The small and large lags of the elastic and anelastic tides

The virtual identity of two rheophysical theories

Instituto de Astronomia Geofísica e Ciências Atmosféricas, Universidade de São Paulo, 05508-090 São Paulo, Brasil
e-mail: sylvio@iag.usp.br

Received: 14 February 2015
Accepted: 18 May 2015

Abstract

The aim of this paper is to discuss the virtual identity of two recent tidal theories: our creep tide theory and one Maxwell model recently developed. 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 semidiurnal argument in the anelastic tide is close to 90 degrees. The results obtained from combining tidal solutions from satellite tracking data and from the Topex/Poseidon satellite altimeter data are extended to determine the phase of the semi-diurnal argument in the Earth’s anelastic tide as σ₀ = 89.80 ± 0.05 degrees.