Earthquakes, faulting, beach-balls,
magnitude scales
Faulting Geometry
Faulting is a complex process and the variety of faults that exists is large. We will consider a simplified
but general fault classification based on the geometry of faulting, which we describe by specifying
three angular measurements: dip, strike, and slip.
Dip
The fault illustrated in the previous section was oriented
vertically. In Earth, faults take on a range of orientations
from vertical to horizontal. Dip is the angle that
describes the steepness of the fault surface. This angle is
measured from Earth's surface, or a plane parallel to
Earth's surface. The dip of a horizontal fault is zero
(usually specified in degrees: 0°), and the dip of a
vertical fault is 90°. We use some old mining terms to
label the rock "blocks" above and below a fault. If you
were tunneling through a fault, the material beneath the
fault would be by your feet, the other material would be
hanging above you head. The material resting on the
fault is called the hanging wall, the material beneath the
fault is called the foot wall.
Strike
The strike is an angle used to specify the orientation of
the fault and measured clockwise from north. For
example, a strike of 0° or 180° indicates a fault that is
oriented in a north-south direction, 90° or 270°
indicates east-west oriented structure. To remove the
ambiguity, we always specify the strike such that when
you "look" in the strike direction, the fault dips to you
right. Of course if the fault is perfectly vertical you
have to describe the situation as a special case. If a
fault curves, the strike varies along the fault, but this is
seldom causes a communication problem if you are
careful to specify the location (such as latitude and
longitude) of the measurement.
Slip
Dip and strike describe the orientation of the fault, we
also have to describe the direction of motion across the
fault. That is, which way did one side of the fault move
with respect to the other. The parameter that describes
this motion is called the slip. The slip has two
components, a "magnitude" which tells us how far the
rocks moved, and a direction (it's a vector). We usually
specify the magnitude and direction separately.
The magnitude of slip is simply how far the two sides of
the fault moved relative to one another; it's a distance
usually a few centimeters for small earthquakes and
meters for large events. The direction of slip is
measured on the fault surface, and like the strike and
dip, it is specified as an angle. Specifically the slip
direction is the direction that the hanging wall moved
relative to the footwall. If the hanging wall moves to the
right, the slip direction is 0°; if it moves up, the slip
angle is 90°, if it moves to the left, the slip angle is
180°, and if it moves down, the slip angle is 270° or
-90°.
Hanging wall movement determines the geometric classification of faulting. We distinguish between
"dip-slip" and "strike-slip" hanging-wall movements.
Dip-slip movement occurs when the hanging wall moved predominantly up or down relative to the
footwall. If the motion was down, the fault is called a normal fault, if the movement was up, the fault
is called a reverse fault. Downward movement is "normal" because we normally would expect the
hanging wall to slide downward along the foot wall because of the pull of gravity. Moving the hanging
wall up an inclined fault requires work to overcome friction on the fault and the downward pull of
gravity.
When the hanging wall moves horizontally, it's a strike-slip earthquake. If the hanging wall moves to
the left, the earthquake is called right-lateral, if it moves to the right, it's called a left-lateral fault. The
way to keep these terms straight is to imagine that you are standing on one side of the fault and an
earthquake occurs. If objects on the other side of the fault move to your left, it's a left-lateral fault, if
they move to your right, it's a right-lateral fault.
When the hanging wall motion is neither dominantly vertical nor horizontal, the motion is called
oblique-slip. Although oblique faulting isn't unusual, it is less common than the normal, reverse, and
strike-slip movement.
Fault Styles
Earthquake Focal Mechanisms (Beach Balls1)
We use a specific set of symbols to identify faulting geometry on maps. The symbols are called
earthquake focal mechanisms or sometimes "seismic beach balls". A focal mechanism is a graphical
summary the strike, dip, and slip directions.
An earthquake focal mechanism is a projection of the intersection of the fault surface and an imaginary
lower hemisphere (we'll use the lower hemisphere, but we could also use the upper hemisphere),
surrounding the center of the rupture.
The intersection between the fault "plane" and the sphere is a curve. The focal mechanism shows
the view of the hemisphere from directly above. We can show the orientation of a plane (i.e. the
strike and dip) using just one curve, to include information on the slip, we use two planes and
shade opposite quadrants of the hemisphere.
1 Enter strike, dip and slip into this online code and it will draw your beach-ball.
The price we pay for the ability to represent slip is that you cannot identify which of the two planes on
the focal mechanism is the fault without additional information (such as the location and trend of
aftershocks).
Some example focal mechanisms are shown below.
