A normal mode expansion for the forced response of a rotating Earth

Summary. It is well known that the forced motion of a conservative physical system can be represented as a sum of the normal modes of that system. Although normal mode expansions have been successfully developed and applied to examine the excitation of a non-rotating earth, these techniques have been less successful when the Earth’s rotation is included. We develop here an expansion formalism for the rotating Earth which completely de-couples all non-trivial normal modes. We consider the response of the Earth both to applied body forces and surface tractions. We consider forces which are purely sinusoidal in time and forces which have power distribution over a continuous frequency interval.