Читать книгу A Study of Recent Earthquakes - Charles Davison - Страница 19

The elements of the wave-motion, as mentioned in the introductory chapter, are four in number, namely, the period, amplitude, maximum velocity, and maximum acceleration. If any two of these are known for each vibration—and the first two are now given by every accurately constructed seismograph—the others can be determined if the vibrations follow the law of simple harmonic motion.[15]

Amplitude.—To ascertain the amplitude, Mallet had to rely chiefly on the fissures made in very inelastic walls. If the parts into which such a wall are fractured are free to move, and yet, being inelastic, obliged to remain in the farthest position to which they are carried by the wave, the distance traversed by the centre of gravity of one of the displaced parts should give a "rude approximate measure" of the horizontal amplitude of the earth-wave. At Certosa, near Padula, he thus found the amplitude to be about 4 inches, at Sarconi about 4¾ inches, and at Tramutola about 4½ inches. From somewhat similar evidence, the amplitude at Polla appears to have been about 2½ or 3 inches; and, from the oscillation of a suspended clock or watch on a rough wall, about 3½ inches at La Sala and 1¾ inches at Barielle. With the exception of Barielle, these places lie nearly on a straight line passing through Mallet's epicentre, and he gives the following table, showing an increase in amplitude with the distance from the epicentre:—

	Polla.	La Sala.	Certosa.	Tramutola.	Sarconi.
Distance in miles	4.0	13.4	19.0	23.8	30.8
Amplitude in inches	2½	3½	4	4½	4¾

The existence of the Montemurro focus must, however, complicate any relation that may connect these two quantities.

Maximum Velocity.—The means at Mallet's disposal for determining the maximum velocity were more numerous than those available for the amplitude. From the dimensions of a fallen column of regular form we should be able, he remarks, to find an inferior limit to the value of the maximum velocity; while a superior limit at the same place may be obtained from some other regular solid which escaped being overthrown. If a loose body is projected by the shock at a place where the angle of emergence is known, the horizontal and vertical distances traversed by the centre of gravity will give the velocity of projection. Or, if two such bodies are projected at one place, the same measures for each will as a rule give both the angle of emergence and the velocity of projection. A third method depends on the fissuring of walls, supposing that we know the force per unit surface which, when suddenly applied, is just sufficient to produce fracture. Sometimes more than one method must be applied to the same object. The two gate-pillars near Saponara (illustrated in Fig. 6) for example required a horizontal velocity of 5.48 feet per second to fracture them, and an additional velocity of 5.14 feet per second to overthrow them.

The well-known seismologist, Professor Milne, urges very forcibly that measurements obtained from the projection or fall of columns are unreliable, for the earlier tremors might cause the columns to rock, and their overthrow need not therefore measure accurately the maximum velocity of the critical vibration.[16] There can be no doubt that Mallet was alive to this difficulty, though he may not have appreciated it at its full value. Thus, at the Certosa de St. Lorenzo, a monastery near Padula, a vase projected from the summit of a slender gate-pier implied a velocity of 21¾ feet per second; and the excess of about 8¼ feet per second above the velocity determined by other means is attributed by him to the oscillation of the pier itself. How far this source of error enters into other observations it is impossible to say; but it is worth noticing how closely the velocities obtained by different methods agree with one another. Thus, from projection only, we have velocities of 11.5 feet per second at the Certosa, 11.8 at Moliterno and Monticchio, 14.8 at Tramutola, and 9.8 feet per second at Sarconi; from overthrow alone, 11.0 feet per second at Viscolione, near Saponara, and 11.6 at Barielle; from overthrow and projection, 13.2 feet per second at Polla and 12.9 at Padula; from fracture and overthrow, 12.3 feet per second at Potenza and 15.6 at Saponara. The comparatively high values at Tramutola and Saponara, Mallet imagined might be due to the oscillation of the hills on which these towns are built. He therefore omits them in calculating the mean maximum velocity, which he finds to be twelve feet per second, a velocity less than that with which a man reaches the ground when he jumps off a table.

With the same omissions, Mallet gives the following table, showing a general decrease in the maximum velocity as the distance from his epicentre increases:—

	Polla.	Padula.	Certosa.	Moliterno.	Sarconi.	Viscolione.
Distance in miles	4.0	19.0	19.0	29.4	30.0	30.8
Max. vel. in ft. per sec.	13.2	12.9	11.5	11.8	11.0	9.8

On the north side of the epicentre we have:—

	Potenza.	Monticchio.	Barielle.
Distance in miles	17.3	27.1	28.2
Max. vel. in ft. per sec.	12.3	11.8	11.6

It is not impossible that the high calculated velocities at Tramutola and Saponara were partly or entirely due to the impulse from the Montemurro focus.

If we take 4 inches for the amplitude of the largest variation, and 12 feet per second for the maximum velocity, and assume the motion to have been of a simple harmonic character, the period of a complete vibration would be less than one-fifth of a second.[17] Now, we know from seismographic records that this is roughly the period of the small tremors that form the commencement of an earthquake-shock, while the period of the largest vibrations may amount to as much as one or two seconds. We may therefore conclude either that the assumption of simple harmonic motion is incorrect, or that the maximum velocity is too great, or more probably perhaps that the amplitude is too small.[18]