Seismic Waves
Wave motion is perhaps most familiar to us
from our observations of waves on water
When a stone is thrown into a pool of water, the surface of the water is disturbed where the
stone strikes, and ripples move outwards from the place of its’ disturbance.
This wave train is produced by movements of the particles of water in the vicinity of the
ripples. The water however, does not actually flow in the direction in which the ripples
travel (think of a cork on the surface). Earthquake waves are quite analogous to those
caused by that of a stone thrown into a pool.
• As we have seen
previously, due to
tectonism, pressure or
strain energy will
accumulate along
faults. Over hundreds
of years, the built up
strain energy may
cause the fault to
break or rupture
causing the sudden
loss of energy,
equivalent to the snap
of the board or pop of
the balloon.
• The shock radiates out
from the rupture as
seismic waves, which
travel to the surface
and produce the
shaking we experience
in an earthquake.
There are 3 basic
types: P waves
(primary waves), S
waves (secondary or
shear waves), and
surface waves.
• P and S waves are
called body waves
because they pass
directly through the
Earth, whereas
surface waves
travel along the
surface like the
ripples in a pond
when a stone is
thrown into it.
Waves traveling outwards from 1964 Great Alaskan
Earthquake
• A P wave is easily understood by a pool player, who “breaks” a set
of pool balls arranged in a tight triangle, all touching. When the
cue ball hits the other balls, the energy of striking momentarily
compresses the next ball elastically. The compression is transferred
to the next ball, then to the next, until the entire set of pool balls
scatters around the table. P waves pass through solid, such as rock,
and they can also pass through water or air. When earthquake
waves pass though the air, sometimes they produce a noise.
• To illustrate an S wave, tie one end of a clothesline to a tree. Hold the line
tight and shake it rapidly from side to side. You can see what looks like
waves running down the clothesline towards the tree distorting the shape of
the clothesline. Similarly, when S waves pass through rock they distort its
shape. S waves cannot pass through liquid or air, and you would not feel
them aboard a ship at sea.
•
Because S-waves involve shearing rather than compression, they move the
particles of the rock transverse to the direction of propagation. These rock
motions may be in a vertical (Sv) or horizontal (Sh) plane.
Only S-waves exhibit the phenomenon
called polarization. As S-waves
travel through the Earth, they
encounter structural discontinuities
that refract or reflect them and
polarize their vibrations.
When an S wave is polarized so that the
particles of rock move only in a
horizontal plane, it is denoted by the
symbol SH. When the particles of
rock all move in the vertical plane
containing the direction of
propagation, the S wave is called an
SV wave
The Speed of P and S Waves
The actual velocities at which P and S-waves travel
depend on the densities and inherent elastic
properties of the rocks through which they travel.
Wave speed depends on the measures of only two
elastic properties, called elastic moduli: the
incompressibility (k) and the rigidity (m) of the rock.
When a uniform pressure is applied to the surface of a
cube of rock, its’ volume is reduced and a measure
of its’ change in volume per unit volume is its;
incompressibility. This type of deformation occurs
when P-waves propagate through the Earth’s
interior.
In general, as k h,P-wave velocity h
A second type of deformation occurs when equal but
opposite tangential pressures are applied to
opposite faces of a cube of rock. The cube will
deform by shearing out of its’ shape without any
change in volume.
This same strain occurs when a cylindrical core of
rock is twisted by equal and opposite pressures
applied at opposite ends. The greater the
resistance, the greater the rigidity.
Because S-waves propagate by shearing the rock, the
rigidity gives a measure of their speed.
In general, as m h, S-wave velocity h
The Elastic Moduli
k = modulus of incompressibility (or bulk modulus)
Granite – k = 27 x 1010 dyne/cm2
water – k = 2.0 x 1010 dyne/cm2
m = modulus of rigidity
Granite – m = 1.6 x 1010 dyne/cm2
water – m = 0.0 dyne/cm2
Velocity Formulae
P-wave velocity – a = (k + 4/3 m)/r
S-wave velocity – b = m/r
Where r = density of the rock through which the wave is traveling
a
b
Granite
5.5 km/s
3.0 km/s
Water
1.5 km/s
0.0 km/s
Because of the great pressures inside the Earth, the
rock density increases everywhere with depth.
As a consequence, it would appear that the position of
the density term in the denominator of each
formula would cause both the P and S-wave
velocities to decrease with depth. However, both
incompressibility and rigidity increase more
rapidly than rock density with depth.
