EARTHQUAKE MOTION AS DEDUCED FROM EXPERIMENT.
Experiments with falling weights—Experiments with
explosives—Results obtained from experiments—Relative motion
of two adjacent points—The effect of hills and excavations
upon the propagation of vibrations—The intensity of artificial
disturbances—Velocity with which earth vibrations are
propagated—Experiments of Mallet—Experiments of Abbot—Experiments
in Japan—Mallet’s results—Abbot’s results—Results obtained in
Japan.
_Experiments with Falling Weights._—A series of experiments, as the
nature of the disturbance produced in the surface of the earth when
a heavy weight is allowed to fall on it, was begun in November 1880
by Mr. T. Gray and the author. These experiments were carried out at
the Akabane Engineering Works in Tokio. The weight used was a ball
of iron weighing about a ton, which in the different experiments was
allowed to fall from heights varying between ten and thirty-five feet.
The position of the place where the ball was allowed to fall was such
that in one direction the vibrations were transmitted up the side of
a steep hill, in another direction across a pond with perpendicular
sides, and in another direction across a level plain the material of
which consisted for the most part of hardened mud extending to a very
considerable depth. The vibrations produced by the fall of the ball
were transmitted through this hard mud with considerable intensity to a
distance of between 300 and 400 feet.
The object of the experiment was to find the nature of the vibrations
produced in the crust of the earth by such a blow, the velocity of
transmission through this comparatively soft material, the effect of
hills and excavations in cutting off such disturbances, and the law
according to which the amplitude of the vibrations diminishes with the
distance from the source.
A considerable variety of apparatus was used during these experiments,
but the most reliable results were obtained from the records of a
rolling sphere seismograph, which wrote the vibrations on a stationary
plate, and from the records of two bracket seismographs, similar to
Professor Ewing’s horizontal lever seismographs, which gave a record
of the vibrations as two rectangular components on a moving plate of
smoked glass.
[Illustration: FIG. 10.]
The general result as to the nature of the disturbance was that two
distinct sets of vibrations were set up by the blow. In one set the
direction of motion was along a line joining the point of observation
with the point from which the disturbance emanated; in the other set
the direction of motion was at right angles to that line. The nature
of the resultant motion will be gathered from fig. 10, which is taken
from the records drawn by the rolling sphere seismograph at a distance
of 50 feet, 100 feet, and 200 feet respectively from the point where
the ball struck the ground. The direct or normal vibrations reached
the instrument first, and were followed at an interval depending on
the distance of the instrument from the origin by the transverse
vibrations. From the records of these two sets of vibrations as
separated by the bracket seismographs, combined with the known rate of
motion of the glass plate, the velocity of transmission was found to
be, for normal vibrations 446–438 feet per second, and for transverse
vibrations 357–353 feet per second.
The effect of the hill in cutting off the disturbance seemed to be
slight, but the direction of the vibrations which ascended the side
was mostly transverse. The pond, on the other hand, seemed completely
to cut off the disturbance, which, however, gradually crept round the
side, so that only a comparatively small triangular area was in shadow.
The amplitude of the vibrations diminished directly as the distance
increased for some distance from the origin, but at greater distance
the rate of diminution seemed to be slower. The transverse vibration
seemed to die out less quickly than the normal vibrations.[9]
These experiments were afterwards very considerably extended by the
author. In these later experiments charges of from one to two pounds of
dynamite were placed in bore-holes of various depths and exploded by
means of electricity. The results obtained confirmed the conclusions
already arrived at from the former experiments. The experiments on
velocity, however, seemed to indicate that the higher the initial
impulse the greater was the velocity. The velocity of propagation of
the transverse vibrations seemed to approach more and more to that of
the directed vibrations as the distance from the origin of disturbance
increased. Fig. 11 shows the nature of the record obtained from the
explosion of two pounds of dynamite at the bottom of a bore-hole eight
feet deep. These records show the interval of time which elapsed
between the arrival of the normal and the transverse vibrations at
points distant 100, 250, and 400 feet from the bore-hole. In the case
of the 100-feet station it will be observed that the motion towards the
origin is greater than that from the origin. It is also to be noticed
that the period of vibration becomes greater as the distance from the
origin increases.
