Elastic models of the mantle corresponding to variations in the external gravity field

Abstract

Static earth-tide theory was modified to include interior loads expressible as spherical harmonics, and elastic moduli were assumed to be functions of radius only. Variations of density from this model and the corresponding stress distributions in the crust and mantle were calculated to correspond to observed variations in the gravitational field plus the surface topography up to 4th-degree spherical harmonics. These solutions were made determinate by imposing the condition of minimization of strain energy. For the elastic parameters derived from seismology, the maximum stress difference obtained from the discrepancy between the observed and equilibrium flattenings of the earth was 163 bars. The maximum stress difference found for the sum of all other terms was 97 bars in the lower mantle and 300 bars in the crust. Displacements were always less than 70 meters. Modifications of the solution which take into account finite strain, creep, and viscous deformation are discussed. A model consisting of a fluid layer 35 to 400 km deep and a rigidity ½ seismic in the rest of the mantle results in a reduction, of the maximum stress difference in the mantle to 54 bars and an increase of the maximum displacement to 1500 meters.