Symmetry of the wave equation and excitation of body waves

The symmetry of the differential system for elastic waves, previously noted for plane geometry, is extended to any linear differential system and, in particular, the elastic-gravitational vibrations in a spherical earth. The result remains valid in a linearly viscoelastic medium. The symmetry allows the inverse of the propagator matrix to be obtained by simply ‘transposing’ the elements of the propagator. With this result, it is shown how the source excitation using a particular integral can be put in a more instructive form, comparable with the result for the excitation of normal modes.