A new method for deriving broad-band polar motion geodetic excitations

While the geodetic excitation χ(t) of polar motion p(t) is essential to improve our understanding of global mass redistributions and relative motions with respect to the terrestrial frame, the widely adopted method to derive χ(t) from p(t) has biases in both amplitude and phase responses. This study has developed a new simple but more accurate method based on the combination of the frequency- and time-domain Liouville's equation (FTLE). The FTLE method has been validated not only with 6-h sampled synthetic excitation series but also with daily and 6-h sampled polar motion measurements as well as χ(t) produced by the interactive webpage tool of the International Earth Rotation and Reference Systems Service (IERS). Numerical comparisons demonstrate that χ(t) derived from the FTLE method has superior performances in both the time and frequency domains with respect to that obtained from the widely adopted method or the IERS webpage tool, provided that the input p(t) series has a length around or more than 25 years, which presents no practical limitations since the necessary polar motion data are readily available. The FTLE code is provided in the form of MatLab function.