• The rock motions that are
produced when the P and S
waves arrive at the Earth’s
surface generate other types
of seismic waves under
certain conditions. These
are called surface waves,
and the most important of
these are called Rayleigh
waves and Love waves.
Both types of waves travel
along the surface of the
Earth, with rock motions
decreasing to zero with
depth.
• Surface waves are
extremely complex. After
reaching the surface, much
earthquake energy will run
along the surface, causing
the ground to go up and
down or sway from side to
side. Some people caught
in an earthquake have
reported that they could
actually see the ground
moving up and down, like
an ocean wave, but faster.
The Instrumental Surveillance of
Earthquakes
• From early times, human
curiosity about the world has
stimulated attempts to make
measurements of natural events.
Earthquake recorders are called
seismographs or seismometers if
they track the complete history
of shaking throughout an
earthquake. The earliest known
seismoscope was constructed by
a Chinese scholar around A.D.
132, and was designed to
indicate both the occurrence of
earthquake waves and their
direction of approach.
• By the late 1800’s the first
seismographs were
developed, and were very
simple instruments. Even
as the entire world shakes
around it, a suspended
mass remains stationary
due to its inertia. Seismic
waves can then be
recorded as wiggly lines by
pen and ink on paper
wrapped around a rotating
drum.
A typical recording of an earthquake records a typical
“train” of seismic waves. First the P waves, followed in
succession by the S and surface waves.
• An earthquake releases a complex array of
waves, with great variation in frequency,
which is the number of waves to pass a
point in a second. A guitar string vibrates
many times per second, but it takes
successive ocean waves many seconds to
reach a waiting surfer. The ocean wave has
low frequency, and the guitar string vibrates
at a high frequency.
High frequency
=
Low frequency
Complex
waveform
Sinusoidal
Components
An earthquake can be compared to
a symphony orchestra, with many
instruments producing sound
waves that vibrate at both high and
low frequencies. A seismologist
can separate out the complex
waveforms into simple sinusoidal
components using high-speed
computers.
• As we have seen, S waves are
slower than P waves, and
seismologists use this fact to
tell how far away it is from
the seismograph to the
earthquake. The seismograph
records the P wave first, then
the S wave. If the
seismologist knows the speed
of each wave, then by
knowing that both waves
started at the same time it’s
possible to work out how far
the earthquake waves have
traveled to reach the
seismograph.
• If we can determine
the distance of the
same earthquake
from several
different
seismograph
stations, we are able
to locate the
epicenter, the point
on the Earth’s
surface directly
above the earthquake
focus.
Focal Depth
Hypocenter
• The focus or
hypocenter is the point
beneath the Earth’s
surface where the
crust or mantle first
ruptures to cause an
earthquake. The depth
of the earthquake
below the surface is
called its focal depth.
Measuring an Earthquake
Magnitude
Charles Richter, inventor of the
magnitude scale.
• The size of an earthquake
was once measured
largely on the basis of
how much damage was
done. This was
unsatisfactory to Caltech
seismologist Charles
Richter, who wanted a
more quantitative measure
of earthquake size, at least
for southern California.
Charles Richter has explained that:
"Magnitude can be compared to the power output in
kilowatts of broadcasting station. Local intensity on the
Mercalli scale is then comparable to the signal strength
on a receiver at a given locality; in effect the quality of the
signal. Intensity like signal strength will generally fall off
with distance from the source, although it also depends
on the local conditions and the pathway from the source
to the point."
• Following earlier work by
the Japanese, in 1935
Richter established a
magnitude scale based on
how much a seismograph
needle was deflected by a
seismic wave generated
by an earthquake about
60 miles (100 km) away.
Complicating matters,
Richter’s scale is
logarithmic, which means
that an earthquake of
magnitude 5 would
deflect the needle of the
seismograph ten times
more than an earthquake
of magnitude 4.
• In order to calculate the
magnitude of an earthquake,
one must first determine the
distance to the epicenter by
finding time difference
between arrival of the first P
wave and first S wave, and
measuring the amplitude (or
height) of the highest seismic
wave recorded. These
values are then plotted on a
nomogram, and the
earthquake magnitude is then
read off the nomogram.
Magnitude Classes
• Earthquakes are often
divided into classes
according to their
magnitude:
Great; M > =8
Major; 7 < =M < 7.9
Strong; 6 < = M < 6.9
Moderate: 5 < =M < 5.9
Light: 4 < =M < 4.9
Minor: 3 < =M < 3.9
Micro: M < 3
• Earthquakes release a tremendous amount of
energy, which is why they can be so destructive.
