Читать книгу A Study of Recent Earthquakes - Charles Davison - Страница 16

Mallet's Method of Determining the Position of the Epicentre.—In many cases the examination of a damaged building or of an overthrown body served more than one purpose, providing materials for ascertaining the depth of the seismic focus as well as the position of the epicentre. For the present, however, it will be convenient to consider alone the method by which the latter object was to be attained.

Fig. 4.—Diagram to illustrate Mallet's method of determining position of epicentre.ToList

Nothing could be simpler than the principle of the method proposed. The horizontal direction PL of the wave-path at any place P (Fig. 4), when produced backwards, must pass through the epicentre E; and the intersection of the directions at two places, P and Q, must therefore give the position of the epicentre. In practice, it is of course impossible to determine the direction with very great accuracy, and Mallet therefore found it necessary to make several measurements in every place, and to visit all the more important towns within and near the meizoseismal area.

In a ruined town there are many objects from which the direction may be ascertained, the most important of all, according to Mallet, being fissures in walls that are fractured but not overthrown. He regarded such fissures, indeed, as "the sheet-anchor, as respects direction of wave-path, to the seismologist in the field," and at least three out of every four of his determinations of the direction were made by their means. If the buildings are detached and large, simple and symmetrical in form, well built and not too much injured, the fissures in the walls should, he argued, occur along lines at right angles to the wave-path, whether that path be parallel or inclined to the principal axis of the building. Cracks in the floors and ceilings should also be similarly directed, and provide evidence which Mallet regarded as only second in value to that given by the walls.

Fig. 5.—Plan of Cathedral Church at Potenza. (Mallet.)ToList

No building showed the different kinds of evidence on which Mallet relied as clearly as the cathedral church at Potenza, the plan of which is given in Fig. 5, and the vertical section along its axis in Fig. 12. This is a modern work, nearly 200 feet long, with its axis directed east and west. The walls are composed of fairly good rubble masonry and brick; and the arches in the nave and transepts, the semi-cylindrical roof and the central dome are made of brick. The fissures represented in both diagrams were drawn to scale by the cathedral architect before Mallet's arrival, and, as the work of an unbiassed observer, are of special value. Most of those in the roof, it will be seen, were transverse to the axial line of the church; but there were others parallel to this line, one in particular running right along the soffit of the nave and chancel. There were also numerous small fissures in the dome, due to local structural causes and therefore of varying direction, and a large portion of the dome slipped westward, leaving open fissures of seven to eight inches in width. The mean direction of the wave-path, as deduced from nine sets of fissures, none of which differs more than four degrees from the mean, is W. 2½° S. and E. 2½° N., which corresponds precisely with the direction of throw on the displaced portion of the dome. The great east and west fissures in the arch of the nave and chancel Mallet attributed to a second shock, of the existence of which there is ample evidence.

Fig. 6.—Fallen gate-pillars near Saponara. (Mallet.)ToList

Next to fissures, Mallet made most use of overthrown objects, such as the two gate piers near Saponara, represented in Fig. 6. They were made of rubble ashlar masonry, three feet square and seven feet in height. Both were fractured clean off at the level of the ground, the mortar being poor, and fell in directions that were accurately parallel, indicating a wave-path towards S. 39½°E. A few observations were also made on projected stones, fissures in nearly level ground, and the swinging of lamps and chandeliers; but their value was small, except as corroboration of the more important evidence afforded by fissures in the walls and roofs of buildings.

Remarks on Mallets Method.—It would have been more difficult in Mallet's day than it is now, to offer objections to his method of determining the position of the epicentre. The focus, as he was well aware, could not be a point, and, at places near the epicentre (the very places where most of his observations were made), there must be rapid changes of direction due to the arrival of vibrations from different parts of the focus. He records the occurrence of the so-called vorticose shocks at several places, though he attributes them to another cause. Perhaps the best known example of such a shock is that which has been so well illustrated by the late Professor Sekiya's model of the motion of an earth-particle during the Japanese earthquake of January 15th, 1887. The motion in this case was so complicated that the model was, for simplicity, made in three parts, the first of which alone is represented in Fig. 7.[10] It is clear that in such an earthquake, Mallet's method would utterly fail in giving definite results.

While this shock was one of great complexity, another Japanese earthquake, that of June 20th, 1894, was unusually simple in character. The movement at Tokio consisted of one very prominent oscillation with a total range of 73 mm. or 2.9 inches in the direction S. 70° W.; the vibrations which preceded and followed it being comparatively small. Most, if not all, of the damage caused by the earthquake must have been due to this great oscillation; and yet the cylindrical stone-lamps so common in Japanese gardens were found by Professor Omori to have fallen in many different directions. Taking only those which had circular bases, twenty-nine were overthrown in directions between north and east, sixteen between east and south, eighty-one between south and west, and fourteen between west and north.[11] Fig. 8 represents Professor Omori's results graphically, the line drawn from O to any point being proportional to the number of lamps which fell in directions between 7½° on either side of the line.

