The swing of mountains.—If an earthquake wave is passing through ground the surface of which is level, so long as this ground is homogeneous, as the wave travels further and further we should expect its energy to become less and less, until, finally, it would insensibly die out. If, however, we have standing upon this plain a mountain, judging from Mallet’s remarks, this mountain would be set in a state of vibration much in the same way as a house is set in vibration, and it would tend to oscillate backward and forward with a period of vibration dependent upon the nature of its materials, size, and form. The upper portion of this mountain would, in consequence, swing through a greater arc than the lower portion, and buildings situated on the top of it would swing to and fro through a greater arc than those which were situated near its foot. This explanation why buildings situated on the top of a mountain should suffer more than those situated on a plain, is one which was offered by Mallet when writing of the Neapolitan earthquake. He tells us that towns on hills are ‘rocked as on the top of masts,’ and if we accept this explanation it would, in fact, be one reason why the houses situated on the Bluff at Yokohama suffered more than those situated in the settlement. This explanation is given on account of the great authority it claims as a consequence of its source. It is not clear how the statement can be supported, as different portions of the mountain receive momentum in opposite directions at the same time.
Want of support on the faces of hills.—When a wave of elastic compression is propagated through a medium, we see that the energy of motion is being continually transmitted from particle to particle of that medium. A particle, in moving forwards, meets with an elastic resistance of the particles towards which it moves, but, overcoming these resistances, it causes these latter particles to move, and in turn to transmit the energy to others further on. So long as the medium in which this transfer of energy is continuous, each particle has a limit to its extent of motion, dependent on the nature of the medium. When, however, the medium, which we will suppose to be the earth, is not continuous, but suddenly terminates with a cliff or scarp, the particles adjacent to this cliff or scarp, having no resistance offered to their forward motion, are shot forward, and, consequently, the ground here is subjected to more extensive vibrations than at those places where it was continuous. This may be illustrated by a row of marbles lying in a horizontal groove; a single marble rolled against one end of this row will give a concussion which will run through the chain, like the bumping of an engine against a row of railway cars, and as a result, the marble at the opposite end of the row, being without support, will fly off. Tyndall illustrates the same thing with his well known row of boys, each one standing with his arms stretched out and his hands resting upon the shoulders of the boy before him. A push being given to the boy at the back, the effect is to transmit a push to the first boy, who, being unsupported, flies forward.
In the case of some earthquakes, most disastrous results have occurred which seem only to admit of an explanation such as this. A remarkable instance of this kind occurred when the great earthquake of 1857 ‘swept along the Alps from Geneva to the east-north-east, and its crest reached the edge of the deep glen between Zermatt and Visp. Then the upper part of the wave-movement, a thousand or two thousand feet in depth from the surface, came to an end; the forward pulsation acted like the breaker of the sea, and heavy falls of rock encumbered the western side of the valley.’
Earthquake shadows.—If a mountain stands upon a plain through which an elastic wave is passing, which is almost horizontal, the mountain is, so to speak, in the shadow of such a wave. If we only consider the normal motion of this wave, we see that the only motion which the mountain can obtain will be a wave of elastic distortion produced by a shearing force along the plain of the base. Should, however, the wave approach the mountain from below, and emerge into it at a certain angle, only the portion of the mountain on the side from which the wave advanced could remain in shadow, whilst the portion on the opposite side would be thrown into a state of compression and extension. Portions in shadow, however, would be subject to waves of elastic distortion. In a manner similar to this we may imagine that certain portions of the bluff, so far as the advancing wave was concerned, were in shadow, and thus saved from the immediate influence of the direct shock. A hypothetical case of such a shadow is shown in the accompanying section, illustrating the contour of the ground at Yokohama. The situation which might be in the shadow of one shock, however, it is quite possible might not be in that of another. We must also remember that a place in shadow for a direct shock might be affected by reflected waves, and also by the transverse vibrations of the direct shock. These effects are over and above the effects produced by the waves of elastic distortion just referred to. It might be asked whether whole countries, like England, which are but seldom shaken, are in shadow.
Fig. 27.—Hypothetical section at Yokohama.
Destruction due to the interference of waves.—Referring to the section of the ground at Yokohama (Fig. 27), it will be seen that both the settlement and the bluff stand upon beds of gravel capping horizontal beds of grey tuff. The gravel of that portion of the settlement on the seaboard originally formed the line of a shingle beach. That portion of the settlement back from the sea stands upon ground which was originally marshy. In the central portions of the settlement this bed of gravel is very thick, perhaps 100 feet or so, but as you near the edge of the bluff it probably becomes thinner, until it finally dies out upon the flanks of the scarps.
On the top of the bluff, the beds of gravel will, in every probability, be generally thinner than they are upon the lower level. The beds of tuff, which is a soft grey-coloured clay-like rock, produced by the solidification of volcanic mud, appear, when walking on the seaboard, to be horizontally stratified. If there is a dip inland, it is in all probability very slight. Here and there the beds slightly faulted. Taken as a whole we may consider these beds as being tolerably homogeneous, and an earthquake in passing through them would meet with but little reflection or refraction. At the junction of these beds with the overlying gravels, both reflection and refraction would comparatively be very great.
On entering the gravel, as the wave would be passing into a less elastic medium, the direction of the wave would be bent towards the perpendicular to the line of junction, and the angle of emergence at the surface would consequently be augmented. At the surface certain reflection would also take place, but the chief reflections would be those at the junction of the tuff and the alluvium.
Under the settlement it is probable that all the reflections which took place would be single. Thus wave fronts like a1 advancing in a direction parallel to the line a1; would be reflected in a direction a2 and give rise to a series of reflected waves a2. These are shown by thicker lines. Similarly all the neighbouring waves to the right and left of a1 would give rise to a series of reflected waves. If the lines drawn representing wave fronts are districts of compression, then, where two of the lines cross each other, there would be double energy in producing compression. Similarly, districts of rarefaction might accord, and, again, compression of one wave might meet with the rarefaction of another and a neutralisation of effect take place. A diagram illustrating concurrence and interference of this description is given in Le Conte’s ‘Elements of Geology,’ p. 115. The interference which has been spoken of, however, is not the greatest which would occur. The greatest would probably be beneath the bluff and the scarps which run down to join the level ground below. This would be the case because it is a probability that there might not only be cases of interference of single reflected waves, but also of waves which had been not only twice but perhaps thrice reflected. For example, a wave like b1 (which is parallel to a1 of the first supposition), advancing in a direction parallel to b1 might be reflected along the line b2 giving rise to waves like b2, which in turn might be reflected along b3 giving rise to waves like b3. The number of districts where there would be concurrence and interference would, in consequence of the number of times waves might be reflected, be augmented. Here the violence of the shock would, at certain points, be considerably increased, but as a general result energy must be lost, so that even if some of the reflected waves found their way into the portion we have regarded as being in shadow, their intensity would not be so great as if they had entered it directly.