The area of locking has interesting implications. Because
an earthquake’s seismic moment is the product of the fault
area, coseismic slip, and rigidity, the fault width and rate at
which slip accumulates give insight into the maximum seismic
moment that the locked fault could release in a future earthquake. The San Andreas data (Fig. 4.5-13) indicate that the
vertically dipping fault is locked to a depth of about 20 km,
which is similar to the maximum depth of small earthquakes
and the inferred lower extent of rupture in large earthquakes
along the fault. As discussed in Section 5.7, this depth is generally consistent with studies of rock strength and friction,
which imply that rocks deeper than about 20 km are weak
and undergo stable sliding rather than accumulate elastic strain
for future earthquakes. The Alaska situation is quite different
because the plate interface has a shallow dip (Fig. 4.5-16),
so there is a large fault area at depths shallow enough to
accumulate strain and then rupture. Hence, as we will see in
Section 4.6, the largest earthquakes occur at shallow-dipping
subduction zones and are much bigger than those for transform
boundaries. In either environment, however, it is not clear
whether the entire locked region contributes to the seismic slip
or whether part of the fault slips rapidly in the earthquake
and another part contributes to aseismic afterslip.
To complicate matters even further, it is worth bearing in
mind that we still do not have good geodetic data spanning
even one full seismic cycle, much less such data combined with
detailed studies of earthquakes at either end. Hence we have
little insight into the different possible time-variable effects like
afterslip or the transient effects due to earthquakes on nearby
faults or other segments of the same fault. Thus it may be quite
some time before many of these issues are resolved.
An intuitive way to summarize some of these ideas is to think
of the seismic cycle as a fault’s “slip budget,” analogous to personal finances. Given our income (plate motion), we spend
some immediately (aseismic slip) and save some (locked slip).
The savings are used for major purchases (earthquakes) at a
rate depending on the price of individual purchases (coseismic
slip), expenses associated with these major purchases (postseismic slip), and our saving rate (locked slip). Thus, although
we can estimate roughly when we might make a future large
purchase, the actual date depends on unpredictable changes in
the price (variable earthquake size) and changes in our savings
beyond our steady income and regular expenses, due to gifts or
unanticipated expenses (effects of other earthquakes). Thus
even in this simple analogy the earthquake cycle is complicated.
4.6 Source parameters
4.6.1 Magnitudes and moment
So far in this chapter we have discussed using seismic waves
radiated by earthquakes to study their source geometry and
focal depth. While recognizing the limitations on what the
seismic waves can tell us about the actual source process, we
have seen that for most earthquakes, assuming a simple fault
geometry and source model allows us to estimate parameters
that are generally consistent with other data and our geological
instincts. We thus proceed further in using seismic waves to
learn more about the faulting process.
In fact, even before earthquake mechanisms were studied,
seismologists’ second need after learning to locate earthquakes
was to quantify their size, both for scientific purposes and to
discuss their effects on society. The first measure introduced
was the magnitude, which is based on the amplitude of the
resulting waves recorded on a seismogram. The concept is
that the wave amplitude reflects the earthquake size once the
amplitudes are corrected for the decrease with distance due to
geometric spreading and attenuation. Magnitude scales thus
have the general form
M = log (A/T) + F(h, ∆) + C,
(1)
where A is the amplitude of the signal, T is its dominant
period, F is a correction for the variation of amplitude with the
earthquake’s depth h and distance ∆ from the seismometer, and
C is a regional scale factor. 1 Magnitude scales are thus logarithmic, so an increase in one unit, as from magnitude “5” to
“6,” indicates a ten-fold increase in seismic wave amplitude.
Measured magnitudes range more than 10 units 2 because the
displacements measured by seismometers span more than a
factor of 10 10 .
The earliest magnitude scale, introduced by Charles Richter
in 1935 for southern California earthquakes, is the local magnitude, M L , often referred to as the “Richter scale.” Figure 4.6-1
shows how M L is determined from the amplitude measured on
a specific seismograph, known as the Wood–Anderson seismograph. The magnitude of the largest arrival (often the S wave)
is measured and corrected for the distance between the source
and the receiver, given by the difference in the arrival times of
the P and S waves. The scale
M L = log A + 2.76 log ∆ − 2.48,
(2)
defined for earthquakes in southern California, is a form of
Eqn 1 with the instrument period (0.8 s) and nearly constant
(shallow) depth incorporated in the constants, and the distance
in km. Richter magnitudes in their original form are no longer
used because most earthquakes do not occur in California
and Wood–Anderson seismographs are rare. However, local
magnitudes are sometimes still reported because many buildings have resonant frequencies near 1 Hz, close to that of a
Wood–Anderson seismograph, so M L is often a good indication of the structural damage an earthquake can cause.
