30 SECTIONAL ADDRESSES 



namely, that of two horizontal strata in which the velocities of propagation 

 of longitudinal disturbances are v^ in the upper and v^ in the lower 

 stratum. The condition that V2 is greater than v-^^ is essential to the 

 method. From the point of view oi plane wave propagation the limiting 

 ray-path would be from the upper surface to the interface, incidence 

 upon which would be at the critical angle 0, given by sin = v^^jv^, then 

 horizontally in the lower medium just grazing the interface, with final 

 emergence, also at the critical angle, into the upper medium to reach the 

 surface again. The first and last parts of the path would be at the 

 velocity v^^ ; the intermediate part would be at the higher velocity v^. 

 Assuming, for the moment, that this represents the path of a real and 

 finite disturbance, it is easy to see that while, at short ranges, the direct 

 disturbance travelling close to the upper surface will reach the seismo- 

 graph first, at sufficiently great distances the reverse will be true. The 

 indirect disturbance, having in part of its path the advantage of the higher 

 velocity in the lower medium, overtakes the direct one which travels all 

 the time in the upper medium with the lesser speed. It spurts, as it were, 

 and is thus able to cover a longer total distance in the same, or even less, 

 time: And if we can measure the instants of arrival of the initial dis- 

 turbance at various distances from the source, including ranges great 

 enough for the indirect disturbance to arrive first, we have at our disposal 

 means of calculating, by very simple geometry, the depth of the interface. 

 But the indirect path described, if the cori-esponding waves are plane, 

 is of no practical interest, because no energy is associated with it ; the 

 conditions clearly imply total internal reflection. Yet the fact remains 

 that disturbances do reach distant points at times consistent with the course 

 indicated. Their appearance in the records of near earthquakes, where 

 the sphericity of the layers of the earth's crust is insufficient to account 

 for the magnitude of the eff"ects observed, led Jeff'reys * to investigate the 

 problem as one of diffraction. He showed on this basis that a small, but 

 finite, disturbance of the nature and apparent speed actually observed 

 was to be expected. The argument, it is true, was limited to the case of 

 two fluids separated by a horizontal interface ; and, strictly, the applica- 

 tion to the solid media of the earth's crust still lacks adequate theoretical 

 justification. But there is no doubt that experimentally, both in regard 

 to natural earthquakes and the seismic prospecting method, the assump- 

 tion of similar paths of propagation depending on diffraction has led in 

 many cases to reasonably certain determination of sub-surface dis- 

 continuities. Moreover, in the solid material of rocks there is more scope 

 for the judicious application of the diffraction principle, since transverse 

 as well as longitudinal disturbances are propagated, and changes from 

 one type to the other may occur at each interface. 



The principles of the method can be readily applied to structures less 

 simple than a single horizontal interface ; and the observations obtained 

 in the field, plotted on time-distance graphs, enable such features as the 

 slopes and curvatures of strata, and the depths of more than one suc- 

 cessive bed to be recognised under favourable conditions. For success 

 the principal requirement is a large velocity-ratio as between the rocks 

 * Pyoc. Camb. Phil. Soc, vol. 23, p. 472 (1926). 



