Remarks on refraction arrivals from a layer of finite thickness

I would like to discuss an unsolved problem which is particularly important from the practical point of view and to show on the basis of physical intuition in which direction the solution might lie. It deals with the character of the refraction arrival through a layer of finite thickness. One cannot arrive at conclusions regarding the character of the refraction arrival by studying only the disturbance which has traveled along the refraction path. To illustrate this point, consider a situation (Fig. 1) where the refracting layer is 5,000 feet deep and 100 feet across. In normal refraction work, the source-detector separation will be at least three times the depth to the refracting layer. our case, this corresponds to a shot distance of 15,000 feet. This means that the difference in the lengths of path traversed by the refracted ray and the ray which has been reflected once from the bottom of the layer is of the order of a foot. The wavelengths which are used in refraction work correspond to frequencies in the neighborhood of 10 cps. It follows that if the velocity in the refracting layer is 10,000 ft/sec, the ratio of wavelength to path difference is of the order of a thousand to one. In other words, a whole series of multiply reflected waves arrive within a time interval corresponding to one period. Therefore, in order to arrive at any conclusion regarding the character of the refraction arrival, one must consider the result obtained by superimposing all the waves which have been reflected at nearly grazing incidence.