EARTHQUAKE MOTION AS DEDUCED FROM OBSERVATION ON EARTHQUAKES.
Result of feelings—The direction of motion—Instruments as indicators
of direction—Duration of an earthquake—Period of vibration—The
amplitude of earth movements—Side of greatest motion—Intensity
of earthquakes—Velocity and acceleration of an earth
particle—Absolute intensity of an earthquake—Radiation of an
earthquake—Velocity of propagation.
_Result of Feelings._—As the result of our experiences, and by
observations upon the movements produced in various bodies, we can
say that an ordinary earthquake consists of a number of backward and
forward motions of the ground following each other in quick succession.
Sometimes these commence and die out so gently that those who have
endeavoured to time the duration of an earthquake have found it
difficult to say when the shock commenced and when it ended. This was
a difficulty which Mr. James Bissett in Yokohama, and the author in
Tokio, had to contend against when, in 1878, they commenced to time
shocks between these two places.
Sometimes these motions gradually increase to a maximum and then die
out as gradually as they commenced.
Sometimes the maximum comes suddenly, and at other times during an
earthquake our feelings distinctly tell us that there are several
maxima.
These have been the experiences of many observers, and have been
recorded by writers since the earliest times. Mallet devotes a
chapter to a consideration of the tremulous motion that precedes and
follows a shock, and he tells us that a single shock is an absolute
impossibility. In speaking of earthquakes, he says: ‘The almost
universal succession of phenomena recorded in earthquakes is, first a
trembling, then a severe shock, or several in quick succession, and
then a trembling gradually but rapidly becoming insensible.’
A quantitative and exact knowledge of the nature of earthquake
motion has only been attained of late years. The chief results which
investigators have aimed at have been the measurement of the amplitude,
the period, the direction, and the duration of the motions which
constitute an earthquake. Attention has also been given to the velocity
with which a disturbance is propagated.
_The Direction of Motion._—One of the most ordinary observations
which are made about an earthquake is its direction. If we were to
ask the inhabitants of a town which had been shaken by an earthquake
the direction of the motion they experienced, it is not unlikely that
their replies would include all the points of the compass. Many,
in consequence of their alarm, have not been able to make accurate
observations. Others have been deceived by the motion of the building
in which they were situated. Some tell us that the motion had been
north and south, whilst others say that it was east and west. A certain
number have recognised several motions, and amongst the rest there will
be a few who have felt a wriggling or twisting. Leaving out exceptional
cases, the general result obtained from personal observation as to
the direction of an earthquake of moderate intensity is extremely
indefinite, and the only satisfactory information to be obtained is
that derived from instruments or from the effects of the earthquake
exhibited in shattered buildings and bodies which had been overturned
or projected.
By the direction in which walls, columns, and other objects had been
overthrown or fractured, Mallet was enabled to determine the position
of the origin of the Neapolitan earthquake. Similar phenomena have many
times been taken advantage of by other investigators of earthquake
phenomena. Effects produced upon structures are, however, only to be
observed as the results of a destructive earthquake, at which time
cities may be regarded as collections of seismometers. (_See_ chapter
on Effects in Buildings.)
To determine the direction of movement during a small earthquake, the
most satisfactory method appears to be an appeal to instruments.
_Instruments as Indicators of Direction._—The relative values of
different kinds of instruments, such as columns, pendulums, and the
like, as indicators of direction have already been discussed.
By the use of pendulum seismographs it has been shown that during an
earthquake the ground may move in one, two, or several directions (see
p. 21); and it is, generally speaking, only in those cases where we
experience a decided shock in the disturbance that we can determine
with any confidence the direction in which the motion has been
propagated. Such directions are usually indicated by the major axis of
certain more or less elliptical figures which have been drawn, which
in themselves appear to indicate the combination of two rectilinear
movements.
Results similar to those indicated by the records of pendulum
seismographs have also been obtained upon moving plates with a double
bracket seismograph. Thus, in the earthquake which shook Tokio at 6
A.M. on July 5, 1881, there were indications of the following
motions:—
Near the commencement of the shock the motion was N. 112° E. One and a
half second after this, the direction of motion appears to have been
N. 50° E. In three-fourths of a second more it gradually changed to a
direction N. 145° E., and after a similar interval to N. 62° E. Half a
second after this it was N. 132° E., and four seconds later the motion
was again in the original direction—namely, N. 112° E.
These particular directions of motion have been selected because they
were so definitely indicated.
The commonest type of earthquake which is experienced in Japan, and
probably also in other earthquake-shaken districts, is the compound or
diastrophic form.
That earthquakes often have motions compounded of two sets of
vibrations, has also been proved by the analysis of the records
obtained from two component seismographs. From an analysis of a record
of this description, Professor Ewing has shown that in the earthquake
felt in Tokio on March 11, 1881, there were approximate circular
(somewhat spiral) movements.
This leads us to the consideration of the twisting and wriggling
motions which are said to be experienced by some observers. Motions
like these, which by the Italians and Mexicans are called _vorticosi_,
are usually supposed to be the cause of objects like chimneys and
gravestones being rotated. These phenomena, it will be seen from what
is said in the chapter upon the effects produced in buildings, can be
more easily explained upon the supposition of a simple rectilinear
movement.
