The Elasticity Theory of Dislocations in Real Earth Models and Changes in the Rotation of the Earth

Abstract

Summary Steketee's Elasticity Theory of Dislocations is generalized to real Earth models. Taken into account are; (i) self-gravitation, (ii) radial variation of elastic properties, density and gravity, (iii) initial hydrostatic stress, (iv) the presence of the liquid core. Volterra's formula for the displacement field is found to hold in the more general circumstances for slip faults. The dilemma, previously pointed out by Jeffreys and Vicente, which arises when the Adams and Williamson condition is assumed not to hold everywhere perfectly in the core, is resolved. This result also bears on the theory of Earth tides and tidal loading. Changes in the inertia tensor are shown to arise only from spheroidal displacement fields of degree zero and two. These fields have virtually no attenuation with distance from the fault. In the one example in which a direct comparison can be made, the present theory gives a factor of 7.5 increase over a mapped half-space theory and a factor of 2.9 increase over the result for a uniform, spherical Earth, in the contribution to secular polar shift and excitation of Chandler wobble. Calculated and observed levels appear now to be in agreement.