An Upper Bound on Rg to Lg Scattering Using Modal Energy Conservation

We use conservation of energy to place an upper bound on Lg generated by explosions through Rg scattering. We assume that all energy in Rg scatters very rapidly into the higher mode surface waves that make up Lg. We consider Rg generated directly by the explosion source and by a collocated but possibly shallower compensated linear vector dipole (CLVD) source. Rg scattering may be a viable mechanism for generating Lg at low frequencies (<1 Hz), but at higher frequencies Lg generated directly by the CLVD or explosion source is comparable to or greater than the upper bound on Lg generated by Rg scattering. For shallow sources at frequencies up to 2-3 Hz the direct CLVD waves may be smaller than the direct explosion or the upper bound limit on the scattered waves. Either the direct waves or scattering from the spherical explosion Rg will dominate over scattering from the CLVD generated Rg at all frequencies.