Latitude dependence of amplitude factor δ for degree 2 tides

Abstract

The study updates the theory of tides by specifying latitude dependence of the gravimetric factor (amplitude factor δ) for diurnal and semidiurnal tidal waves in the oceanless elastic Earth. The strain of an elastic flattened gravitating sphere with latitude-dependent geopotential, density, and Lamé constants is described by a system of sixth-order ordinary differential equations. The elliptical sphere is presented as consisting of layers, with density and elasticity varying as a function of latitude along the sphere surface as mean radiuses of equidensity and equielasticity ellipsoids that cross this surface. Dissipation is taken into account as a logarithmic creep function. Integration of the derived equations allows avoiding the use of approximate methods. The predicted δ factors for degree 2 tides depend on latitude and increase from the equator to the pole by 0.12 to 0.18% for different Earth models. The obtained latitude dependences are compared with superconducting gravimeter (SG) data after including effects associated with the inertial and Coriolis forces, as well as dynamic resonance. The theoretical predictions and the observations show good fit, to hundredths of percent. The average δ factors predicted in this study for the PREM model are intermediate between those computed with the hydrostatic and nonhydrostatic tidal gravity models of Dehant, Defraigne, and Wahr (DDW/H and DDW/NH), while the estimates obtained with reference to the IASP91 model coincide with the DDW/NH results to the fifth decimal digit.