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Abstract

Normal mode theory is applied to investigate the phenomenon of refraction along an embedded highspeed layer. At any single frequency an infinite number of normal modes exist, each of which is characterized by some propagation constant. The real and imaginary parts of the propagation constant respectively specify the phase velocity and attenuation constant for the disturbance. It is shown that at low frequencies both a symmetric and an antisymmetric unattenuated mode exist. At higher frequencies, these modes transform into attenuated modes which continually radiate energy from the layer into the surrounding medium. Some computed properties of the symmetric attenuated mode for a specific set of elastic parameters are consistent with model seismic studies. The phase velocity curve exhibits a distinct plateau region for wavelengths in the vicinity of three times the layer thickness. In this region the refraction velocity corresponds to that of extensional waves in a thin plate while the attenuation is approximately 8 db per wavelength.

It seems that the simple concept of group velocity has little physical meaning in this study. Group velocities greater than the P-wave velocity are obtained and cannot possibly correspond to the velocity with which energy is propagated.

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