Part 9 (2/2)

DEPTH OF THE SEISMIC FOCI.

Two methods of estimating the depth of the seismic focus have been described in the preceding pages--namely, Mallet's, depending on the angle of emergence, and Falb's, based on the interval between the initial epochs of the sound and shock. To these, Major Dutton adds a third method, in which he relies on the rate at which the intensity of the shock varies with the distance from the epicentre.

_Dutton's Method of determining the Depth of the Focus._--If the seismic focus is either a point or a sphere, and the initial impulse equal in all directions, and if the intensity of the shock diminishes inversely as the square of the distance from the focus, then the continuous curve in Fig. 31 will represent the variation of intensity along a line pa.s.sing through the epicentre E. The form of the curve on these a.s.sumptions does not depend in any way on the initial intensity of the impulse; it is governed solely by the depth of the focus. The deeper the focus, the flatter becomes the curve, as we have seen in discussing the Ischian earthquakes (p. 68). In all directions from the epicentre, the intensity at first diminishes slowly; but the rate of change of intensity with the distance soon becomes more rapid, until it is a maximum at the points C, C; after which it again diminishes and dies out very slowly when the distance becomes great. It will be evident from Fig. 18 that the deeper the focus the greater also is the distance EC of the points where the intensity of the shock changes most rapidly. It may be easily shown, indeed, that this distance always bears to the depth of the focus the constant ratio of 1 to sqrt(3), or about 1 to 1.73.[42]

Now, if a series of isoseismals could be drawn corresponding to intensities which differ by constant amounts, we should have a series of circles like those surrounding the Woodstock epicentre in Fig. 29, the distance between successive lines at first decreasing gradually until it is a minimum at the dotted circle and afterwards gradually increasing. This dotted circle is obviously that which pa.s.ses through all points where the intensity of the shock changes most rapidly.

Major Dutton calls it the _index-circle_ and, when its radius is known, the depth of the focus is at once obtained by multiplying the radius by 1.73.

In 1858, Mallet proposed a method which bears some resemblance to the above,[43] but depending only on the intensity of the longitudinal waves. Major Dutton claims for his method that the effects of the longitudinal and transverse waves are not separated, that it takes account of the ”total energy irrespective of direction or kind of vibration.”

[Ill.u.s.tration: FIG. 31.--Diagram to ill.u.s.trate Dutton's method of determining depth of seismic focus.]

_Objections to Dutton's Method._--I have described this method somewhat fully, though it seems to me open to more serious objections than Mallet's first method which it is intended to replace.

We have, in the first place, no reason for supposing that the focus is either a point or a sphere, or that the initial impulse is uniform in all directions. If the earthquake were caused by fault-slipping, both a.s.sumptions would be untrue, and it is for those who employ the method to prove their validity.

But of greater consequence is the fact that, if the method were correct, all earthquakes originating at the same depth must have index-circles of equal radii. If the depth of the focus were, say, ten miles, then the index-circle must have a radius of about six miles, whether the initial disturbance be of extreme violence or so weak that it is not felt at the surface at all, much less so far as six miles from the epicentre. The law of the inverse square is of course only true for a perfectly elastic and continuous medium, and the real curve of intensity is not that of the continuous line in Fig. 31, but something of the form represented by the dotted line. In this case, the rate of change of intensity is greatest at some point C', nearer than C to the epicentre, and the application of Major Dutton's rule would give a point F', nearer the surface than F, for the focus. Thus, a.s.suming that the method can be applied in practice--and the test involved is one so delicate that it would be difficult to apply except with refined measurements--then all that we can a.s.sert is that the calculated depth is certainly less than the true depth.

_Dutton's Estimate of the Depth of the Seismic Foci._--In applying the method, the chief difficulty is to obtain a series of isoseismal lines corresponding to equidistant degrees of intensity. As already pointed out, those given in Fig. 29 are merely diagrammatic; but the index-circle of the Woodstock focus, represented by the dotted line, is made to pa.s.s through the places where the rate of change of intensity was found to be greatest. The radius of this circle being very nearly seven miles, it follows that the resulting depth of the Woodstock focal point would be about twelve miles. Major Dutton regards this estimate as probably correct within two miles.

In the neighbourhood of the Rantowles epicentre, the isoseismals in both Figs. 28 and 29 are elongated in form. The _index-circuit_, as it would be called in such a case, cannot be drawn completely, but its radius parallel to the shorter axis of the curves is about 4-1/2 miles, and the resulting depth of the Rantowles focal point would be nearly eight miles.

