On the Surface Waves of Earthquakes.

Abstract

There can be litt,le doubt that the oscillatory character of the portion of a seismic disturbance arriving later than the P and S phases and their reflexions, and variously known as the third phase, the principal portion, and the main shock, is due to dispersion ; that is, to a dependence of the wave-velocity upon the period. This view was put forward by Love in 1911 in his Problems of Geodynarnics, but it does not appear that subsequent investigators of these waves have given much attention to the general theory of dispersion, mainly due to Kelvin. I n particular, Stoneley, in the above paper, is the first to point out that a particular period is propagated, not with the wavevelocity, but with the group-velocity, and that dispersion by itself introduces a progressive reduction of amplitude as the waves travel, which is comparable in amount with the observed reduction usually attributed to damping. The principal reason for regarding dispersion as the explanation of the oscillatory character of the principal portion is that the P and S phases do not show any marked periodicity, while their durations are very small fractions of that of the principal portion. These facts make it practically impossible that the periodicity is due to a periodic character of the initial shock itself. The arrival of different waves a t a station a t different times is then definite evidence that they travel with different velocities. Further, it has been shown by Love that in a heterogeneous crust such as covers the earth two different types of surface waves exist, both of which are subject to dispersion.