[Illustration: FIG. 11.—Records obtained at three stations
of the motion of the ground produced by the explosion of 2 lbs. of
dynamite.]
_The Intensity of Artificial Disturbances._—The data which we have at
our disposal for determining the intensity of an earth particle which
has been caused to vibrate by the explosion of a charge of dynamite are
a series of records similar to that given on p. 60. These disturbances
are practically surface movements, and may be compared with the
movements of an earthquake which spreads over an area the radius of
which is great as compared with its depth.
To find the mean acceleration of an earth particle, which quantity
has been taken to represent intensity, during any simple backward or
forward motion of the earth, it will be first necessary to determine
the amplitude of this motion and its maximum velocity, the mean
V^2
acceleration being equal to ———.
2A
[Illustration: FIG. 12.]
The second and third movements in a shock invariably exhibited the
greatest intensity, and to a distance of 400 feet from the origin,
where about three pounds of dynamite had been exploded in a bore-hole
about six feet deep, these intensities decreased directly as the
distance from the origin. The less intense movements also decreased
directly as the distance from the origin to a certain point, but after
that they decreased more slowly. A mean result of the more prominent
vibrations in four sets of experiments is shown in the curve, fig. 12,
where the horizontal measurements represent distance from the origin
in feet, and the vertical measurements mean acceleration in thousands
of millimetres per second.
This curve approximates to an equi-angular hyperbola. The area between
the curve and its asymptotes is proportional to the whole energy of
the shock. The area of the diagram is proportional to the energy given
up to the ground by the explosion of three pounds of dynamite. If we
call the unit shock the effect produced by the explosion of one pound
of dynamite, the above artificial earthquake had an intensity equal to
three.
The only other investigations which have been made in this interesting
branch of observational seismology are those by Mr. Robert Mallet,[10]
and those by General Henry L. Abbot.[11]
_Mallet’s Results._—The velocity with which earth vibrations were
transmitted as deduced by Mr. Mallet were as follows:—
Feet per second
In sand 824·915
In contorted stratified rock, quartz, and slate
at Holyhead 1,088·669
In discontinuous and much shattered granite 1,306·425
In more solid granite 1,664·574
A striking result which was obtained by Mallet in his experiments at
Holyhead was that the transit velocity increases with an increase in
the intensity of the initial shock. Thus with a charge of 12,000 pounds
of powder the transit rate was 1,373 feet per second, whilst with 2,100
pounds the transit rate was 1,099 feet per second. In these experiments
tremors were observed as preceding and following the main shock.
_Abbot’s Results._—The important results obtained by General Abbot are
contained in the following table:—
A. No. of Observation
B. Distance to Station in miles
C. Type of Seismometer
D. Velocity in feet per second
+--+----------------+--------------------------+--------+---+-------+
| A| Date | Cause of Shock | B | C | D |
+--+----------------+--------------------------+--------+---+-------+
| 1| Aug. 18, 1876 | 200 lbs. of dynamite | 5 ± | B | 5,280 |
| 2| Sept. 24, 1876 | Hallet’s Point Explosion | 5·134 | A | 3,873 |
| 3| „ | „ „ „ | 8·330 | B | 8,300 |
| 4| „ | „ „ „ | 9·333 | A | 4,521 |
| 5| „ | „ „ „ | 12·769 | B | 5,309 |
| 6| Oct. 10, 1876 | 70 lbs. dynamite | 1·360 | A | 1,240 |
| 7| Sept. 6, 1877 | 400 „ „ | 1·169 | A | 3,428 |
| 8| „ | „ „ „ | 1·169 | B | 8,814 |
| 9| Sept. 12, 1877 | 200 „ „ | 1·340 | A | 6,730 |
|10| „ | „ „ „ | 1·340 | B | 8,730 |
|11| „ | 70 „ „ | 1·340 | A | 5,559 |
|12| „ | „ „ „ | 1·340 | B | 8,415 |
+--+----------------+--------------------------+--------+---+-------+
A seismometer of type A means that the telescope used in observing the
tremor produced on the surface of a vessel of mercury by the passage of
the shock had a magnification of 6, whilst a telescope of the type B
had a magnification of 12.