That at the time of an earthquake there may be motion in more than one
direction has been recognised since the time of Aristotle; and it is
possible that two sets of rectilinear motion, as, for instance, the
normal and transverse movements, may have led observers to imagine that
there has been a twisting motion taking place, and this especially when
the two sets of movements have quickly succeeded each other.
Persons inside flexible buildings may possibly have experienced more
or less of a rotatory motion, although the shock was rectilinear; the
building assuming such a motion in consequence of its construction and
its position with regard to the direction of the shock.
In the case of destructive earthquakes, especially at points situated
practically above the origin, the universal testimony, Mallet tells
us, is that a twisting, wriggling motion in different planes, attended
by an up-and-down movement of greater range, is experienced. To such
disturbances the word _sussultatore_ is sometimes applied. Mallet has
given many elliptical and other closed curves to illustrate the nature
of such motions.
_Duration of an Earthquake._—When reading accounts of earthquakes
it is often difficult to determine the length of time a shaking was
continuous. In Japan, in A.D. 745, there was a shaking which is said
to have lasted sixty hours; and in A.D. 977 there were a series of
shakings lasting 300 days. Often we meet with records of disturbances
which have lasted from twenty to seventy days.
At San Salvador, in 1879, more than 600 shocks were felt within ten
days; in 1850, at Honduras, there were 108 shocks in a week; in 1746,
at Lima, 200 shocks were felt in twenty-four hours; at the island of
St. Thomas, in 1868, 283 shocks were felt during about ten hours.
Disturbances like these, which succeed each other with sufficient
rapidity to cause an almost continual trembling in the ground, may be
regarded as collectively forming one great seismic effort which may
last a minute, an hour, a day, a week, or even several years. Strictly
speaking, they are a series of separate earthquakes, the resultant
vibrations of which more or less overlap. Whenever a large earthquake
occurs it is generally succeeded by a large number of smaller shocks.
The seismic disturbance as regards time is, as Mallet remarks, very
often ‘like an occasional cannonade during a continuous but irregular
rattle of musketry.’ In the New Zealand earthquake of 1848, shocks
continued for nearly five weeks, and during a large portion of the time
there were at least 1,000 shocks per day.[12]
The earthquake of Lisbon, which in five minutes destroyed the whole
town, was followed by a series of disturbances lasting over several
months. After Basle had, on October 18, 1356, been laid in ruins,
it is stated shocks followed each other for a period of a year. The
Calabrian earthquake was continued with considerable strength for a
year, and it is said that the earth did not come completely to rest for
ten years. During this cannonade the heavy shocks announced, as they
do in most earthquake countries at the present day, a series of weaker
disturbances. In certain exceptional cases this order of events has
been inverted, and slight shocks have announced the coming of heavy
ones. Fuchs gives an example of this in the earthquake of Broussa, when
the first shock was on February 28, 1855. On March 9 and 23 there were
heavier shocks, but the heaviest did not arrive until March 28.
Under certain conditions it is possible to have a sensible vibration
produced in the ground which is practically of unlimited duration;
thus, for instance, it has been noticed that the falling of water
at certain large waterfalls, by its continuous rhythmical impact on
the rocks, produces in them tremors which are to be observed at
great distances. Of this the author convinced himself at the Falls
of Niagara, where he observed the reflected and ever-moving image of
the sun in a pool of water. Under favourable circumstances almost
continual condensation of steam might take place in volcanic foci, each
condensation giving rise to a blow sufficiently powerful to produce
vibrations in the surrounding ground. Those who have stood near a large
geyser, like the one in Iceland, when it makes an ineffectual effort
to erupt, will recognise how powerful such a cause might be. Humboldt
has remarked shocks on Vesuvius and Pichincha which were periodic,
occurring twenty to thirty seconds before each ejection of vapour and
ashes.
Earthquakes like these may be of vast extent, gradually spreading
further and further outwards. This spreading of earth vibrations may
be observed at a large factory containing heavy machinery or a steam
hammer. After the machinery comes to rest, it is probably some time
before the ground returns to rest. Examples of disturbances of this
nature are spoken of under the head of Earth Tremors.
The record of the duration of an ordinary earthquake as observed at a
given point is dependent upon the sensibility of our instruments.
Continuous motions perceptible to our senses without the aid of
instruments usually last from thirty seconds to about two or three
minutes. In Japan the shocks, as timed by watches, usually last from
twenty to forty seconds. Occasionally a continuous shaking is felt for
more than one and a half minutes, and cases have been recorded where
the motion has continued for as much as four minutes and thirty-three
seconds.
Seismometers having a multiplication of 6 to 12 usually indicate that
motion continues longer than is perceptible to the senses.
_Period of Vibration._—When an earthquake contains several prominent
vibrations which might be called the _shocks_ of the disturbance, our
feelings tell us that these have occurred at unequal intervals.
About the time which is taken for the complete backward and forward
oscillation of the ground which constitutes the shock a little has
already been said. This was deduced from the records of disturbances as
drawn by seismographs. From the same sources we can readily obtain the
period of all the prominent vibrations in a disturbance.
In any given earthquake there are irregularities in period, and
different earthquakes differ from each other. About the early attempts
to determine the period of earth vibrations something has been said in
the chapter on Earthquake Instruments.