You should memorize the top three, which correspond to dip-slip reverse and normal faulting on a fault
dipping 45°, and strike-slip faulting on a vertical fault. The lower two mechanisms correspond to a lowangle reverse earthquake (the dip is low) and the last example is an oblique event with components of
both strike-slip and dip-slip movement. The strike of any plane can be read from a focal mechanism by
identifying the intersection of the fault (shown as the boundary between shaded and unshaded regions)
with the circle surrounding the mechanism (and using the dip-to-the-right rule).
The place and character of the beach-ball tells us much about the seismo-tectonics of an earthquake. I
connect you here to three global maps by Don Anderson Professor of Geophysics at Caltech that show
the distribution of thousands of computed beach-balls corresponding to a couple of decades of
earthquakes:
Tectonic Map of the Central Pacific
Tectonic Map of Northern Hemisphere
Tectonic Map of Southern Hemisphere
The plate-tectonic character of our planet is revealed!
Earthquake Magnitude
The magnitude is the most often cited measure of an earthquake's size, but it is not the only measure,
and in fact, there are different types of earthquake magnitude. Early estimates of earthquake size were
based on non-instrumental measures of the earthquakes effects. For example, we could use values such
as the number of fatalities or injuries, the maximum value of shaking intensity, or the area of intense
shaking. The problem with these measures is that they don't correlate well. The damage and devastation
produced by an earthquake will depend on its location, depth, proximity to populated regions, as well
as its "true" size. Even for earthquakes close enough to population centers values such as maximum
intensity and the area experiencing a particular level of shaking did not correlate well.
With the invention and deployment of seismometers it became possible to accurately locate
earthquakes and measure the ground motion produced by seismic waves.
The development and deployment of seismometers lead to many
changes in earthquake studies, magnitude was the first quantitative
measure of earthquake size based on seismograms. The maximum or
"peak" ground motion is defined as the largest absolute value of ground
motion recorded on a seismogram. In the example above the surface
wave has the largest deflection, so it determines the peak amplitude.
It was natural for these instrumental measures to be used to compare earthquakes, and one of the first
ways of quantifying earthquakes using seismograms was the magnitude.
Richter's Magnitude Scale
In 1931 a Japanese seismologist named Kiyoo Wadati constructed a chart of maximum ground motion
versus distance for a number of earthquakes and noted that the plots for different earthquakes formed
parallel, curved lines (the larger earthquakes produced larger amplitudes). The fact that earthquakes of
different size generated curves that were roughly parallel suggested that a single number could quantify
the relative size of different earthquakes.
In 1935 Charles Richter constructed a similar diagram of peak ground motion versus distance and used
it to create the first earthquake magnitude scale (a logarithmic relationship between earthquake size and
observed peak ground motion). He based his scale on an analogy with the stellar brightness scale
commonly used in astronomy which is also similar to the pH scale used to measure acidity (pH is a
logarithmic measure of the Hydrogen ion concentration in a solution).
Sample of the data used by Richter to construct the magnitude scale for
southern California. The symbols represent observed peak ground
motions for earthquakes recorded during January of 1932 (different
symbols represent different earthquakes). The dashed lines represent
the reference curve for the decrease in peak-motion amplitude with
increasing distance from the earthquake. A magnitude 3.0 earthquake
is defined as the size event that generates a maximum ground motion
of 1 millimeter (mm) at 100 km distance.
To complete the construction of the magnitude scale, Richter had to establish a reference value and
identify the rate at which the peak amplitudes decrease with distance from an earthquake. He
established a reference value for earthquake magnitude when he defined the magnitude as the base-ten
logarithm of the maximum ground motion (in micrometers) recorded on a Wood-Anderson short-period
seismometer one hundred kilometers from the earthquake. Richter was pragmatic in his definition, and
chose a value for a magnitude zero that insured that most of the earthquakes routinely recorded would
have positive magnitudes. Also, the Wood-Anderson short-period instrument that Richter chose for his
reference records seismic waves with a period of about 0.8 seconds, roughly the vibration periods that
we feel and that damage our buildings and other structures.
Example seismogram recorded on a Wood-Anderson short period
seismogram. The top waveform shows the broad-band displacement,
the lower trace shows the corresponding ground motion that would
register on a Wood-Anderson seismograph.
Richter also developed a distance correction to account for the variation in maximum ground motion
with distance from an earthquake (the dashed curves shown in the above diagram show his relationship
for southern California). The precise rate that the peak ground motions decrease with distance depends
on the regional geology and thus the magnitude scale for different regions is slightly dependent on the
"distance correction curve".
Thus originally, Richter's scale was specifically designed for application in southern California.