Fig. 7.—Model to illustrate the motion of an earth-particle during an earthquake. (Sekiya.)ToList

Fig. 8.—Plan of directions of fall of overturned stone-lamps at Tokio during the earthquake of 1894.ToList

It will be seen from this figure that most of the stone lamps fell in directions between west and south-west, and it is remarkable that the mean direction of fall is S. 70° W.,[12] which is exactly the same as that of the great oscillation. Somewhat similar results were obtained by this able seismologist at different places affected by the great Japanese earthquake of 1891 (Figs. 43 and 44), and the study of the apparent directions observed during the Hereford earthquake of 1896 leads to the same conclusion.

It thus appears that an isolated observation may give a result very different from the true direction. Indeed, if we may judge from Professor Omori's measurements in 1894, the chance that a single direction may be within five degrees of the mean direction is about 1 in 9. But, on the other hand, it is equally clear from these and other observations that the mean of a large number of measurements will give a result that agrees very closely with the true direction.

One other point may be alluded to before leaving Professor Omori's interesting observations. It would seem, from the list that he gives, that he exercised no selection in his measurements, but continued measuring the direction of every fallen lamp indifferently until he had obtained sufficient records for his purpose. Now, if the number of fallen lamps at his disposal had been small, say 12 instead of 144, the mean observed direction would probably have differed from the direction given from the seismograph.[13] But, on the other hand, a preliminary survey without any actual measurements would have revealed at once the predominant direction of overthrow, and a fairly accurate result might have been obtained by neglecting discordant directions and taking the mean of those only which appeared to agree with the mentally determined average.

This, indeed, appears to have been the course followed, more or less unconsciously, by Mallet in his Neapolitan work. "When the observer," he says, "first enters upon one of those earthquake-shaken towns, he finds himself in the midst of utter confusion. The eye is bewildered by 'a city become an heap.' He wanders over masses of dislocated stone and mortar, with timbers half buried, prostrate, or standing stark up against the light, and is appalled by spectacles of desolation. … Houses seem to have been precipitated to the ground in every direction of azimuth. There seems no governing law, nor any indication of a prevailing direction of overturning force. It is only by first gaining some commanding point, whence a general view over the whole field of ruin can be had, and observing its places of greatest and least destruction, and then by patient examination, compass in hand, of many details of overthrow, house by house and street by street, analysing each detail and comparing the results, as to the direction of force, that must have produced each particular fall, with those previously observed and compared, that we at length perceive, once for all, that this apparent confusion is but superficial."

Fig. 9.—Meizoseismal area of Neapolitan earthquake. (Mallet.)ToList

Mallet's Determination of the Epicentre.—Within the third isoseismal line Mallet made altogether 177 measurements of the direction of the wave-path at 78 places. These are plotted on his great map of the earthquake; but, owing to the small scale of Fig. 9, it is only possible to represent, by means of short lines, the mean or most trustworthy direction at each place.[14] Producing these directions backwards, he found that those at sixteen places passed within five hundred yards of a point which is practically coincident with the village of Caggiano; those at sixteen other places passed within one geographical mile (1.153 statute miles) of this point; the directions at sixteen more places within two and a half geographical miles; while those at twelve places passed through points not more than five geographical miles from Caggiano. As the direction of the shock at places near the epicentre must have been influenced by the mere size of the focus, this approximate coincidence is certainly remarkable, and there can be little doubt, I think, that the epicentre, or, at any rate, an epicentre must have been situated not far from the position assigned to it by Mallet's laborious observations.

Existence of Two Epicentres.—It is difficult, however, to realise that the impulse at the focus corresponding to Mallet's epicentre was the origin of all the destruction of life and property that occurred. The position of the epicentre close to the north-west boundary of the meizoseismal area, the extraordinary extension of that area towards the south-east, and especially the great loss of life at Montemurro and the adjoining towns, can hardly be accounted for in this manner. Mallet himself recognised that these facts required explanation, and he suggested that the situation and character of the towns were in part responsible for their ruin, and the physical structure of the country for the course of the isoseismal lines. But the comparative escape of places much nearer Caggiano, and the wide extent of the meizoseismal area, embracing many towns and villages of varied character and site and many different surface-features, point unmistakably to a different explanation.

Fig. 10.—Distribution of death-rate within meizoseismal area of Neapolitan earthquake.ToList

One clue to the solution of the problem is afforded by the seismic death-rate of the damaged towns. From a table given by Mallet (vol. ii. pp. 162–163), we know the population before the earthquake of the different communes in the province of Basilicata, and the loss of life in each due to the shock; and from these figures we can find the percentage of deaths at nearly every place of importance. As will be seen from Fig. 10, it varies from seventy-one at Montemurro and fifty at Saponara down to less than one at all the places marked to which figures are not attached. There is thus a group of places, with its centre near Montemurro, where the loss of life far exceeded that in the surrounding country; and also a slightly less-marked group, with its centre near Polla, in the north-west of the meizoseismal area; while in the intermediate region the death-rate was invariably small. Too much stress should not be laid upon the exact figures, for there were no doubt local conditions that affected the death-roll. But it seems clear that one focus was situated not far from Montemurro; while the north-westerly group of places, combined with Mallet's observations on the direction, point to a second focus near Polla, about twenty-four miles to the north-west. It will be seen in a later section that the observations on the nature of the shock also imply the existence of a double focus.