Surface wave energy from point sources in plane layered Earth models

The total energy contained in a surface wave can be computed from its propagation-corrected spectrum by integrating over the surface of the earth and over the depth of the wave guide. The former requires knowledge of the radiation pattern of the source. The latter requires only a knowledge of the variation of physical properties with depth. In this paper the depth integration is performed for a continental and an oceanic earth model for three Rayleigh modes and four Love modes. The results are presented in tables and graphs in such a way that it is convenient to convert an observed surface wave displacement or displacement spectrum to total energy density. If the surface radiation pattern is known, the surface integration then yields the total energy in the observed spectrum. The partioning of energy between surface wave modes is computed for several simple sources at the surface and at depth, making it possible to estimate the energy contained in frequency bands or modes which are inaccessible for direct analysis. The increasing importance of the higher modes in the total energy budget at short periods and for channel depth sources is demonstrated. The shapes of the spectrums are diagnostic of source orientation and depth.