A comparison of short-wave and long-wave velocities in layered media
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Ray theory based on Snell's law is strictly valid only when the variation of physical constants is small within a wavelength. In explosion seismology, Snell's law may apply to the arrival times of the ‘first breaks’, but not to those of the seismic ‘reflections’. For a stack of homogeneous, isotropic plane layers, the average velocity at its short-wavelength limit is greater than that at the long-wavelength limit for any given angle of incidence. Considering a few example of layered media, calculations are made for both short-wave and long-wave average velocities as a function of the angle of incidence. The former velocity shows a steady increase with the angle of incidence whereas the latter velocity may sometimes pass through a minimum before attaining its maximum value for horizontal propagation.
KeywordsReflection Arrival Time Average Velocity Steady Increase Isotropic Plane
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