Читать книгу A Study of Recent Earthquakes - Charles Davison - Страница 17

Mallet's Method of Determining the Depth of the Focus.—In ascertaining the position of the epicentre, Mallet's work was remarkable only for the novelty of the method employed by him; but, in his attempt to calculate the depth of the seismic focus, he was breaking new ground. That the depth must be comparatively small had already been recognised, and was indeed obvious from the limited area disturbed by nearly every earthquake. No one, however, had tried to estimate the depth in miles; and it is impossible not to sympathise with Mallet while he accumulated his observations with feverish activity and subjected them to the first rough examination even if one cannot share his confidence that he had succeeded in measuring the depth "in miles and yards with the certainty that belongs to an ordinary geodetic operation."

Fig. 11.—Diagram to illustrate Mallet's method of determining depth of seismic focus.ToList

The method employed by him for the purpose is no less simple theoretically than that used for locating the epicentre. If the position of the latter (E) is known, one accurate measurement of the angle of emergence EPF, at any other point P would be sufficient to fix the depth of some point within the focus F (Fig. 11). Here, again, Mallet relied chiefly on fissures in walls that were fractured but not overthrown. In detail, these fissures are nearly always jagged or serrated, for they tend to follow the lines of joints rather than break through the solid stone, though they sometimes traverse bricks and mortar alike. But the general course of the fissures, he urged, would be at right angles to the wave-path, and their inclination to the vertical should be equal to the angle of emergence.

In obtaining measurements of this angle, the buildings to be chosen are those of large size, with few windows or other apertures, and with walls made of brick or small short-bedded stones. The cathedral-church at Potenza perhaps satisfies these conditions more closely than any other structure examined by Mallet. The plan of the fissures in the walls and roof has been given in Fig. 5, and Fig. 12 represents the fissures In the vertical section along the axial line and looking north, as drawn by the cathedral architect. From these fissures Mallet calculated the mean angle of emergence at Potenza to be 23° 7'. The distance of Potenza from Caggiano being seventeen miles, and the height of the former being 2,580 feet, the depth of the focus resulting from this observation alone would be 6¾ miles below the level of the sea.

Fig. 12.—Vertical section of Cathedral Church at Potenza. (Mallet.)ToList

Objection to Mallet's Method.—The weakest point in Mallet's method is probably his assumption that the wave-paths are straight lines extending outward from the focus. Even if the depth of the focus is not more than a few miles, the waves must traverse rocks of varying density and elasticity, and, at every bounding surface, they must undergo refraction. If the rocks are so constituted that the velocity of the earth-waves in them increases with the depth, then the wave-paths must be bent continually outwards from the vertical, so that the angle of emergence at the surface may be considerably less than it would have been with a constant velocity throughout. In this case, the actual depth will be greater, perhaps much greater, than the calculated depth. For instance, if the angle of emergence at Potenza were diminished only 5° by refraction, the calculated depth of the focus would be too small by 1¾ miles.

Fig. 13.—Diagram of wave-paths at seismic vertical of Neopolitan earthquake. (Mallet.)ToList

Mallet's Estimate of the Depth of the Focus.—Mallet measured the angle of emergence at twenty-six places, the mean angle (i.e. the mean of the greatest and least observed angles) varying from 72° at Vietri di Potenza and 70° degrees at Pertosa, which are about two miles from the calculated epicentre, to 11½° at Salerno, distant about 40 miles. Fig. 13 reproduces part of the diagram on which he plotted the mean angle of emergence at different places. The horizontal line represents the level of the sea, and the vertical line one passing through the epicentre and focus, called by Mallet the "seismic vertical." The lines on the left-hand side represent the commencing wave-paths (assumed straight) to the observing stations situated to the westward of the meridian through the epicentre, those on the right-hand side corresponding to places to the eastward of the same meridian. Small horizontal marks are added to indicate the depth in miles below the level of the sea.

It will be seen, from this diagram, that all the wave-paths start from the seismic vertical at depths between three and nine miles; but the points of departure are clustered thickly within a portion, the length of which is about 3½ miles and the mean depth about 6½ miles. So great was Mallet's confidence in these calculations that he assigns the diverging origin of the wave-paths to different points of the focus, and thus concludes that, while the mean depth of the focus was about 6½ miles, its dimensions in a vertical direction did not exceed 3½ miles.

How far Mallet's results should be accepted as correct, it is difficult to say in our ignorance of the constitution of the earth's interior. There can be no doubt that the focus was of considerable size, and that, in consequence, the wave-paths would diverge from different points of it. But that each wave-path should actually intersect the focus, and so enable its magnitude to be determined, would surely involve an approach to some law connecting the direction of a wave-path with the depth of its own origin, and no such law seems to be ascertainable. Nor can the limitation of these apparent origins between certain depths be held to argue that the focus, or any part of it, was equally confined, for the wave-paths would to a great extent be similarly refracted. I fear that the only conclusions that we can with safety draw from Mallet's admirable work are that his figures indicate the order of magnitude both of the vertical dimensions and of the mean depth of the focus.