PP and crustal structure

Haskell's formulation for reflection of P waves at the base of a solid crust is extended to include overlying liquid layers. Normalized displacement and the phase shift at the base of the crust as a function of angle of incidence and frequency are calculated for two continental models and an oceanic model. Complex reflection coefficients are inverse Fourier transformed to the time domain to show the change of pulse shape upon reflection. These time traces show that the water layer of the oceanic model causes the main difference between continental and oceanic reflections. Sample seismograms from a deep shock were compared to the theoretical records; they were found to be consistent. It is concluded that the amplitude ratio PP/P as a function of frequency obtained from seismograms can be used to decipher the detailed structure at the point of reflection only after the radiation pattern of the source, attenuation of waves during propagation, and crustal transmission response at the receiver are properly taken into account.