With time, various local and global magnitude scales
evolved. For global studies, the primary two were the body
4.6 Source parameters 263
1 We use the notations “log” for log 10 , and “ln” for the natural log e .
2 Magnitudes can be negative for very small displacements; a magnitude −1 earthquake might correspond to a hammer blow.
an earthquake’s seismic moment is the product of the fault
area, coseismic slip, and rigidity, the fault width and rate at
which slip accumulates give insight into the maximum seismic
moment that the locked fault could release in a future earthquake. The San Andreas data (Fig. 4.5-13) indicate that the
vertically dipping fault is locked to a depth of about 20 km,
which is similar to the maximum depth of small earthquakes
and the inferred lower extent of rupture in large earthquakes
along the fault. As discussed in Section 5.7, this depth is generally consistent with studies of rock strength and friction,
which imply that rocks deeper than about 20 km are weak
and undergo stable sliding rather than accumulate elastic strain
for future earthquakes. The Alaska situation is quite different
because the plate interface has a shallow dip (Fig. 4.5-16),
so there is a large fault area at depths shallow enough to
accumulate strain and then rupture. Hence, as we will see in
Section 4.6, the largest earthquakes occur at shallow-dipping
subduction zones and are much bigger than those for transform
boundaries. In either environment, however, it is not clear
whether the entire locked region contributes to the seismic slip
or whether part of the fault slips rapidly in the earthquake
and another part contributes to aseismic afterslip.
To complicate matters even further, it is worth bearing in
mind that we still do not have good geodetic data spanning
even one full seismic cycle, much less such data combined with
detailed studies of earthquakes at either end. Hence we have
little insight into the different possible time-variable effects like
afterslip or the transient effects due to earthquakes on nearby
faults or other segments of the same fault. Thus it may be quite
some time before many of these issues are resolved.
An intuitive way to summarize some of these ideas is to think
of the seismic cycle as a fault’s “slip budget,” analogous to personal finances. Given our income (plate motion), we spend
some immediately (aseismic slip) and save some (locked slip).
The savings are used for major purchases (earthquakes) at a
rate depending on the price of individual purchases (coseismic
slip), expenses associated with these major purchases (postseismic slip), and our saving rate (locked slip). Thus, although
we can estimate roughly when we might make a future large
purchase, the actual date depends on unpredictable changes in
the price (variable earthquake size) and changes in our savings
beyond our steady income and regular expenses, due to gifts or
unanticipated expenses (effects of other earthquakes). Thus
even in this simple analogy the earthquake cycle is complicated.
4.6 Source parameters
4.6.1 Magnitudes and moment
So far in this chapter we have discussed using seismic waves
radiated by earthquakes to study their source geometry and
focal depth. While recognizing the limitations on what the
seismic waves can tell us about the actual source process, we
have seen that for most earthquakes, assuming a simple fault
geometry and source model allows us to estimate parameters
that are generally consistent with other data and our geological
instincts. We thus proceed further in using seismic waves to
learn more about the faulting process.
In fact, even before earthquake mechanisms were studied,
seismologists’ second need after learning to locate earthquakes
was to quantify their size, both for scientific purposes and to
discuss their effects on society. The first measure introduced
was the magnitude, which is based on the amplitude of the
resulting waves recorded on a seismogram. The concept is
that the wave amplitude reflects the earthquake size once the
amplitudes are corrected for the decrease with distance due to
geometric spreading and attenuation. Magnitude scales thus
have the general form
M = log (A/T) + F(h, ∆) + C,
(1)
where A is the amplitude of the signal, T is its dominant
period, F is a correction for the variation of amplitude with the
earthquake’s depth h and distance ∆ from the seismometer, and
C is a regional scale factor. 1 Magnitude scales are thus logarithmic, so an increase in one unit, as from magnitude “5” to
“6,” indicates a ten-fold increase in seismic wave amplitude.
Measured magnitudes range more than 10 units 2 because the
displacements measured by seismometers span more than a
factor of 10 10 .
The earliest magnitude scale, introduced by Charles Richter
in 1935 for southern California earthquakes, is the local magnitude, M L , often referred to as the “Richter scale.” Figure 4.6-1
shows how M L is determined from the amplitude measured on
a specific seismograph, known as the Wood–Anderson seismograph. The magnitude of the largest arrival (often the S wave)
is measured and corrected for the distance between the source
and the receiver, given by the difference in the arrival times of
the P and S waves. The scale
M L = log A + 2.76 log ∆ − 2.48,
(2)
defined for earthquakes in southern California, is a form of
Eqn 1 with the instrument period (0.8 s) and nearly constant
(shallow) depth incorporated in the constants, and the distance
in km. Richter magnitudes in their original form are no longer
used because most earthquakes do not occur in California
and Wood–Anderson seismographs are rare. However, local
magnitudes are sometimes still reported because many buildings have resonant frequencies near 1 Hz, close to that of a
Wood–Anderson seismograph, so M L is often a good indication of the structural damage an earthquake can cause.
With time, various local and global magnitude scales
evolved. For global studies, the primary two were the body
4.6 Source parameters 263
1 We use the notations “log” for log 10 , and “ln” for the natural log e .
2 Magnitudes can be negative for very small displacements; a magnitude −1 earthquake might correspond to a hammer blow.