Pure Appl. Geophys. 170 (2013), 2163–2172
Ó 2013 Springer Basel
DOI 10.1007/s00024-013-0667-9
Pure and Applied Geophysics
Relative Motion Between the Rivera and North American Plates Determined
from the Slip Directions of Earthquakes
GERARDO SUÁREZ,1 SAID H. JARAMILLO,1 and W. L. BANDY1
Abstract—So far, the direction and rate of relative motion
between the Rivera and the North American plates (RIV-NAM) has
been determined by the combination of two Euler poles: Rivera
(RIV), with respect to Pacific (PAC), and PAC with respect to North
America. Here, we estimate the relative motion of this plate pair
(RIV-NAM) assuming that the horizontal projection of the direction
of slip of the earthquakes occurring on the RIV-NAM boundaries
reflect their relative plate motion. A catalog of earthquakes for which
focal mechanisms are reported since 1976 is used in the analysis.
Earthquakes were considered in the three segments of the RIV-NAM
plate boundary: the subduction zone of the Rivera plate beneath the
Jalisco block, the Tres Marias Escarpment and the events associated
with the Tamayo Fracture Zone. The best fitting Euler pole is
determined using a grid search of 64 potential poles. The slip
direction predicted for each grid point is compared to the slip
direction of the focal mechanisms of the earthquakes on the plate
boundary. The best fitting Euler pole, determined in a root mean
square sense (RMS), is located at 21.8°N, 107.6°W. A rate of rotation
of 5.3°/year is estimated assuming the seismic earthquake cycle of the
1932 and 1995 great earthquakes represents a lower bound of the rate
of plate motion in the subduction zone. The best fitting Euler pole
shows that the subduction of the Rivera plate takes place in a
direction perpendicular to the trench with a relative velocity of
4.3 cm/year, offshore Manzanillo. The rate of relative motion RIVNAM decreases from SE to NW. North of approximately 21°N, the
subduction of the Rivera plate becomes oblique to the trench and the
relative velocity between the two plates decreases to an average of
1.9 cm/year. This slow rate of convergence may explain the rapid
decrease of seismicity in the trench and the apparent absence of large
earthquakes in this region. In the Tres Marias Escarpment, our bestfitting pole suggests that subduction stops, giving way to high-angle
reverse faulting perpendicular to the Tres Marias Escarpment, in
agreement with the reverse faulting earthquakes occurring here. To
the north of 22.5°N, the slip predicted by the best-fitting pole suggests
right-lateral faulting in a direction parallel to the Tamayo Fracture
Zone, at a very low velocity (0.5–1.0 cm/year). The best fitting Euler
pole determined here lies very close to the RIV-NAM plate boundary
in the vicinity of the Tamayo Fracture Zone. This location of our best
fitting Euler pole explains the low relative plate velocity, the relatively low level of seismic activity and the presence of a broad zone
of deformation that accommodates the RIV-NAM motion.
1
Instituto de Geofı́sica, Universidad NacionalAutónoma
de México, Ciudad Universitaria, 04510 México D.F., Mexico.
E-mail: [email protected]; [email protected]
1. Introduction
The collision of the Farallon-Pacific spreading
center with the western margin of North America at
about 28 Ma, marked the beginning of a profound
change in the tectonic environment of western North
America. The Farallon plate was segmented into a
series of smaller plates, one of which is the Rivera
plate (ATWATER 1970).
The exact location of the plate boundaries and the
direction and velocity of relative motion between
the Rivera and North America and the Rivera and the
Cocos plate have been debated in the literature since
the discovery that the Rivera behaved as a separate
plate (e.g., LARSON 1972; MINSTER and JORDAN 1979;
KLITGORD and MAMMERICKX 1982; MAMMERICKX and
KLITGORD 1982; NESS et al. 1985; BANDY and YAN
1989; DEMETS and STEIN 1990; BANDY 1992;
LONSDALE 1995; DEMETS and WILSON 1997; BANDY
et al. 1997; and SUÁREZ et al. 1999) (Fig. 1). One of
the major difficulties in obtaining accurate poles of
instantaneous motion for some of these plate
boundaries is the fact that the Rivera plate has
deformed and some of the plate boundaries have
changed locations and their style of deformation over
time (e.g., DEMETS and TRAYLEN 2000; BANDY et al.
