the Liouville equation is solved numerically as an initial value problem. The gyro is driven by consistent atmospheric and oceanic angular momenta. Mass redistributions influence the free rotation by rotational deformations. In order to assess the dependence of the numerical results on the initial values and rheological or geometrical input parameters like the Love numbers and the Earth’s principal moments of inertia, a sensitivity analysis has been performed. The study reveals that the pole tide Love number k2 is the most critical model parameter. The dependence of the solution on the other mentioned parameters is marginal