Earthquakes and other earth movements

by John Milne

With the exception of the determination for the two last disturbances these calculations have been made with the assistance of the method of Seebach, which depends, amongst other things, on the assumptions of exact time determinations, direct transmission of waves from the centrum, and a constant velocity of propagation.

Admitting that our observations of time are practically accurate, it appears that the other assumptions may often lead to errors of such magnitude that our results may be of but little value.

From what has been said respecting the velocity with which earth disturbances are propagated, it seems that these velocities may vary between large limits, being greatest nearest to the origin.

If we refer to Seebach’s method, we shall see that a condition of this kind would tend to make the differences in time between various places, as we recede from the epicentrum, greater than that required for the construction of the hyperbola. The curve which is obtained would, in consequence, have branches steeper than that of the hyperbola, and the resultant depth, obtained by the intersection of the asymptotes of this curve with the seismic vertical, indicates an origin which may be much too great.

Another point worthy of attention, which is common to the method of Mallet as well as to that of Seebach, is the question whether the shock radiates directly from the origin, or is propagated from the origin more or less vertically to the surface, and then spreads horizontally. We know that earthquakes, both natural and artificial, may be propagated as undulations on the surface of the ground, and that the vertical motion of the latter, as testified by the records of well-constructed instruments, has no practical connection with the depth from which the disturbance originated.

In cases like these, the direction of cracks in buildings, and other phenomena usually accredited to a normal radiation, may in reality be due to changes in inclination of the surface on which the disturbed objects rested. When our points of observation are at a distance from the epicentrum of the disturbance which, as compared with the depth of the same, is not great, calculations or observations based on the assumption of a direct radiation of the disturbance may possibly lead to results which are tolerably correct. The calculations of Mallet for the Neapolitan earthquake appear to have been made under such conditions.

For smaller earthquakes, and for places at a distance from the seismic vertical of a destructive earthquake, the results which are deduced from the observations on shattered buildings, and all observations based upon the assumption of direct radiation, we must accept with caution.

Another error which may enter into calculations of this description is one which has been discussed by Mallet at some length. This is the effect which the form and the position of the focal cavity may have upon the transmission of waves.

Should the impulse originate from a point or spherical cavity, then we might, in a homogeneous medium perhaps, regard the isoseismals as concentric circles, and expect to find that equal effects had been produced at equal distances from the epicentrum. Should, however, this cavity be a fissure, it is evident that even in a homogeneous medium the inclination of the plane of such a cavity will have considerable effect upon the form of the waves which would radiate from its two walls.

For example, let it be assumed that the first impulse of an earthquake is due to the sudden formation of a fissure, rent open from its centre, and that the waves leave the walls at all points normal to its surface. Then, as Mallet points out, it is evident that the disturbance will spread out in ellipsoidal waves, the greatest axis of which will be perpendicular to the plane of the fissure.