The effect of faulting on the moment of inertia of a two-layer planet with Burgers-body mantle

We study the change in the moment of inertia due to shallow faulting in a planet composed of an elastic lithosphere and a viscoelastic mantle. The rheology of the mantle is that of a Burgers body, which is characterized by two viscosity values, η1 and η2, and by two rigidity values, μ1 and μ2. Here η1 is the long-term viscosity, while μ1 is the instantaneous rigidity of the mantle. It is found that an earthquake produces an instantaneous elastic change in the moment of inertia, followed by a long-term viscoelastic change. The viscoelastic change occurs through two jumps with timescales controlled, respectively, by the two viscosity values of the mantle. The magnitudes of the two jumps depend instead upon the ratio μ2/μ1 between the two rigidity values of the mantle. For a thin-lithosphere planet (such as the Earth) the total viscoelastic change in the moment of inertia is four times larger than the elastic change. In this case, it is found that the earlier jump in the moment of inertia would be such as to excite significantly the Chandler wobble only if η2 is at least four orders of magnitude less than η1 and the rigidity μ2 is smaller than the instantaneous rigidity μ1. However, such viscosity values are not compatible with observations of the Chandler wobble period.