Earth tides in MacDonald's model

Abstract

We expand the equations used in MacDonald's 1964 theory and Fourier analyze the tidal variations of the height at one point on the Earth surface, and also the tidal potential at such point. It is shown that no intrinsic law is relating the lag of the tide components to their frequencies. In other words, no simple rheology is being intrinsically fixed by MacDonald's equations. The same is true of the modification proposed by Singer(1968). At variance with these two cases, the modification proposed by Williams and Efroimsky (2012) fix the standard Darwin rheology in which the lags are proportional to the frequencies and their model is, in this sense, equivalent to Mignard's 1979 formulation of Darwin's theory.