Richter's method became widely used because it was simple, required only the location of the
earthquake (to get the distance) and a quick measure of the peak ground motion, was more reliable than
older measures such as intensity. It became widely used, well established, and forms the basis for many
of the measures that we continue to use today. Generally the magnitude is computed from seismographs
from as many seismic recording stations as are available and the average value is used as our estimate
of an earthquake's size.
We call the Richter's original magnitude scale ML (for "local magnitude"), but the press usually reports
all magnitudes as Richter magnitudes.
Teleseismic Magnitude Scales
To study earthquakes outside southern California, Richter extended the concepts of his local magnitude
scale for global application. In the 1930's through the 1950's together with Beno Gutenberg, Richter
constructed magnitude scales to compare the size of earthquakes outside of California. Ideally they
wanted a magnitude scale that gave the same value if the earthquake is recorded locally or from a great
distance. That way you could compare the seismicity of earthquakes in different parts of Earth. But the
extension of methods to estimate the local magnitude is complicated because the type of wave
generating the largest vibrations and the period of the largest vibrations recorded at different distances
from an earthquake varies. Near the earthquake the largest wave is a short-period S-wave, at greater
distances longer-period surface waves become dominant.
To exploit the best recorded signal (the largest) magnitude scales were developed for "teleseismic"
(distant) observations using P waves or Rayleigh waves. Eventually the teleseismic P-wave scale
became known as "body-wave magnitude" and the Rayleigh wave based measure came to be called
"surface-wave magnitude". The surface-wave magnitude is usually measured from 20s period Rayleigh
waves, which are very well transmitted along Earth's surface and thus usually well observed.
Gutenberg and Richter developed two magnitudes for application to
distant earthquakes: mb is measured using the first five seconds of a
teleseismic (distant) P-wave and Ms is derived from the maximum
amplitude Rayleigh wave.
Problems with Magnitude Scales
There are several problems associated with using magnitude to quantify earthquakes, and all are a
direct consequence of trying to summarize a process as complex as an earthquake in a single number.
First, since the distance corrections depend on geology each region must have a slightly different
definition of local magnitude. Also, since at different distances we rely on different waves to measure
the magnitude, the estimates of earthquake size don't always precisely agree. Also, deep earthquakes do
not generate surface waves as well as shallow earthquakes and magnitude estimates based on surface
waves are biased low for deep earthquakes.
Also, measures of earthquake size based on the maximum ground shaking do not account for another
important characteristic of large earthquakes - they shake the ground longer. Consider the example
shown in the diagram below. The two seismograms are the P-waves generated by magnitude 6.1 and
7.7 earthquakes from Kamchatka. The body-wave magnitude for these two earthquakes is much closer
because the rule for estimating body-wave magnitude is to use the maximum amplitude in the first five
seconds of shaking. As you can see, the difference in early shaking between the two earthquakes is
much less than the shaking a little bit later which indicates the larger difference in size.
Teleseismic (distant) P-waves generated by two earthquakes in
Kamchatka and recorded at station CCM, Cathedral Caves, MO, US. The
signals that would be recorded on a on a short-period seismometer are
shown using the same scale. The time is referenced to the onset of
rupture for each earthquake.
Even after 5 seconds the amplitude ratio of these P waves does not accurately represent the difference
in size of these two earthquakes. The magnitude 6.1 event probably ruptured for only a few seconds,
the magnitude 7.7 ruptured for closer to a minute.
Earthquake Dimensions - Rupture Size and Offset
Another measure of earthquake size is the area of the fault that slipped during the earthquake. During
large earthquakes the part of the fault that ruptures may be hundreds of kilometers long and 10s of
kilometers deep. Smaller earthquake rupture smaller portions of the fault. Thus the area of the rupture
is an indicator of the earthquake size.
The size of the area that slips during an earthquake increases with
earthquake size. The shaded regions on the fault surface are the areas
that rupture during different size events. The largest earthquakes
generally rupture the entire depth of the fault, which is controlled by
temperature. The temperature increases with depth to a point where
the rocks become plastic and no longer store the elastic strain energy
necessary to fail suddenly.
Usually we estimate fault rupture areas using the location of aftershocks, but we may also estimate the
area of rupture from seismograms if the observations are of high quality.
Another measure of an earthquake size is the dimension of the offset produced during an earthquake that is, how far did the two sides move? Small earthquakes have slips that are less than a centimeter,
large earthquakes move the rocks about 10-20 meters.
Kanimori's moment magnitude scale2
Seismic moment is a quantity that combines the area of the rupture and the amount of fault offset with
a measure of the strength of the rocks - the shear modulus µ.