In the earthquake of March 11 (referred to on p. 70) we find that both
components commenced with a series of small vibrations, about five or
six to the second; next came the shock, consisting of two complete
vibrations executed in two seconds. In this it is to be observed that
the motion eastwards was performed much more quickly than the motion
westwards. Next, by reference to the east and west component, it is
seen that there are a number of large vibrations, about one per second,
on which a number of smaller motions are superposed. As the motion
proceeds, these become less and less definitely pronounced and more
irregular in their intervals, until finally the motion dies away.
This earthquake, as recorded at the author’s house in Tokio, lasted
about one and a half minute.
The same earthquake, as recorded by Professor Ewing at a station
situated about one and a half mile distant, but on flat ground, appears
to have lasted four and a half minutes. The largest wave had a period
of 0·7 second.
In the earthquake of March 8, 1881, there were on an average 1·4
vibrations per second. These vibrations were executed in a direction
transverse to the line joining the observing station and the locality
from which the disturbance must have originated as determined by time
observations. It can, therefore, be assumed that these vibrations,
having so slow a period, were transverse motions, this slowness or
sluggishness being due to the fact that the modulus for distortion
is less than the modulus which governs the propagation of normal
vibrations.
_The Amplitude of Earth Movements._—In making estimates of the
distances through which we are moved backward and forward at the time
of an earthquake, if we judge by our feelings, we may often be misled.
If a person is out of doors and walking, an earthquake may take place
sufficiently strong to cause chimneys to fall and unroof houses, which,
so far as the actual shaking of the ground is concerned, will be passed
by unnoticed. On the other hand, to persons indoors, especially on an
upper story, it is impossible even for a tremor to pass by without
creating considerable alarm by the angular movement that has been taken
up by the building.
Many observers have endeavoured to make actual measurements of the
maximum extent through which the earth moves at the time of an
earthquake. Among the reports of the British Association for 1841 is
the report of a committee which had been appointed ‘for obtaining
instruments and registers to record shocks of earthquakes in Scotland
and Ireland’. We read that in one earthquake which had been measured
the displacement of the ground had been half an inch, and in another
it had been less than half an inch. The instruments used to make these
observations depended upon the inertia of pendulums which at the time
of the disturbance were supposed to remain at rest. Observations
similar to these have been made in Japan. One long series were made by
Mr. E. Knipping for Dr. Gr. Wagener. They extended from November 1878
to April 1880, and were as follows:—
Number of Maximum horizontal
Earthquakes motion of the ground
10 ·0 to 0·15 mm.
7 ·15 „ 0·5 „
8 ·5 „ 2·5 „
2 2·5 „ more „
With his apparatus for vertical motion Dr. Wagener also made
observations on the absolute vertical motion. This seldom reached ·02
mm. The greatest value was that observed for the destructive shock of
Feb. 22, 1880, which was ·56 mm.
By means of a number of instruments distributed at various localities
round Tokio, the chief of which were pendulums with friction pointers
to render them ‘_dead beat_,’ and with magnifying apparatus to show
the actual motion of the ground, the author arrived at results similar
to those obtained by Dr. Wagener—namely, that the earth’s maximum
horizontal motion at the time of a small earthquake was usually only
the fraction of a millimetre, and it seldom exceeded three or four
millimetres. When we get a motion of five or six millimetres, we
usually find that brick and stone chimneys have been shattered.
The results obtained for vertical motion were also very small. In Tokio
it is seldom that vertical motion can be detected, and when it is
recorded it is seldom more than a millimetre.
These results, which were put forward some years ago, have since
received confirmation by the use of a variety of instruments in the
hands of different observers.
Mallet, in his account of the Neapolitan earthquake of 1857,
approximated to the amplitude of an earth particle by observing the
width, at the level of the centre of gravity, of fissures formed
through and remaining in great masses of very inelastic masonry.
Taking stations situated on or very nearly on the same line passing
through the seismic vertical (_epicentrum_), Mallet observed the
amplitude increased as some function of the distance, as will be seen
from the following table:—
+-------------------------+------+-------+-------+---------+-------+
| Station |Polla |La Sala|Certosa|Tramutola|Sarconi|
+-------------------------+------+-------+-------+---------+-------+
| Distance from Seismic } | | | | | |
| Vertical in } | 3·45 | 11·60 | 16·50 | 20·60 | 26·7 |
| geographical miles } | | | | | |
| Amplitude in inches | 2·5 | 3·5 | 4·0 | 4·5 | 4·75 |
+-------------------------+------+-------+-------+---------+-------+
The possibility of a law such as this having an existence for places at
a distance from the seismic vertical comparable with the vertical depth
of the centrum will be shown farther on.
With regard to the maximum displacement of an earth particle. Mallet
was of opinion that there was evidence to show that it had in some
cases been over one foot. M. Abella, in an earthquake which occurred in
the Philippines in 1881, made a rough observation of the motion of the
earth to a distance of about _two metres_. This, as might be expected,
was beyond the elastic limits of the material, and caused fissures to
be formed, which were seen to open and shut.
_Intensity of Earthquakes._—In speaking of the strength of an
earthquake, we usually employ terms like ‘weak,’ ‘strong,’ ‘violent,’
&c. Although these expressions, accompanied by illustration of the
effects which an earth quake has produced, convey a general idea of
the strength of a shock as felt at some particular locality, our ideas
nevertheless wanting in definiteness; and if we endeavour to compare
one shock with another, as a whole, our want of exactness is augmented.
