The explicit scalar equations of infinitesimal elastic-gravitational motion in the rotating, slightly elliptical fluid outer core of the Earth

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Smith (1974) derived a set of scalar equations of infinitesimal elastic-gravitational motion for a rotating, slightly elliptical Earth. In the fluid outer core (FOC), the tangential tractions vanish identically and the differential equations for the transverse displacement fields do not hold any longer, but the derivative of the transverse displacements are needed in other differential equations, it is therefore the purpose of this paper to get the derivative of the transverse displacements as well as other differential equations in an explicit and ready-to-program format. Our derivation is shown to be more direct and explicit than that suggested by Smith (1974).