The small and large lags of the elastic and anelastic tides. The virtual identity of two rheophysical theories

TL;DR

This paper demonstrates the fundamental equivalence of two recent tidal theories, highlighting their similarities and differences in elastic and anelastic components, and extends observational results to determine Earth's anelastic tide phase.

Contribution

It shows the mathematical equivalence of the creep tide theory and Maxwell model, clarifying their differences as a numerical factor, and applies this to Earth's tidal phase analysis.

Findings

The two theories are mathematically equivalent except for a numerical factor.

The geodetic lag of Earth's tide is close to zero.

The phase of Earth's semi-diurnal anelastic tide is approximately 89.80 degrees.

Abstract

The aim of this letter is to discuss the virtual identity of two recent tidal theories: the creep tide theory of Ferraz-Mello (Cel. Mech. Dyn. Astron. 116, 109, 2013) and the Maxwell model developed by Correia et al. (Astron. Astrophys. 571, A50, 2014). It includes the discussion of the basic equations of the theories, which, in both cases, include an elastic and an anelastic component, and shows that the basic equations of the two theories are equivalent and differ by only a numerical factor in the anelastic tide. It also includes a discussion of the lags: the lag of the full tide (geodetic), dominated by the elastic component, and the phase of the anelastic tide. In rotating rocky bodies not trapped in a spin-orbit resonance (e.g., the Earth) the geodetic lag is close to zero and the phase of the semi-diurnal argument in the anelastic tide is close to 90 degrees. The results obtained from combining tidal solutions from satellite tracking data and from Topex/Poseidon satellite altimeter data, by Ray et al., are extended to determine the phase of the semi-diurnal argument in the Earth's anelastic tide as sigma_0=89.80 \pm 0.05 degrees.