We have seen that Palmieri’s seismograph indicates intensity by a
certain number of degrees, which, to a certain extent, is a measure of
the violence of the motion as indicated at a particular locality. The
degrees, as before stated, refer to the height to which in consequence
of the shaking, a certain quantity of mercury was washed in a tube,
which is a function of the depth of mercury in the tube, and also of
the duration of the disturbance.
From this it seems possible that a very slow motion of small amplitude,
continuing over a sufficient period of time, might, if it agreed with
the period of the mercury, indicate an earthquake of many degrees of
intensity, whilst residents in the neighbourhood might not have noticed
the disturbance; and, on the other hand, a short but intense shock
creating considerable destruction might have been recorded as of only a
few degrees of intensity.
Although objections like these might be raised to such a method of
recording intensity, in practice it would appear that such results are
not pronounced, and the indications of the instrument usually give us
approximate indications of relative intensity.
In writing about the Neapolitan earthquake of 1857, Mallet says that
‘area alone affords no test of seismic energy.’
The area over which a shock is felt will depend not only upon the
initial force of the disturbance, but also upon the focal depth of
a shock, the form and position of that focus, the duration of the
disturbance, and the nature and arrangement of the materials which are
shaken.
From observations in Japan, it is clearly shown that massive mountain
ranges exert a considerable influence upon the extension of seismal
disturbances. On one side of a large range of mountains large cities
might be laid in ruins, whilst on the other side the disturbance
creating this destruction might not be noticed.
_Velocity and Acceleration of an Earth Particle._—We now pass on to
methods of determining the intensity of an earthquake which are less
arbitrary than those which have just been discussed. These methods have
already been discussed when speaking of artificial disturbances, where
it was shown that the intensity of an earthquake as measured by its
destructive effects greatly depended upon the suddenness with which the
backward and forward motions of the ground were commenced or ended.
Amongst the earlier investigators of seismic phenomena who observed
that there existed a connection between the distance to which bodies
had been projected during an earthquake and the suddenness or initial
velocity with which the ground had been moved beneath them, was
Professor Wenthrop of Cambridge, Massachusetts, who noted that bricks
from his chimneys had, by the New England earthquake of 1755, been
thrown thirty feet. From this and the known height of the chimney, he
calculates that the bricks had been projected with an initial velocity
of twenty-one feet per second.[13]
The calculations made by Mallet respecting the maximum velocity of
an earth particle at the time of the Neapolitan earthquake in 1857
depended upon the overthrow, projection, and fracture of bodies.
The principles which guided him in making the calculations will be
understood from the following illustration.
[Illustration: Fig. 14.]
If a column, A B C D, receive a shock or be suddenly moved in the
direction of the arrow, the centre of gravity, G, of this column will
revolve round the edge, and tend to describe the path G O. If it passes
O, the column will fall. The work done in such a case as this is equal
to lifting the column through the height _o_ _h_.
If G A = _a_, the angle G A _h_ = φ, and the weight of the body = W,
then the above work equals
W_a_ (1 - cos φ).
This must equal the work acquired—that is to say, the kinetic energy of
rotation of the body, or
W _w_^2 K^2
W_a_ (1 - cos φ) = ———————————.
2 _g_
Where _w_ is the angular velocity of the body at starting, K the radius
of gyration round A, and _g_ the velocity acquired by a falling body in
one second. Whence
_w_^2 K^2 = 2 _ga_ (1 - cos φ),
but _w_, the angular velocity, is equal to the statical couple applied,
divided by the moment of inertia, or,
V_a_ cos φ
_w_ = ——————————,
K^2
squaring and substituting
K^2 1 - cos φ
V^2 = 2_g_ × ——— × —————————,
_a_ cos^2 φ
K^2
and since the length of the corresponding pendulum is _l_ = ———,
_a_
1 - cos φ
V^2 = 2_gl_ × —————————.
cos^2 φ
To apply this to any given case we must find the value of _l_ or of
K^2
———.
_a_
Mallet finds these values for the cube, solid and hollow rectangular
parallelopipeds, solid and hollow cylinders, &c. In these formulæ we
have a direct connection between the dimensions and form of a body and
the velocity with which the ground must move beneath it to cause its
overthrow.
[Illustration: FIG. 15.]
Not only is the case discussed for horizontal forces, but also for
forces acting obliquely. Similar reasonings are applied to the
productions of fractures in walls, but as there is uncertainty in our
knowledge of the co-efficient of force necessary to produce fracture
_through joints across_ beds of masonry, the deductions ought not to
be applied as the measures of velocity. Where the fractures occur at
the base or in horizontal planes, or in those of the continuous beds of
the masonry, or through homogeneous bodies, the uncertainty is not so
great, and for cases like these Mallet gives several illustrations. The
distance to which bodies had been projected, as, for example, ornaments
from the tops of pedestals, coping-stones from the edges of roofs, were
also used as means of determining the angle at which the shock had
emerged, or, if this be known, for determining the velocity.