2011). Furthermore, the RIV-NAM pole is obtained
by a combination of two Euler poles. The PAC-RIV
pole runs into the unavoidable problem of having a
big uncertainty because the Pacific-Rivera boundary
is very short. The errors in this pole are compounded
in the calculation of the Rivera-North American pole
of motion.
This paper discusses the relative motion between
the Rivera and the North American plates (RIVNAM). The Euler poles proposed to date, that
describe the motion between RIV-NAM, lie very
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G. Suárez et al.
close to the Rivera plate. Thus small changes in the
location of the pole induce large variations in both the
direction and in the rate of motion between
RIV-NAM. Therefore, the poles of relative motion of
RIV-NAM have been calculated combining the
Rivera-Pacific Euler pole with the one describing the
motion of the Pacific relative to North America. As
discussed above, this process compounds the errors of
each of the Euler poles involved.
An alternative method to estimate the pole of
relative motion between RIV-NAM, is to assume that
the horizontal projection of slip vectors of earthquakes occurring along the RIV-NAM plate
boundary reflects the instantaneous relative motion of
these plates. The purpose of this work is to calculate
the RIV-NAM best-fitting Euler pole, using the slip
directions of all earthquakes with published focal
mechanisms on the boundaries of the Rivera and
North American plates: earthquakes where the Rivera
Pure Appl. Geophys.
plate subducts the Jalisco block, events beneath the
Tres Marias Escarpment (TME) to the northwest of
the subduction zone, and earthquakes on the Tamayo
Fracture Zone (TFZ).
This last plate boundary is not clearly defined
(Fig. 1). Some authors suggest that here, the RIVNAM boundary coincides with two fractures zones
extending to the southeast from the East Pacific Rise
at 22°N and 22.5° (LONSDALE 1995; DEMETS and
WILSON 1997). However, practically all of the seismicity takes place in the vicinity of the TFZ (Fig. 1)
suggesting that a large fraction of the relative plate
motion takes place along this plate boundary. This
region has been defined as a diffuse plate boundary
where deformation takes place over a broad area.
Here, the slip direction was measured on the nodal
planes oriented nearly east west showing right-lateral
strike-slip motion (Fig. 2). We believe that it is valid
to use slip vectors in the area of the TFZ. Although
Figure 1
Black dots represent the epicentral locations of earthquakes reported by the ISC from 1976 to 2007. The area enclosed by a dashed line and the
shadowed zone represents the rupture length of 3 June and 18 June, 1932 earthquakes, respectively. The oval enclosed by a continuous line
represents the aftershocks zone of the 9 October 1995. The boundaries of the Rivera plate are shown as: TTF-Tamayo Transform Fault; TFZTamayo Fracture Zone (dashed line); TME-Tres Marias Escarpment (solid line); EPR-East Pacific Rise; RTF-Rivera Transform Fault; MSSMoctezuma Spreading Segment; MAT-Middle American Trench (line with triangles)
Vol. 170, (2013)
Relative Motion Between the Rivera and North American Plates
2165
Figure 2
Focal mechanisms of the earthquakes used in this work are shown in low-hemispheric projections, where dark areas represent compressional
arrivals. The earthquakes are grouped as: 1) events on the subduction zone (5, 7, 8, 11, 13, 14 and 16); 2) earthquakes on the TME (1, 2 and
15); and 3) events in the vicinity of the TFZ (3, 4, 6, 9, 10 and 12)
the earthquakes here may not represent the full
motion between the plates (RIV-NAM), it has been
shown in other areas of diffuse deformation, like the
plate boundary between the Australian and Indian
plates, that the general direction of motion coincides
with the orientation of the slip vectors (GORDON et al.