Seismic Moment = M = µ · A · s
0
where A is the fault's rupture area and s is the area-averaged slip.
Usually we measure the moment directly from seismograms, since the size of the very long-period
waves generated by an earthquake is proportional to the seismic moment. The physical units of seismic
moment are force x distance, or dyne-cm.
For scientific studies, the moment is the measure we use since it has fewer limitations than the
magnitudes, which often reach a maximum value (we call that magnitude saturation).
To compare seismic moment with magnitude, Mw , we use a formula constructed by Hiroo Kanamori
of the California Institute of Seismology:
Mw = 2 / 3 · log(M ) - 10.7
0
where the units of the moment are in dyne-cm. If the units of measure of the seismic moment are more
conventional SI base units, i.e. newton-meters,
Mw = 2 / 3 · log(M ) – 6.1
0
Magnitude Summary
The symbols used to represent the different magnitudes are
Magnitude
Symbol
Wave
Period
Local (Richter)
ML
S or Surface Wave*
0.8 s
Body-Wave
mb
P
1s
Surface-Wave
Ms
Rayleigh
20 s
Mw
Moment
Rupture Area, Slip
> 100 s
*at the distances appropriate for local magnitude, either the S-wave or the surface waves generally
produce the largest vibrations.
2 Hanks, T C and Kanamori, H; 1977, A Moment Magnitude Scale, JGR 84, B5, 2348-2350. Click here!
Magnitude and energy release
Clearly, the larger the earthquake and, in general, the larger the magnitude, the more pent-up strain
energy is released in the event. The energy released (or better that pre-release potential energy for
release) is not easily determined. You might note that the units of the seismic moment are N·m
describing a rotational moment and that these same units can describe work done by a force measured
in N [newtons] acting through a distance measured in m [metres]. The scale of the seismic moment for
an earthquake and the amount of energy pent-up or released is, however, not 1:1. It depends on the
very character of the earthquake. The seismic moment is that moment that produces the radiating Pwave field of observation. All energy is not released into the P-wave field and can be distributed into
other wave fields and into other tectonic work like surface uplifts and the straight-forward damage to
rock and structure. Roughly, for shallow earthquakes,
ES = 5 x 10-5 M0,
but may range orders of magnitude larger or smaller!
Kanimori (1977)3 explored the question of energy release in great earthquakes.
Giant Earthquakes
The seismic moment and moment magnitude give us the tool we need to compare the size of the largest
quakes. We find that the "moment release" in shallow earthquakes throughout the entire century is
dominated by several large subduction zone earthquake sequences. First, let's compare the amount of
energy released in the different plate settings:
or we can just compare the largest four earthquakes (those with magnitudes greater than 9) with all the
other shallow earthquakes.
3 Kanimori, H; The Energy Release in Great Earthquakes, JGR 82, 20, 2981-2987. Click here!
How often do Giant Earthquakes occur?
The following diagram shows all great (MW > 7.9) during the 20th century through to the Honshu
(March 11, 2011) event. Great earthquakes are infrequent but it is they which release most of the
tectonic stress in the Earth's lithosphere4.
4 See this IRIS “one-page”: How often do earthquakes occur?
In the previous graph, the straight line fit represents a Gutenberg-Richter power law of the form
log N = a – b·MW
with b = 1.34. Here, b was calculated discounting the outlying M W ~ 9.5 Chile-Peru-1960 event. I argue, with
this admittedly restricted fit, that MW ~ 9.5 events might only be expected to recur on a 400-500 year interval. A
classical Gutenberg-Richter estimate for active seismic regions of b ~ 1 would suggest much more frequent
extremely large events. The period of observations extends through the 20 th century to the Honshu (March 11,
2011) event. Also, note that the moment magnitudes used here are those reported by the USGS (their rapid CMT
determination) and these have been and are being subsequently corrected. For example, the Banda Aceh 5
(December 26, 2004) event has been upgraded to MW ~ 9.26 and even 9.3 from 9.1 in some subsequent analyses.
These very great earthquakes are infrequent and the building of a statistical-predictive model based on so very
few events is problematical if not foolish.
Acknowledgement: Much of the story, presented here with some editorial additions, is due to Charles Ammon,
Professor of Seismology at Penn-State University. On leave at Saint Louis University in the early 2000s, he gave
an excellent introductory and comprehensive course in seismology (EAS A 193). Recall that SLU was
established as the first geophysical school in North America in 1808.
5 Also called the Great Sumatra-Adaman earthquake
6 See IRIS analysis: http://www.iris.edu/hq/gallery/photo/3770