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A method for calculating the static displacement field following earthquake faulting in a layered spherical earth is presented. At shallow levels, the Earth's layering is characterized by sharp jumps in bulk and shear moduli at the Conrad discontinuity and the Moho and is therefore important to consider when evaluating crustal deformation. The solution to the equations of static equilibrium is represented as a superposition of spheroidal and toroidal components that each depend on spherical harmonic degree and the moment tensor. A method that has recently been applied to the problem of wave propagation on a layered spherical earth is here applied to the static deformation field. By representing the point source in terms of discontinuities in the displacement-stress vector, the Green's function for a particular source geometry is derived directly. Numerical tests are presented to verify the accuracy of the method and to illustrate the effects of sphericity and layering on the calculated deformation fields. The effect of sphericity is generally less than about 2 per cent (of maximum deformation) within 100 km of an earthquake source at crustal depths. Comparisons between the deformation calculated on a spherical homogeneous earth and spherical layered earth show that up to 20 per cent errors would be introduced if the Earth's layered structure were ignored. The effect of layering is strongest for sources with a strong horizontal slip component.
Fred F. Pollitz (Mon,) studied this question.