VELOCITY OF THE EARTH-WAVES.

The recognition of the double epicentre is, from a geological point of view, the most important fact established by the investigation of the Charleston earthquake. But of equal interest, from a physical point of view, is the estimate of the velocity of the earth-waves, which is probably more accurate than that determined for any previous shock.

Owing to the existence of the standard time system in the United States, the exact time is transmitted once a day to every town and village within reach of a telegraph line; and the effect of small errors in the observations is considerably lessened by the great distance traversed by the earth-waves, sixty good reports coming from places more than 500 miles from the epicentre, and ten from places more than 800 miles distant.

The total number of time-records collected is 316, but of these 130 had to be rejected, either because they were obviously too early or too late, or because they were only given to the nearest five-minutes' interval. There remain 186 observations which are divided by Major Dutton into four cla.s.ses according to their probable value.

In an earthquake of such great duration (about 70 seconds at Charleston), it is necessary in the first place to select some special phase of the movement as that to which the records mainly refer, and then to determine as accurately as possible the time of occurrence of this phase at the origin.

There can be little doubt as to which phase should be chosen. The shock began with a series of tremors, which pa.s.sed somewhat abruptly into the oscillations that formed the first and stronger maximum.

These were clearly felt all over the disturbed area, and, as the beginning of the first maximum at places near the epicentre and the beginning of the shock at distant stations were probably due to the same vibrations, this particular phase may be fairly selected as that to which the time-measurements refer.

The time of this phase at the origin can only be ascertained from the time at which it reached Charleston, and our knowledge of this depends chiefly on the evidence of stopped clocks. How unreliable this may be is well known. Clocks may indeed be stopped at almost any phase of the movement; and, whenever stopped clocks can be compared with really good personal observations, they almost invariably show a later time.

At Charleston three good clocks were stopped by the vibrations from the Woodstock focus, two of them being in close agreement (p. 121); and, allowing for a few oscillations before their final arrest, Major Dutton places the time of arrival of the selected phase at Charleston at 9h. 51m. 12s. P.M. The evidence of these clocks is also supported by that of other observations, which show that 9.51 was certainly the nearest minute to the time of arrival, and favour a somewhat later instant much more strongly than one a little earlier.

Now, the distance of Charleston from the Woodstock epicentre is sixteen miles, and from the corresponding focus (with the calculated value of its depth) twenty miles. A first estimate of the velocity gives a value of a little more than three miles a second, and the time at the Woodstock focus may therefore be taken as 9h. 51m. 6s. with a probable error of a few seconds.[44]

Proceeding to the observations at a distance, we find them, even after all rejections, to be very different in value. They were therefore divided into groups consisting of observations which are as nearly as possible h.o.m.ogeneous.

The first group contains five records from places between 452 and 645 miles from the Woodstock epicentre. They give the time to within 15 seconds, obtained from an accurately kept clock, or from a clock or watch that was compared with such within a few hours of the earthquake. The resulting velocity is 3.236 plus or minus .105 miles (or 5205 plus or minus 168 meters) per second.[45]

In the second group there are eleven observations (between distances of 438 and 770 miles) which satisfy the same conditions as those in the first group, except that the time is only given to the nearest minute or half-minute. The velocity obtained from them is 3.226 plus or minus .147 miles (or 5192 plus or minus 236 metres) per second.

The third group included all but the above records and those obtained from stopped clocks. They are 125 in number (between distances of 80 and 924 miles), but it is uncertain whether they correspond to the selected phase of the movement, and the errors of the clocks and watches used were unknown. They give a mean velocity of 3.013 plus or minus .027 miles (or 4848 plus or minus 43 metres) per second.

In the fourth group, we have the evidence of 45 stopped clocks (at places between 20 and 855 miles), which apparently give a velocity of 2.638 plus or minus .105 miles (or 4245 plus or minus .168 metres) per second. At six places, however, the times indicated by stopped clocks can be compared with good personal observations; and these show that the time of traverse from the origin obtained from the former is on an average 1.28 times the time of traverse obtained from the latter. If a similar correction be made for all the stopped clocks, the corrected velocity of the earth-waves would be from 3.17 to 3.23 miles (or 5100 to 5200 metres) per second.

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