Earthquake focal mechanisms within the boundary zone are
consistent with the overall plate motions and illustrate some of
their complexities. In the Gulf of California we see both strikeslip faulting along oceanic transforms and normal faulting on
ridge segments. The San Andreas fault system, composed of the
main fault and some others, has both pure strike-slip earthquakes (Parkfield) and earthquakes with some dip-slip motion
(Northridge (Section 4.5.3), San Fernando, and Loma Prieta)
when it deviates from pure transform behavior. The seismicity
also shows that the plate boundary zone is quite broad.
Although the San Andreas fault system is the locus of most
of the plate motion (Fig. 4.5-13) and hence large earthquakes,
seismicity extends as far eastward as the Rocky Mountains. For
example, the Landers earthquake shows strike-slip motion east
of the San Andreas, and the Borah Peak earthquake illustrates
the extensional faulting that occurs in the Basin and Range.
These focal mechanisms are consistent with the motions shown
by space-based geodetic measurements, discussed shortly, and
with geologic studies.
5.2.2 Global plate motions
The relative plate motions show how the plate boundary geometry is evolving and has evolved. The Juan de Fuca plate is
subducting under North America faster than new lithosphere
is being added to it by sea floor spreading at its boundary with
the Pacific plate, so this plate was larger in the past and is
shrinking. Rotating the Pacific plate backwards with respect
to North America shows that 10 million years ago the Gulf of
California had not yet begun to open by sea floor spreading.
These changes are part of the evolution of the plate boundary
in western North America, in which the large oceanic Farallon
plate that used to be between the Pacific and North American
plates began subducting under North America at about
40 Ma, 3 leaving the Juan de Fuca plate as a remnant and
forming the San Andreas fault.
At this point you may be wondering how Euler poles are
found. Until recently, this was done by combining three different types of data from different boundaries. The rates of
spreading are found from sea floor magnetic anomalies, which
form as the hot rock at ridges cools and acquires magnetization
parallel to the earth’s magnetic field. Because the history of
reversals of the earth’s magnetic field is known, the anomalies
can be dated, so their distance from the ridge where they
formed shows how fast the sea floor moved away from the
ridge. The directions of motion are found from the orientations
of transform faults and the slip vectors of earthquakes on transforms and at subduction zones. Euler vectors are found from
the relative motion data, using geometrical conditions we have
discussed. The process is easy to visualize. Because slip vectors
and transform faults lie on small circles about the pole, the pole
must lie on a great circle at right angles to them (Fig. 5.2-2).
Similarly, the rate of plate motion increases with the sine of
the distance from the pole (Eqn 2). These constraints make it
possible to locate the poles. Determination of Euler vectors for
all the plates can thus be treated as an overdetermined least
squares problem whose solution (Section 7.5) gives a global
relative plate motion model. Because these models use spreading rates determined from magnetic anomaly data that span
several million years, they describe plate motions averaged
over the past few million years. 4
Table 5.2-1 gives such a model, known as NUVEL-1A, 5
which specifies the motions of plates (Fig. 5.2- 4) with respect
to North America. The vectors follow the convention that each
named plate moves counterclockwise relative to North America.
Although the table lists only Euler vectors with respect to
North America, the motion of plates with respect to other
plates is easily found using vector arithmetic. For example,
ω ij = −ω ji ,
(9)
so we reverse the plate pair using the negative of the Euler
vector. The pole for the new plate pair is the antipole, with
latitude of opposite sign and longitude increased by 180°. The
magnitude (rotation rate) stays the same. We can also reverse
the plate pair by keeping the same pole and making the rotation rate negative (clockwise rather than counterclockwise).
Although we usually use positive rotation rates, negative ones
sometimes help us visualize the motion. For example, the table
shows the Pacific–North America pole at about −49°N, 102°E,
so the North America–Pacific pole is at about 49°N, (102 + 180
= 282)°E, which is in southeastern Canada. Thus, about this
pole, North America rotates counterclockwise with respect to
the Pacific, or the Pacific rotates clockwise with respect to
North America, as shown in Fig. 5.2-3.
For other plate pairs we assume that the plates are rigid, so
all motion occurs at their boundaries. We can then add Euler
vectors,
ω jk = ω ji + ω ik
(10)
because the motion of plate j with respect to plate k equals
the sum of the motion of plate j with respect to plate i and the
motion of plate i with respect to plate k. Thus if we start with a
set of vectors all with respect to one plate, e.g., i, we use
ω jk = ω ji − ω ki
(11)
to form any Euler vector needed. These operations are easily
done using the Cartesian components (Eqn 4), as shown in
this chapter’s problems. We can also perform the analogous
operations on linear velocity vectors at a specific site.
3 “Ma” is often used to denote millions of years before the present.
4 The most recent magnetic reversal occurred about 780,000 years ago, so any plate
model based on paleomagnetic data must average at least over that interval.
5 NUVEL-1 (Northwestern University VELocity) was developed as a new
(“nouvelle”) model (DeMets et al., 1990). The multiyear development prompted
the suggestion that “OLDVEL” might be a better name. Due to changes in the
paleomagnetic time scale the model was revised to NUVEL-1A (DeMets et al., 1994).
This change caused a slight difference in the rates of relative motion, but not in the
poles and hence directions of relative motion.
