Chandler Wobble and Frequency Dependency of the Ratio Between Gravity Variation and Vertical Displacement for a Simple Earth Model with Maxwell or Burgers Rheologies

International audienceTo study the Earth global deformation at periods ranging from a few hours to a few thousand years, we consider a homogeneous compressible Earth model with either a Maxwell or a Burgers rheology. First, we compute, for the harmonic degree l = 2, the ratio between the gravity variation and the vertical surface displacement due to surface loading as a function of the forcing period. In the elastic domain, up to the relaxation time of the rheological model, which is 226 years, the ratio is almost constant and equal to -0.26 µGal/mm. In the viscoelastic domain, above 10,000 years, the ratio tends to -0.08 µGal/mm. In between, the transition is smooth. Second, we compute the period TCW and quality factor Qanel of the Chandler wobble as a function of the rheological parameters of a Burgers model. The influence of both the steady-state and transient viscosities on TCW is significant only forviscosity values smaller than what can usually be found in the literature for the mantle viscosities and Qanel is more sensitive than TCW to the transient viscosity