Thus by a shock in the direction O C, a ball, A, on the top of a
pedestal would describe a trajectory to the point C. Let the angle
which O C makes with the horizon be _e_, the vertical height through
which the ball has fallen be _b_, and the horizontal distance of
projection be _a_; then
_a_^2
_b_ = _a_ tan _e_ + ————————————,
4H cos^2 _e_
H being the height due to the velocity of projection. Whence
___________________
2H ± √4H(H + _b_) - _a_^2
Tan _e_ = ——————————————————————————.
_a_
_a_^2 _g_
V^2 = ———————————————————————————————.
2 cos^2 _e_ (_b_ - _a_ tan _e_)
For the back motion or subnormal wave in the direction C O,
___________________
2H ± √4H(H + _b_) - _a_^2
Tan _e_ = ——————————————————————————.
_a_
_a_^2 _g_
V^2 = ———————————————————————————————.
2 cos^2 _e_ (_b_ + _a_ tan _e_)
A serious error which may enter into calculations of this description
when practically applied has been pointed out when speaking of columns
as seismometers. It was then shown that such bodies before being
overthrown may often be caused to rock, and therefore that their final
overthrow may not have any direct connection with the impulse of the
succeeding shock.
Another point to which attention must be drawn respecting the above
calculations is that if there was no friction or adherence between the
projected body and its pedestal, in consequence of its inertia it
would be left behind by the forward motion of the shock, and simply
drop at the foot of its support. In the case of frictional adherence it
would be carried forward by the velocity acquired before this adherence
was broken, and thrown in a direction _opposite_ to that given in the
figure—that is to say, in the direction of the shock.[14]
_The Absolute Intensity of the Force exerted by an Earthquake._—No
doubt it has occurred to many who have experienced an earthquake
that the power which gave birth to such a disturbance must have been
enormously great. The estimates which we shall make of the absolute
amount of energy represented by an earthquake cannot, on account of the
nature of the factors with which we deal, be regarded as accurate. They
may, however, be of assistance in forming estimates of quantities about
which we have at present no conception. One method of obtaining the
result we seek is that which was employed by Mallet in his calculations
respecting the Neapolitan earthquake. Although disbelieving in the
general increment of temperature as we descend in the earth at an
average rate of 1° F. for every fifty or sixty feet of descent, for
want of better means. Mallet assumes this law to be true, and, knowing
from a variety of observations the depth of various parts of the cavity
from which the disturbance sprang, he calculates the temperatures of
this cavity in various parts as due to its depth beneath the surface.
Next, it is assumed that steam was suddenly admitted into this cavity,
which might exert the greatest possible pressure due to the maximum
temperature. This was calculated as being about 684 atmospheres.
Next, he determined the column of limestone necessary to balance such a
pressure, which is about 8,550 feet in height. As the least thickness
of strata above this cavity was 16,700 feet, the pressure of 684
atmospheres was not sufficient to blow away its cover, but if suddenly
admitted or generated in the cavity it might have produced the wave of
impulse by the sudden compression of the walls of the cavity.
The pressure of 684 atmospheres is equivalent to about 4·58 tons on
the square inch, and, as the total area of the walls of the cavity is
calculated at twenty-seven square miles, the total accumulated pressure
would be more than 640,528 millions of tons. Mallet, however, shows
that it is probable that the temperature of the focal cavity was much
greater than that due to the hypogeal increment, and that therefore the
pressure may have been greater.
The capability of producing the earthquake impulse, however, depends
on the _suddenness_ with which the steam is flashed off. According
to the experiments of Boutigny and others, Mallet tells us that the
most sudden production of steam would take place at a temperature of
500°-550° C., which is but a few degrees below that calculated for the
mean focal depth.
Assuming the above calculated pressure to be true, and knowing the
co-efficient of compression of the materials on which it acted, the
volume of the wave at a given moment near the instant of starting—that
is, at the focus—can be calculated, and from this the wave amplitude on
reaching the surface may be deduced.
Proceeding backwards, if we have observed the wave amplitude,
calculated the depth of the focus, and know the co-efficient of
expansion, then the total compression may be calculated and the
temperature due to the pressure producing this may be arrived at. In
this way earthquakes may be used as a means of calculating subterranean
temperature at depths that can never be attained experimentally.
A method of proceeding which is probably more definite than that
adopted by Mallet would be the application of the method indicated when
speaking of the intensity of artificial disturbances.
If for a given earthquake the origin of which is known we have
determined by seismographs the mean acceleration of an earth particle
at two or more stations at different distances from that origin, we are
enabled to construct a curve of intensity the area between which and
its asymptotes was shown to be a measure of the total intensity of the
shock. Comparing this area with that of a unit disturbance produced,
say, by the explosion of a pound of dynamite, one may approximately
calculate in terms of this unit the initial intensity of the earthquake.
_Radiation of an Earthquake._—The tremors preceding the more violent
movements of an earthquake may be due, as Mallet has suggested,[15]
to the free surface waves reaching a distant point before the direct
vibrations.
The fact that earth vibrations produced by striking a blow on or near
the surface of the ground are wholly obliterated in reaching a cutting
or valley, there being no underground waves of distortion to crop up
on the opposite side of the valley, indicates that the disturbance is
one that travels on the surface; the same fact is illustrated when we
endeavour to transmit vibrations through the side of a hill into a
tunnel.
In the tunnel, although the distance may be small, no sensible effects
are produced, whilst the same disturbance may be recorded at a long
distance from its origin on the surface of the ground outside the
tunnel.
