A simple digital filter for the geophysical excitation of nutation

A simple digital filter is derived for application to studies concerning geophysical excitation of nutation. Attention is focused on the inverse solution, i.e., inferring the excitation function from the time-series of the celestial pole offsets observed by very long baseline interferometry (VLBI). Filter properties are discussed by comparing its transfer function with that of the original differential equation of nutation. An excellent agreement in both the amplitude and phase response is shown at frequencies between −5 and + 5 cycles per year, which is the frequency band with expected geophysical signals. The difference appears at higher frequencies, leading to a spurious oscillation produced by the filter. This undesired effect is considered and the algorithm enabling its removal is described.