5.2 Plate kinematics 293
consistent with the overall plate motions and illustrate some of
their complexities. In the Gulf of California we see both strikeslip faulting along oceanic transforms and normal faulting on
ridge segments. The San Andreas fault system, composed of the
main fault and some others, has both pure strike-slip earthquakes (Parkfield) and earthquakes with some dip-slip motion
(Northridge (Section 4.5.3), San Fernando, and Loma Prieta)
when it deviates from pure transform behavior. The seismicity
also shows that the plate boundary zone is quite broad.
Although the San Andreas fault system is the locus of most
of the plate motion (Fig. 4.5-13) and hence large earthquakes,
seismicity extends as far eastward as the Rocky Mountains. For
example, the Landers earthquake shows strike-slip motion east
of the San Andreas, and the Borah Peak earthquake illustrates
the extensional faulting that occurs in the Basin and Range.
These focal mechanisms are consistent with the motions shown
by space-based geodetic measurements, discussed shortly, and
with geologic studies.
5.2.2 Global plate motions
The relative plate motions show how the plate boundary geometry is evolving and has evolved. The Juan de Fuca plate is
subducting under North America faster than new lithosphere
is being added to it by sea floor spreading at its boundary with
the Pacific plate, so this plate was larger in the past and is
shrinking. Rotating the Pacific plate backwards with respect
to North America shows that 10 million years ago the Gulf of
California had not yet begun to open by sea floor spreading.
These changes are part of the evolution of the plate boundary
in western North America, in which the large oceanic Farallon
plate that used to be between the Pacific and North American
plates began subducting under North America at about
40 Ma, 3 leaving the Juan de Fuca plate as a remnant and
forming the San Andreas fault.
At this point you may be wondering how Euler poles are
found. Until recently, this was done by combining three different types of data from different boundaries. The rates of
spreading are found from sea floor magnetic anomalies, which
form as the hot rock at ridges cools and acquires magnetization
parallel to the earth’s magnetic field. Because the history of
reversals of the earth’s magnetic field is known, the anomalies
can be dated, so their distance from the ridge where they
formed shows how fast the sea floor moved away from the
ridge. The directions of motion are found from the orientations
of transform faults and the slip vectors of earthquakes on transforms and at subduction zones. Euler vectors are found from
the relative motion data, using geometrical conditions we have
discussed. The process is easy to visualize. Because slip vectors
and transform faults lie on small circles about the pole, the pole
must lie on a great circle at right angles to them (Fig. 5.2-2).
Similarly, the rate of plate motion increases with the sine of
the distance from the pole (Eqn 2). These constraints make it
possible to locate the poles. Determination of Euler vectors for
all the plates can thus be treated as an overdetermined least
squares problem whose solution (Section 7.5) gives a global
relative plate motion model. Because these models use spreading rates determined from magnetic anomaly data that span
several million years, they describe plate motions averaged
over the past few million years. 4
Table 5.2-1 gives such a model, known as NUVEL-1A, 5
which specifies the motions of plates (Fig. 5.2- 4) with respect
to North America. The vectors follow the convention that each
named plate moves counterclockwise relative to North America.
Although the table lists only Euler vectors with respect to
North America, the motion of plates with respect to other
plates is easily found using vector arithmetic. For example,
ω ij = −ω ji ,
(9)
so we reverse the plate pair using the negative of the Euler
vector. The pole for the new plate pair is the antipole, with
latitude of opposite sign and longitude increased by 180°. The
magnitude (rotation rate) stays the same. We can also reverse
the plate pair by keeping the same pole and making the rotation rate negative (clockwise rather than counterclockwise).
Although we usually use positive rotation rates, negative ones
sometimes help us visualize the motion. For example, the table
shows the Pacific–North America pole at about −49°N, 102°E,
so the North America–Pacific pole is at about 49°N, (102 + 180
= 282)°E, which is in southeastern Canada. Thus, about this
pole, North America rotates counterclockwise with respect to
the Pacific, or the Pacific rotates clockwise with respect to
North America, as shown in Fig. 5.2-3.
For other plate pairs we assume that the plates are rigid, so
all motion occurs at their boundaries. We can then add Euler
vectors,
ω jk = ω ji + ω ik
(10)
because the motion of plate j with respect to plate k equals
the sum of the motion of plate j with respect to plate i and the
motion of plate i with respect to plate k. Thus if we start with a
set of vectors all with respect to one plate, e.g., i, we use
ω jk = ω ji − ω ki
(11)
to form any Euler vector needed. These operations are easily
done using the Cartesian components (Eqn 4), as shown in
this chapter’s problems. We can also perform the analogous
operations on linear velocity vectors at a specific site.
3 “Ma” is often used to denote millions of years before the present.
4 The most recent magnetic reversal occurred about 780,000 years ago, so any plate
model based on paleomagnetic data must average at least over that interval.
5 NUVEL-1 (Northwestern University VELocity) was developed as a new
(“nouvelle”) model (DeMets et al., 1990). The multiyear development prompted
the suggestion that “OLDVEL” might be a better name. Due to changes in the
paleomagnetic time scale the model was revised to NUVEL-1A (DeMets et al., 1994).
This change caused a slight difference in the rates of relative motion, but not in the
poles and hence directions of relative motion.
5.2 Plate kinematics 293