Lastly, we may refer to the experiences of miners underground.
Occasionally it has happened that miners when deep underground, as in
the Marienberg in the Saxon Erzgebirge, have felt shocks which have not
been noticed on the surface. These observations are rare, and it is
possible that they may be explained by the caving in of subterranean
excavations.
The usual experience is, that if a shock is felt underground it is also
felt on the surface, as for example in the lead mines in Derbyshire at
the time of the Lisbon disturbance (1755).
The most frequent observation, however, is that a shock may be felt on
the surface while it is not remarked by the miners beneath the surface,
as at Fahlun and Presburg in November, 1823.
At the Comstock Lode in Colorado about twelve years ago many
earthquakes were felt. On one particular day twenty-four were counted.
Superintendent Charles Foreman told the author when he visited Virginia
City in 1882, that special observations were made to determine whether
these shocks were felt as severely deep down in the mines as on the
surface, where they were on the verge of being destructive. The
universal testimony of many observers was that in most cases they were
not felt at all underground, and when a shock was felt it was extremely
feeble. At Takashima Colliery, in Japan, it is seldom that shocks are
felt underground.
The explanation of these latter observations appears to be either
that, in consequence of a smaller amplitude of motion in the solid
rocks beneath the surface as compared with the extent of motion on
the surface, the disturbances are passed by unnoticed, or else the
disturbance is, at a distance from its origin, practically confined to
the surface.
_Velocity of Propagation of an Earthquake._—Although many have written
upon earthquakes and have endeavoured to give to us the velocity with
which they were propagated, the subject is one about which we have as
yet but little exact information.
The importance of this branch of investigation is undoubtedly great.
By knowing the velocity with which an earthquake has travelled in
various directions we are assisted in determining the locality of
its origin; we may possibly make important deductions respecting the
nature of the medium through which it has passed; perhaps also we
may learn something regarding the intensity of the disturbance which
created the earthquake. In the Report of the British Association for
1851 Mallet gives the table on next page, in which are placed together
the approximate rates of transit of shocks of several earthquakes
which he discusses. Some of these, it will be observed, are records of
disturbances which must have passed through or across the bed of the
ocean.
In Mallet’s British Association Report for 1858, he gives data compiled
by Mr. David Milne[16] respecting the Lisbon earthquakes of 1755 and
1761, from which data the tables of velocities (p. 89) have been
calculated, omitting those which Mr. Mallet has marked as uncertain.
The distances are marked in degrees of seventy English miles each, and
the time is reduced to Lisbon time.
+---------------------+-------+--------------------------+----------+
| |Approx.| | |
| |rate in| Formation constituting | |
| Occasion and Place |feet | Range on surface as far |Authority |
| | per | as known or conjectured | |
| |second | | |
+---------------------+-------+--------------------------+----------+
|Rev. John Mitchell’s |1,760 |Sea bottom, probably on | Mitchell |
| guesses from the | | slates, secondary and | |
| Lisbon earthquakes | | crystalline rocks | |
|Von Humboldt’s |1,760 |From observations in | Humboldt |
| guesses from South | to | various South American | |
| America |2,464 | rocks in great part | |
| | | volcanic | |
| | | | |
| _Lisbon Earthquake | | | |
| of 1761._ | | | |
|Lisbon to Corunna |1,994 |Transition, carboniferous | ‘Annual |
| | | and granitoid |Register’ |
|Lisbon to Cork |5,228 |Transition, carboniferous | „ |
| | | crystalline slates and | |
| | | granitoid, probably, | |
| | | under sea bottom | |
|Lisbon to Santa Cruz |3,261 |The same with many | „ |
| | | alterations | |
| | | | |
| _Antilles._ | | | |
|Pointe à Pitre to |6,586 |Probably volcanic rocks |Stier and |
| Cayenne (doubtful) | | under sea bottom | Perrey’s |
| | | | memoran- |
| | | |dum, Dijon|
| | | | |
| _India._ | | | |
|Cutch to Calcutta, |1,173 |Alluvial, secondary, | ‘Royal |
| 1819 | | granitoid and later | Asiatic |
| | | igneous rocks | Journal’ |
|India, Nepauls, and | | | |
| basin of the Ganges,| | | |
| 1834:-- | | | |
|Rungpur to Arrah |2,314 }|Deep alluvia, with | ‘Royal |
|Monghyr to Gorackpur |3,520 }| occasional transition, | Asiatic |
|Rungpur to Monghyr | 990 }| carboniferous, granitoid,| Journal’ |
|Rungpur to Calcutta |1,210 }| and later igneous rocks | |
|Ships ‘Rambler’ and |1,056 |Sea bottom resting on |‘Nautical |
| ‘Millwood,’ at sea, | | unknown rock |Magazine’ |
| 1851; between lat. | | | |
| 16° 30′ N.L., 54° | | | |
| 30′ W., and lat. 23°| | | |
| 30′ N.L., 58° 0′ W. | | | |
+---------------------+-------+--------------------------+----------+
THE LISBON EARTHQUAKE ON NOVEMBER 1, 1755.
