Earthquakes and other earth movements

by John Milne

Nature of Elastic Waves and Vibrations.—When it is stated that an earthquake consists of elastic waves of compression and distortion, the student of physics has a clear idea of what is meant and a knowledge of the mechanical laws which govern such disturbances. The ordinary reader, however, and the majority of the inhabitants of earthquake countries, who of all people have the greatest interest in this matter, may not have so clear a conception, and it will, therefore, not be out of place to give some general explanation on this point.

The ordinary idea of a wave is that it is a disturbance similar to that which we often see in water. Waves like these must not, however, be confounded with elastic waves. A disturbance produced in water, say, for instance, by dropping a stone into a pond, is propagated outwards by the action of gravity. First, a ridge of water is raised up by the stone passing beneath the surface. As this ridge falls towards its normal position in virtue of its weight, it raises a second ridge. This second ridge raises a third ridge, and so on. The water moves vertically up and down, whilst the wave itself is propagated horizontally.

To understand what is meant by elastic waves, it is first necessary to understand what is meant by the term elastic. In popular language the term elastic is confined to substances like india-rubber, and but seldom to rock-like materials, through which earthquake waves are propagated. India-rubber is called elastic because after we remove a compressive force it has a tendency to spring back to its original shape. The elastic force of the india-rubber is in this case the force which causes it to resist a change of form. Now, a piece of rock may, up to a certain point, like the india-rubber, be compressed, and when the compressing force is removed it will also tend to resume its original form. However, as the rock offers more resistance to the compressing force than the india-rubber offers, we say that it is the more elastic. It may be here observed that a substance like granite offers great resistance, not only to compression or a change of volume, but also to a change of form or shape; whereas a substance like air, which is also elastic, only offers resistance to compression, but not to a change of shape.

With these ideas before us we will now proceed to consider how, after a body has been suddenly compressed or distorted, this disturbance is propagated through the mass. For the elastic body let us take a long spiral spring hung from the ceiling of a room and kept slightly stretched by a weight. If we give this weight an upward tap from below, say with a hammer, we shall observe a pulse-like wave which runs up the spring until it reaches the ceiling of the room. Here it will, so to speak, rebound, like a billiard ball from the end of a table, and run towards the weight from which it started. Whilst this is going on we may also observe that the weight is moving up and down.

Here, then, we have two distinct things to observe—one being the transmission of motion up to the ceiling, which we may liken to the transmission of an earthquake wave between two distant localities on the earth’s surface, and the other being the up and down motion of our weight, which we may compare to the backward and forward swinging which we experience at the time of an earthquake.

These two motions—namely, the pulse-like wave produced by the transmission of motion, and the backward and forward oscillation of the weight or of any point on the spring—must be carefully distinguished from each other.

First, we will consider the backward and forward motion of the weight. The distance through which the weight moves depends upon the force of the blow. The number of up and down oscillations it makes, say in a second, depends upon the stiffness of the spring. The weight, supposing it to be always the same, will move more quickly at the end of a stiff spring than at the end of a flaccid one; that is to say, its velocity is quicker. As in any given spring the number of up and down oscillations are always the same in a given interval of time, if these oscillations are of great extent, the weight must move more quickly with large than with small oscillations.

At the time of an earthquake the manner in which we are moved backward and forward is very similar to the manner in which the weight is moved. If we stand on a hard rock-like granite, we are to a great extent placed as if we were attached to a stiff quickly-vibrating spring. If, however, we are on a soft rock, it is more like being on a loose flaccid spring.

All that has thus far been considered has been a backward and forward kind of motion, where there is a rectilinear compression and extension amongst the particles on which we stand.

We might, however, imagine our rock, which for the moment we will consider to be a square column, to be twisted, and thus have its shape altered. When the twisting force is taken off it seems evident that the column would endeavour to untwist itself or regain its original form. Now the force which a body offers against a change of volume may be very different from that which it offers against a change of form.