THE AMPLITUDE AND CHARACTER OF REFRACTION WAVES

Abstract

In seismic exploration it is assumed that elastic waves can be refracted into and out of a high speed medium at the angle of total reflection and meanwhile travel along the interface between the two media. That such a path is in agreement with the general theory of elastic waves has been proved by Muskat. The present paper is an extension of the work of Muskat, and shows in addition that the general theory can explain the low amplitude and low frequencies of these refracted waves, and is otherwise in agreement with observation. Equations are developed for the effect at any point of the low speed medium of an impulse or of a periodic disturbance initiated at any other point of the same medium. Details are worked out for the case where the recorder is so situated that the refracted wave arrives first. The direction of the arriving wave is found to be that of the angle of total reflection, and its amplitude to diminish with the square of the distance from the shot point—in agreement with Muskat. The amplitude of the refracted wave is also found to be only a small fraction of that of the direct wave, or of that of the reflected wave which arrives still later. The motion produced by the refracted wave is found to be a unidirectional pulse which lasts until the arrival of the direct wave. Finally, the appearance of a record of motion is given for certain assumed numerical data. For this case it is found that the average amplitude of the refracted wave is 8 per cent of that of the direct wave.