+----------------------------+---------+--------+--------+
| | Moment |Distance|Velocity|
| Localities |observed | from |in feet |
| |of shock |presumed| per |
| | | origin | second |
+----------------------------+---------+--------+--------+
| | h. m. | ° ′ | |
| Presumed focus of shock, | } 9 23 | -- | -- |
| lat. 30°, long. 11° W. | } | | |
| A ship at sea in lat. 38°, | } 9 24 | 0 30 | 3,091 |
| long. 10° 47′ W. | } | | |
| Colares | 9 30 | 1 30 | 1,325 |
| Lisbon | 9 32 | 1 30 | 1,030 |
| Oporto | 9 38 | 2 30 | 1,030 |
| Ayamont | 9 50 | 4 0 | 916 |
| Cadiz | 9 48 | 5 0 | 1,236 |
| Tangier and Tetuan | 9 46 | 5 30 | 1,478 |
| Madrid | 9 43 | 6 0 | 1,855 |
| Funchal | 10 1 | 8 30 | 1,382 |
| Portsmouth | 10 3 | 12 30 | 1,431 |
| Havre | 10 23 | 13 0 | 1,339 |
| Reading | 10 27 | 13 30 | 1,304 |
| Yarmouth | 10 42 | 15 0 | 1,174 |
| Amsterdam | 10 6 | 17 0 | 2,444 |
| Loch Ness | 10 42 | 18 0 | 1,409 |
+----------------------------+---------+--------+--------+
THE LISBON EARTHQUAKE OF MARCH 31, 1761.[17]
+----------------------------+---------+--------+--------+
| | Moment |Distance|Velocity|
| Localities |observed | from |in feet |
| |of shock |presumed| per |
| | | origin | second |
+----------------------------+---------+--------+--------+
| | h. m. | ° ′ | |
| Presumed focus, lat. 43°, | } 11 51 | -- | -- |
| long. 11° W. | } | | |
| Ship at sea in lat. 43°, | } | | |
| many leagues from coast | } 11 52 | 0 30 | 3,091 |
| of Portugal | } | | |
| Ship in lat. 44° 8′ and | } 11 54 | 1 45 | 3,607 |
| about 80 leagues from | } | | |
| coast | } | | |
| Corunna | 11 51 | 2 30 | 2,576 |
| Ship lat. 44° 8′ and 80 | } | | |
| leagues NNW. of Cape | } 11 58 | 3 30 | 3,091 |
| Finisterre | } | | |
| Lisbon | noon | 4 30 | 3,091 |
| Madeira | 12 6 | 10 0 | 4,122 |
| Cork | 12 11 | 9 30 | 2,937 |
+----------------------------+---------+--------+--------+
These tables, owing to the nature of the materials which Mallet had at
his disposal, are but rude approximations to the truth. Two interesting
facts are, however, observable: the first being that the velocities
for the earthquake of 1761 are much higher than those obtained for the
earthquake of 1755; and, secondly, that in both cases the velocities as
determined from the observations of ships at sea closely approximate
to each other, in all cases being nearly the same as that with which a
sound wave would travel through water.
The great differences in transit velocity obtained for different
earthquakes is a point worthy of attention.
Seebach’s velocity is a _true_ transit velocity, and its determination
is dependent on the assumption that the shock radiated from the
_centrum_ and not from the _epicentrum_, Seebach’s method is explained
when speaking about the determination of origins.
Some interesting observations on the velocity with which the earthquake
of October 7, 1874, was propagated, are given by M. S. di Rossi.[18]
One assumption is that the disturbance radiated from an origin
to surrounding points of observation, whilst another is that the
disturbance followed natural fractures, the direction of which is
derived from the crest of certain mountain ranges. These velocities are
as follows, Maradi being at or near the origin of the disturbance:—
+-----------------------------+-----------------------------------+
| Velocity in feet per second | Velocity in feet per second by |
| with direct radiation | propagation along mountain chains |
+-----------------------------+-----------------------------------+
| Modigliana 820 | By the Valley of Marenzo 1,080 |
| Bologna 656 | „ „ Saveno 1,080 |
| Forli 874 | „ „ Montone 1,080 |
| Modena 518 | „ „ Panaro {1,080 |
| | { 984 |
| Firenze 273 | „ „ Sieve 540 |
| Compiobbi 328 | „ „ „ 540 |
+-----------------------------+-----------------------------------+
Another set of interesting results are those of P. Serpieri on the
earthquake of March 12, 1873. The curious manner in which this shock
radiated is described in the chapter on the Geographical Distribution
of Earthquakes (see p. 231). Two large areas appear to have been
almost simultaneously struck, so that, there being no time for elastic
yielding, the velocities calculated between places situated on either
of the areas are exceedingly great.[19]
From Ragusa to Venice the velocity was 2,734 feet per second
„ Spoleto „ „ 4,101 „ „
„ Perugia to Orvieto „ 601 „ „
„ „ „ Ancona „ 1,640 „ „
„ „ „ Rome „ { 1,640 „ „
{or, 2,186
The following are examples of approximate earthquake velocities which
have been determined in Japan.
_The Tokio Earthquake of October 25, 1881._—From records respecting
this earthquake it appears to have been felt over the whole of Yezo
and the northern and eastern coast of Nipon, a little farther south
than Tokio. It was severest at Nemuro and Hakodate, and at the former
place a little damage was done. From these facts, together with the
indications of instruments recording direction of movement and a
general inspection of the time records, it seems that the disturbance
must have originated beneath the sea on the east coast of Yezo at a
very long distance to the north-east of Tokio, from which place it
passed in a practically direct line on to Yokohama.
