By taking a number of cases of fissures lying in various directions and drawing the ellipsoidal waves which would result from an elastic pressure, like that of steam suddenly admitted into such cavities, the differences in effect which would be simultaneously produced by these waves on reaching the surface can be readily understood. The following example of an investigation on this subject will serve as an example to illustrate the general nature of the many other cases which might be taken.
Fig. 33.
Let a disturbance simultaneously originate from all points of the fissure f f. This will spread outwards in ellipsoidal shells to the surface of the earth e e. The major axis of these ellipsoidal shells will be the direction of greatest effect. In the direction c d the waves will plunge into the earth, and places to the right side of the fissure will, to use an expression due to Stokes, when speaking of analogous phenomena connected with sound, be in earthquake shadow. The same expression has been employed, somewhat differently, when speaking of the effects produced on buildings.
For places, like s and p, situated at equal distances from the seismic vertical, it is evident that the intensity of the shock will be different, and also its time of arrival. It will also be observed that the isoseismals will take the form of ovals or distorted ellipses, the larger or fuller end of which being to the left of the fissure.
Other cases, like those just given, which are discussed by Mallet in his account of the Neapolitan earthquake, are where the fissure forms the division between materials of different elasticities. In the hard and more elastic material the waves will be more crowded, the velocity of a wave particle will be greater, and the transit will be quicker than in the less elastic medium.
The result is that the distance of equal effect from the seismic vertical will be greatest in the direction of the more compressible material.
Unless these considerations are kept carefully before the mind when investigating the depth and, we may add, the position and form of the centrum of an earthquake, serious errors may arise.
Greatest depth of an earthquake origin.—A curious but instructive calculation which Mallet made was a determination of the greatest possible depth at which an earthquake may occur. This calculation is based upon the idea that the impulsive effect of an earthquake has an intimate relationship with the height of neighbouring volcanoes, the column of lava supported on a volcanic cone being a measure of the internal pressure tending to rupture the adjacent crust of the earth.
Mitchell, in 1700, virtually propounded this idea, when he suggested that the velocity of propagation of an earthquake was related to the height of such a column.[88]