The mean velocity given by six observations with type A is 4,225 feet
per second, while that given by the same number with type B is 7,475
feet per second.
[Illustration: FIG. 13.]
If we assume that the first tremor observed in the mercury is to
determine the true rate of transmission, General Abbot tells us that we
must reject all observations made with type A, inasmuch as they do not
reveal the velocity of the leading tremor. However, he also tells us
that a still higher power above 12 might have detected still earlier
tremors.
When gunpowder was the explosive, the observers noted that the
disturbance observed in the mercury took a much longer time to reach a
maximum than it did when dynamite was employed.
It was also observed that explosions fired beneath deep water gave
a higher velocity than similar explosions which took place beneath
shallow water. In the latter case much of the energy was probably
expended in throwing a jet of water into the air.
Another point which was observed appears to have been that the rate
varied with the initial shock. Thus:—
Feet per second
400 lbs. of dynamite gave 8,814
200 „ „ 8,730
70 „ powder (deep) gave 8,415
Also it is probable that the rate of a wave diminished with its
advance. For,
Feet per second
200 lbs. of dynamite gave for 1 mile 8,730
„ „ „ „ 5 miles 5,250
50,000 „ „ „ 8 „ 8,300
„ „ „ „ 13½ „ 5,300
General Abbot’s general conclusions are:—
1. A high magnifying power of telescope is essential in seismometric
observations.
2. The more violent the initial shock the higher is the velocity of
transmission.
3. This velocity diminishes as the general wave advances.
4. The movements of the earth’s crust are complex, consisting of many
short waves first, increasing and then decreasing in amplitude; and
with a detonating explosive the interval between the first wave and
the maximum wave, at any station, is shorter than with a slow burning
explosive.
_Results obtained in Japan._—From some experiments made by the author
in the grounds of the Meteorological Department in Tokio, the following
results were obtained:—
A. Velocity in feet per second for the first 200 ft. (A to B)
B. Velocity in feet per second for the second 200 ft. (B to C)
C. Velocity in feet per second for 400 ft. (A to C)
D. Number of Cartridges of Dynamite (6 = 1 lb.)
+--------------------+-----+-----+-----+------+
| No. of Explosion | A | B | C | D |
+--------------------+-----+-----+-----+------+
| { I. | 464 | 186 | 265 | 8·3 |
| Vertical { III. | -- | 211 | -- | 10·1 |
| vibrations { IV. | 352 | 234 | 281 | 7·1 |
| { V. | 343 | 232 | 277 | 5·0 |
| Normal { VI. | -- | -- | 407 | 10·0 |
| vibrations { VII. | -- | -- | 516 | 12·5 |
| Transverse } VIII. | -- | -- | 344 | 12·5 |
| vibrations } | | | | |
+--------------------+-----+-----+-----+------+
The general results to be deduced from the above appear to be:—
1. For vertical motion.
(_a_) For the first 200 feet. The velocity depends upon the initial
force—the greater the charge of dynamite the greater the
velocity.
(_b_) For the second 200 feet. The above law only appears in
experiments IV. and V., but it must be remembered that the
origins of I. and III. were farther removed from A than IV.
and V.
The speed of the wave during the second 200 feet is always less
than during the first 200 feet.
2. For normal vibrations.
Here the speed between A and C is all that was measured, but we
again see that the greater the initial force, or the nearer
we are to the origin of the disturbance, the greater is the
velocity. This velocity is greater than the velocity of the
vertical or transverse vibrations.
3. For transverse vibrations.
If we assume that the vertical vibrations are a component of the
transverse motions we see the same law as before—namely, that
the nearer we are to the origin of the disturbance the greater
is the speed with which that disturbance is propagated.
It will be observed that the chief law here enunciated respecting the
decrease in speed of earth vibrations is the same as that pointed
out by General Abbot, from which it only differs by its being in all
cases proved without the introduction of personal errors, for the same
explosion, along the same line of ground and for different kinds of
vibrations.