The table below shows magnitudes with the
approximate amount of TNT needed to release the
same amount of energy.
Magnitude
Approximate Equivalent
TNT Energy
4.0
1010 tons
5.0
31800 tons
6.0
1,010,000 tons
7.0
31,800,000 tons
8.0
1,010,000,000 tons
9.0
31,800,000,000 tons
• For earthquakes that occurred between about 1890 (when modern
seismographs came into use) and 1935 when Charles Richter developed the
magnitude scale, people went back to the old records and compared the
seismograms from those days with similar records for later earthquakes. For
earthquakes prior to about 1890, magnitudes have been estimated by looking
at the physical effects (such as amount of faulting, landslides, sandblows or
river channel changes) plus the human effects (such as the area of damage or
felt reports or how strongly a quake was felt) and comparing them to modern
earthquakes. Many assumptions have to be made when making these
comparisons. For example, how do you compare the shaking for people living
in log cabins or tents in the early 1800's with shaking for people living in
high-rise steel and concrete buildings (with waterbeds!) in the 1990's?
Because different researchers can get widely varying magnitudes from using
different assumptions on how to make these comparisons, many of the old
earthquakes have big differences in the magnitudes assigned to them. For
example, magnitude estimates for the quakes that occurred near New Madrid,
Missouri in 1811 and 1812 vary from the upper magnitude 6 range to as high
as 8.8, all because of the choices the researchers made about how to compare
the data.
Ground rupture, Hector Mine Earthquake
• An increase one
magnitude unit
represents about a 30fold increase in release
of stored-up seismic
strain energy. So the
Hector Mine
Earthquake of
magnitude 7 in the
Mojave Desert on
October 16, 1999 would
be the equivalent of
about thirty earthquakes
the size of the Whittier
Narrows Earthquake of
October 1, 1987, which
was magnitude 6.
Damage caused by Whittier Earthquake
• Richter never claimed that
his magnitude scale, now
called local magnitude and
labeled ML, was an accurate
measure of earthquakes.
Nevertheless, the Richter
magnitude scale caught on
with the media and the
general public, and it is still
the first thing a reporter asks
a professional about an
earthquake: “How big was it
on the Richter scale?”
Compare the fault area of the magnitude 7.3
(top) with that of the magnitude 5.6 (smallest
one near the bottom).
• The Richter magnitude
scale works reasonably
well for small to
moderate-size
earthquakes, but it works
poorly for very large
earthquakes, the ones we
call great quakes. For
these, other magnitude
scales are necessary.
• To record earthquakes at
seismographs thousands of miles
away, seismologists had to use
long-period (low frequency)
surface waves, because the high
frequency waves die out a few
hundred miles away from the
epicenter. To understand this
problem, think about how music
is heard a long distance away
from its source. Far away all
you can usually make out are the
very deep, or low-frequency,
bass tones which transmit
through the air more efficiently
than the treble (high-frequency)
notes.
In this same way, low frequency
earthquake waves can be recorded
thousands of miles away from the
earthquake source. A commonly used
earthquake scale is the surface wave
magnitude, or MS, which measures the
largest deflection (amplitude) of the
needle on the seismograph for a
surface wave that has a frequency of
about 20 seconds.
• The magnitude scale most useful to professionals is the
moment magnitude scale, or MW, which comes closest to
measuring the true size of an earthquake, particularly a
large one. This scale relates magnitude to the area of the
fault that ruptures and the amount of slip that takes place
on the fault. For large earthquake, this can be done by
measuring the length of the fault which ruptures at the
surface and figuring out how deep the zone of
aftershocks extends, thereby calculating the area of
rupture. The amount of slip can be measured at the
surface as well.
• For small to intermediate-size
earthquakes, the magnitude scales are
designed so that there is relatively
little difference between Richter
magnitude, surface-wave magnitude,
and moment magnitude. But for large
earthquakes, the difference is
dramatic. For example, both the 1906
San Francisco Earthquake and the
1964 Alaska Earthquake had a
surface-wave magnitude of 8.3.
However, the San Francisco
Earthquake had a moment magnitude
of only 7.7, whereas the Alaska
Earthquake had a moment magnitude
of 9.2, which made it the second
largest earthquake of the 20th century.
San Francisco Earthquake, 1906
Alaska Earthquake, 1964
Acceleration
When you step on the accelerator in
the car or put on the brakes, the
car goes faster or slower. When
it is changing from one speed to
another, it is accelerating
(faster) or decelerating (slower).
