An application of the Haskell-Thomson matrix method to the synthesis of the surface motion due to dilatational waves

The surface motion arising from a plane dilatational wave striking the base of a layered system is obtained by Fourier synthesis using the frequency dependent transmission coefficients which may be computed by the Haskell-Thomson matrix method. Theoretical seismograms illustrating the effect of thin, low-velocity surface layers on the surface motion are constructed from the transmission coefficients of four crustal models.