As the disturbance was felt at Yokohama twenty-one seconds later than
at Tokio, and the distances between these two places is about sixteen
geographical miles, for this portion of its course the disturbance
must have travelled at a rate of at least 4,300 _feet per second_. If
we assume that the shock, after having reached Hakodate, travelled on
at the same rate as it did between Tokio and Yokohama in order to reach
Saporo, where the shaking was felt eighteen seconds after Hakodate,
it must have had about thirteen geographical miles to travel after
Hakodate was shaken before Saporo felt its effect.
Drawing from Hakodate a tangent to the eastern side of a circle of
thirteen miles radius described round Saporo, the origin of the
disturbance must be on the line bisecting this tangent at right angles.
As it also lies on a line drawn through Tokio and Yokohama, it lies in
a position about 41 N. lat. and 144° 15′ E. long., which is a position
somewhat nearer to Nemuro than Hakodate, as we should anticipate. If
this be taken as approximately indicating the origin, then the shock,
after reaching Hakodate from the Hakodate _homoseist_, travelled about
218 miles to reach Tokio in 128 seconds, which gives a _velocity of
10,219 feet per second_.
The method here followed is equivalent to that of the hyperbola and one
direction (see p. 204). The hyperbola is described on the assumption
that the velocity deduced from the time taken to travel between Tokio
and Yokohama is correct, and also that the earth waves travelled with
approximately the same velocity in the vicinity of Saporo as near
Tokio. The probability, however, is that they travelled more quickly.
If this be so, then the origin is thrown somewhat to the south-east and
the velocity between the Hakodate homoseist and Tokio reduced. Thus,
if the velocity in the Saporo district be double that observed in the
Tokio district, the origin is shifted about twenty-eight miles to the
south-west, and the last-mentioned velocity is reduced to about 9,000
feet per second.
If we work by the method of circles, and assume the velocity to have
been constant in all directions, then this velocity must have been
about 6,000 feet per second. If we assume that the indications of
direction obtained from seismographs and other sources give to us by
this intersection a proper origin, the velocity in some directions may
have been as much as 17,000 feet per second.
An origin thus determined, or even if determined by the method of
circles, is in discord with the fact that places like Nemuro, in the
north-east of Yezo, were nearer to the origin than any of the other
places which have been mentioned.
The conclusion which we are therefore led to with regard to this shock,
assuming of course that the time observations are tolerably correct,
is that the velocity of propagation was variable, being greater when
measured between points near to the origin than between points at a
distance. The velocities estimated vary between 4,000 and 9,000 feet
per second.
In the case of the earthquake which has just been discussed, we have
an example of a disturbance which must have passed between Tokio and
Yokohama in what was almost a straight line from the origin. As this
direction ought to give the maximum time of transit if all earthquakes
are propagated with the same velocity, the following table is given of
the interval between the time of observation of several shocks at these
two stations:—
FROM YOKOHAMA TO TOKIO. FROM TOKIO TO YOKOHAMA.
1880 December 20th 36 seconds | 1882 October 25th 21 seconds
1881 January 7th 14–31 „ | 1883 February 6th 23 „
„ March 8th 60 „ | „ March 1 53 „
„ „ 17th. 66 „ | „ „ „ 63 „
„ November 15th 31 „ | „ 8th 27 „
1882 February 16th 22 „ | „ „ 11th 26 „
As these are observations which have been made with the assistance of a
telegraphic signal daily employed to correct and rate the clocks from
which the observations were obtained, they may be regarded as being
tolerably, correct.
The disturbance of February 6, the two shocks of March 1, appear, like
that of October 25, to have passed in almost a direct line from an
origin in the N.N.E, through Tokio on to Yokohama. Their velocities of
propagation as calculated from the above intervals are approximately
3,900, 1,900, and 1,400 feet per second. The shock of February 16
appears to have had its origin near to a point in Yedo Bay about eight
miles east of Yokohama. Assuming this to be the case, the shock between
the Yokohama homoseist and Tokio travelled at the rate of 2,454 feet
per second, but between the Tokio homoseist and Chiba at the rate
of 750 feet per second; that is to say, the velocity of propagation
rapidly decreased as the disturbance spread outwards.
At Yokohama it was recorded at 5.31.54, at Tokio at 5.32.16, and at
Chiba at 5.33.48. These times are given in Tokio mean time.
The shock of March 11, which was recorded at Tokio at 7.51.22 P.M.
and at Yokohama at 7.51.33 P.M., appears, from the indications of
instruments which were exceptionally definite in their records, to have
originated in the N.E. corner of Yedo Bay, about nineteen miles S.S.W.
from Chiba. This shock was rather severe, fracturing several chimneys.
From the Tokio homoseist it appears to have travelled on to Yokohama at
the rate of about 2,200 feet per second. Assuming these observations
to be _approximately_ accurate, if we take them with the records of
previous observers they lead us to the following conclusions:—
1. Different earthquakes, although they may travel across the same
country, have very variable velocities, varying between several
hundreds and several thousands of feet per second.
2. The same earthquake travels more quickly across districts near to
its origin than it does across districts which are far removed.
3. The greater the intensity of the shock the greater is the velocity.