This change from one speed, or
velocity, to another is called
acceleration. During an
earthquake when the ground is
shaking, it also experiences
acceleration. The peak
Acceleration, Velocity, Displacement (Image courtesy of Charles acceleration is the largest
Ammon, Penn State)
acceleration recorded by a
particular station during an
earthquake.
g
g is the acceleration of gravity 9.8
(m/s2) or the strength of the
gravitational field (N/kg) (which it
turns out is equivalent). G is the
proportionality constant 6.67x10-11
(N-m2/kg2) in Newton's law of
gravity. On the other hand, the
force of gravity, or F = mg, at the
surface of the earth, or F =
GMm/r^2 at a distance r from the
center of the earth (where r is
greater than the radius of the
earth). When there is an
earthquake, the forces caused by
the shaking can be measured as a
percentage of gravity, or percent
g.
• These are maps of peak
ground acceleration
(measured in % g) and
peak ground velocity
(measured in cm/sec) for
the 1994 Northridge
earthquake. As we will
see, the damage caused by
an earthquake is strongly
tied to both PGA and
PGV.
Intensity
Giuseppe Mercalli, developer of the
Mercalli Intensity Scale.
• Measuring the size of an
earthquake by the energy it
releases is all well and good,
but it’s still important to
measure how much damage it
does at critical places. This
measurement is called
earthquake intensity, which is
measured on the Abridged
Modified Mercalli (MM)
Scale. Developed by Giuseppe
Mercalli, the scale ranges from
Roman numeral I to XII, with I
being generally not felt, to XII
which means total damage.
The Abridged Modified Mercalli (MM) Intensity Scale (1956 version)
I.
Not felt. Marginal and long-period effects of large earthquakes.
II.
Felt by persons at rest, an upper floors, or favorably placed.
III.
Felt indoors. Hanging objects swing. Vibration like passing of light trucks. Duration estimated. May not be recognized as an earthquake.
IV.
Hanging objects swing. Vibration like passing of heavy trucks; or sensation of a jolt like a heavy ball striking the walls. Standing cars rock. Windows,
dishes, doors rattle. Glasses clink. Crockery clashes. In the upper range of IV, wooden walls and frames creak. 0.015 – 0.02g.
V.
Felt outdoors; direction estimated. Sleepers wakened. Liquids disturbed, some spilled. Small unstable objects displaced or upset. Doors swing, close, open.
0.03 – 0.04g.
VI.
Shutters, pictures move. Pendulum clocks stop, start, change rate. 0.06 – 0.07g.
VII.
Felt by all. Many frightened and run outdoors. Persons walk unsteadily. Windows, dishes, glassware broken. Knickknacks, books, etc. off shelves.
Pictures off walls. Furniture moved or overturned. Weak plaster and masonry D cracked. Small bells ring (church, school). Trees, bushes shaken visibly,
or heard to rustle. 0.10 – 0.15g.
VIII.
Difficult to stand. Noticed by drivers. Hanging objects quiver. Furniture broken. Damage to masonry D, including cracks. Weak chimneys broken at roof
line. Fall of plaster, loose bricks, stones, tiles, cornices, also unbraced parapets and architectural ornaments. Some cracks in masonry C. Waves on ponds,
water turbid with mud. Small slides and caving in along sand or gravel banks. Large bells ring. Concrete irrigation ditches damaged. 0.25 – 0.30g.
IX.
Steering of cars affected. Damage to masonry C; partial collapse. Some damage to masonry B; none to masonry A. Fall of stucco and some masonry
walls. Twisting. fall of chimneys, factory stacks, monuments, towers, elevated tanks. Frame houses moved on foundations if not bolted down; loose panel
walls thrown out. Decayed piling broken off. Branches broken from trees. Changes in flow or temperature of springs or wells. Cracks in wet ground and
on steep slopes. 0.50 – 0.55g.
X.
General panic. Masonry D destroyed; masonry C heavily damaged, sometimes with complete collapse; masonry B seriously damaged. General damage to
foundations. Frame structures, if not bolted. shifted off foundations. Frames racked. Serious damage to reservoirs. Underground pipes broken.
Conspicuous cracks in ground. In alluviated areas sand and mud ejected, earthquake fountains, sand craters. Greater than 0.60g.
XI.
Most masonry and frame structures destroyed with their foundations. Some well-built wooden structures and bridges destroyed. Serious damage to dams,
dikes, embankments. Large landslides. Water thrown on banks of canals, rivers, lakes, etc. Sand and mud shifted horizontally on beaches and flat land.
