On the Calculation of Changes in the Earth's Inertia Tensor due to Faulting

Summary Recent interest has arisen in the possibility that changes in the Earth's inertia tensor accompanying earthquakes may provide the excitation for the ‘Chandler’ wobble of the rotation axis. We present a simple procedure for calculating these changes based on the elastic reciprocal theorem and Volterra's formula. In particular, if t is the shear stress created in the slip direction on a prospective fault surface when a perfect, unfaulted sphere is steadily rotated at unit angular velocity about some axis, then the change in moment of inertia about that same axis is shown to be twice the work of τ when carried through the actual slip displacement which occurs in faulting. It is shown that changes of products of inertia may be computed in a similarly simple way. The method is applied to two homogeneous Earth models, the relation to previous treatments is discussed, and it is noted that inertia changes accompanying less-catastrophic mass movements may be calculated in a similar way. The development in the body of the paper is in the context of classical linear elasticity. An Appendix extends the reciprocal theorem and Volterra's formula, and hence the basis for similar inertia change calculations, to the linearized incremental deformation of self-gravitating, initially stressed elastic systems, such as real-Earth models.