Excitation function reconstruction using observations of the polar motion of the Earth

ABSTRACT. Reconstruction of the excitation functions from the observations of the motion of the Earth’s pole was performed with use of Jeffreys-Wilson filter, regularization, corrective smoothing in the frequency domain. Corrective smoothing procedures found preferable for solv-ing the inverse problem of reconstruction of the excitation functions from observations. Exci-tation functions were reconstructed since 1900 year for chandler and annual components of the polar motion, divided from each other and separated from noise with use of singular spectral analysis (SSA). Excitation was predicted with use of SSA and neural networks (NN). Kalman filter was used for prediction of the trajectory of the pole. 1. DYNAMICAL MODELLING AND RECONSTRUCTION OF THE CAUSES Reconstruction of the excitation functions from the observations of the Earth rotation belongs to the class of the ill-posed inverse problems. So far as different input excitations can produce the motion along the observed trajectory, a priori assumptions should be made. The errors of observations can cause a big deviation of the evaluated excitation from the real one. That’s why it was recommended to use the corrective procedures for solving the ill-posed problems [Tikhonov et al., 1977]. The motion of the pole can be described by the equation [Yatskiv, 2000] i σc dm(t) dt +m(t) = χ(t), (1) where σc = 2πFc(1 + i/2Q). It was suggested to use the values Fc = 0.843 cycles per year and Q = 175 [Vicente, Wilson, 2002]. The frequency characteristic of the system (1) is given by the expression L(f) = σc σc − 2πf. (2) Fig. 1 represents the gain-frequency (GFCh) and phase-frequency (PFCh) characteristics of the system given by (2). The resonance at the chandler frequency can be well seen. When an excitation transfers from one frequency half plane to another, divided by the frequency σc/2π, the phase of the polar motion changes by π. For reconstruction of χ(t) Wilson suggested the filter [Vicente, Wilson, 2002] χ(t) = ie−iπFc∆t σc∆t mt+∆t