Rails bent slightly.
XII.
Rails bent greatly. Underground pipelines completely out of service.
XIII.
Damage nearly total. Large rock masses displaced. Lines of sight and level distorted. Objects thrown into the air.
Masonry A. Good workmanship, mortar, and design; reinforced especially laterally, and bound together by
using steel, concrete, etc.; designed to resist lateral forces.
Masonry B. Good workmanship and mortar; reinforced. but not designed in detail to resist lateral forces.
Masonry C. Ordinary workmanship and mortar, no extreme weaknesses like failing to tie at corners, but
neither reinforced nor designed against horizontal forces.
Masonry D. Weak materials, such as adobe; poor mortar; low standards of workmanship; weak horizontally.
Earthquake intensities are based on a post-earthquake survey of a
large area: damage is noted, and people are questioned about
what they felt. An intensity map is a series of concentric lines,
irregular rather than circular, in which the highest intensities are
generally, but not always, closest to the epicenter of the
earthquake.
The Mercalli intensity
scale is also useful in
“predicting” what
might happen given a
scenario earthquake.
Since ground
conditions and
building types are
known for a given
location, given an
earthquake of a
certain magnitude, it
is possible to
determine the
Mercalli intensities at
that location.
The above scenario is for a theoretical
magnitude 7.4 earthquake on the southern
San Andreas fault. Computer calculated
Mercalli intensities are color coded for
easier recognition.
As mentioned, it is
possible to relate
earthquake intensity to the
maximum amount of
ground acceleration (peak
ground acceleration, or
PGA) that is measured
with a special seismograph
called a strong-motion
accelerograph. This is
shown on the previous
MMI scale. Acceleration
is measured as a
percentage of the Earth’s
gravity. A vertical
acceleration of 1 g would
be just enough to lift you
(or anything else) off the
ground. Obviously this
would have a major impact
on damage done by an
earthquake at a given site.
Intensity map for the 1994 Northridge earthquake. Note that damage
is strongly related to both PGA and PGV at the bottom of the map.
Fault Plane Solutions
In the early days of seismology, it was
enough to locate an earthquake
accurately and to determine its
magnitude. But seismic waves contain
much more information, including the
type of faulting. The seismogram shows
that the first motion of an earthquake P
wave is either a push toward the
seismograph or a pull away from it.
With the network of seismographs in
California, its possible to determine the
push or pull relationship at many
stations, leading to information about
whether the earthquake was on a reverse
fault, a normal fault, or a strike-slip
fault.
1st motion of P wave up
is a compression (push)
towards the
seismograph
1st motion of P wave
down is an extension
(pull) away from the
seismograph
The first motions of P waves
show which way the fault
moved during an earthquake.
E
E
C
C
C
C
C
C
E
E
C = Compression
E = Extension
E
For a left lateral strike-slip fault, the fault
plane solution will look like this. The
circle, or “beach ball”, is actually a 2-D
representation of a 3-D fault zone, with the
red areas indicating areas in compression,
the white being areas in extension.
Fault plane
Auxiliary plane
Areas in compression
Areas in extension
Note that a secondary, or auxiliary plane is also
present in these cases.
Fault plane
• Many earthquakes are not accompanied by surface faulting, so the fault-plane
solutions are the best evidence of the type of fault causing the earthquake.
Typical Fault Plane Solutions
Strike-Slip Fault
Right-lateral
Left-lateral
Thrust Fault
Normal Fault
Can you figure out what created
the following two fault plane
solutions?
Hints:
Records a compression
everywhere
Records an extension
everywhere
Aftershocks
Aftershock zones can be defined in two different
ways...
An aftershock is actually just a normal earthquake in
every physical detail. Out of context, there is no way
to tell the difference between any arbitrary earthquake
and an "aftershock". The only real difference between
the two is that an aftershock follows closely in the
wake of a larger earthquake, and in roughly the same
location as its predecessor. That larger, initial
earthquake is usually referred to as the "mainshock".
More specifically, there are two guidelines for labelling
an earthquake as an aftershock. First, it must occur
within an "aftershock zone." This is sometimes
defined as within one fault-rupture length of the
mainshock rupture surface, or alternatively, within an
area defined by seismologists based upon early
aftershock activity. Second, it must occur within that
designated area -- the "aftershock zone" -- before the
seismicity rate in that area returns to its
"background", meaning pre-mainshock, level. If an
earthquake meets these two criteria, seismologists
consider it an "aftershock."