1990; GORDON, 1998; ROYER et al. 2007).
The slip vectors of the published focal mechanisms are used in a grid search of potential Euler
poles. The pole of rotation that best fits the direction
of slip of all earthquakes in a root mean squares sense
(RMS) is assumed to be the best fitting pole for
RIV-NAM.
2. Tectonic Boundaries and Poles of Relative Motion
of the Rivera Plate
2.1. Plate Boundaries of the Rivera Plate
The limits between the Rivera and Pacific plates
are the Rivera Transform Fault (RTF) to the south
and the East Pacific Rise (EPR) to the northwest
(MINSTER and JORDAN 1979; EISSLER and MCNALLY
1984; DEMETS and STEIN 1990) (Fig. 1). The Euler
pole defining the relative motion between these two
plates is fairly well constrained, although changes in
its location since 0.78 Ma are still being debated.
The plate boundary and the style of tectonic
deformation between Rivera and Cocos are controversial. There are no bathymetric features that can be
clearly associated with the Rivera-Cocos plate boundary. The relative plate motion has been interpreted as
strike-slip, a rift, or a compressional environment
(e.g., KLITGORD and MAMMERICKX 1982; NIXON 1982;
EISSLER and MCNALLY 1984; MAMMERICKX and
CARMICHAEL 1989; DEMETS and STEIN 1990; BOURGOIS
and MICHAUD 1991; LONSDALE 1995; DeMETS and
WILSON 1997; MICHAUD et al. 1997; BANDY et al. 1995,
1998a, b, 2000; KOSTOGLODOV and BANDY 1995;
SUÁREZ et al. 1999; SERRATO-DÍAZ et al. 2004).
The Middle American Trench (MAT), between
approximately 18.5° North and the Islas Marias,
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G. Suárez et al.
marks the boundary between the Rivera and the North
American plate. Although this segment of the MAT is
a plate boundary with relatively low seismicity, some
of the larger subduction earthquakes in the MAT have
originated in this segment of the trench: the great
Jalisco earthquake of 1932 and, more recently, the
1995 Colima-Jalisco earthquake (e.g., SINGH et al.
1985; PACHECO et al. 1997) (Fig. 1).
To the northwest of the MAT, the plate boundary
appears to be delimited by the TME and the TFZ.
EISSLER and MCNALLY (1984) suggested that the TFZ
acts as a right-lateral transform fault between these
two plates. Other authors, however, have suggested
that in this region the Rivera plate has been accreted
to the North American plate since 1.5 Ma (LONSDALE
1995; DEMETS and WILSON 1997; BIRD 2003).
Relative Motion Between Rivera and North
American Plates. There is a debate regarding the
location of the Euler pole and the rate of rotation
between the Rivera-North American (RIV-NAM)
plates (e.g., KOSTOGLODOV and BANDY 1995). However, all of these models agree that for the past 3 Ma,
the location of the pole lies very close to the Rivera
plate. Thus small changes in the location of the pole
Pure Appl. Geophys.
result in drastic changes in the rate and direction of
relative plate motion.
3. Methodology Used to Determine RIV-NAM Pole
of Rotation
3.1. Earthquakes Selected for the Analysis
The seismicity of western Mexico is dominated by
the subduction of the Cocos and Rivera plates beneath
the North American plate. Along the MAT, the
seismicity varies drastically along the strike-slip. To
the north of 20°N, the seismicity in the subduction
zone decreases rapidly both in the number and in the
magnitude of the earthquakes, with respect to that
observed in the south. The seismicity beneath the
TME and along the TFZ is sparse and diffuse (Fig. 1).
All published source mechanisms earthquakes in
the region encompassing the RIV-NAM plate boundary, occurring from 1976 to 2010, were collected
from the Global Centroid Moment Tensor Catalog
(GCMT) and other sources (Fig. 2; Table 1). The
epicentral locations of the earthquakes are those
reported by the International Seismological Centre.
Table 1
Epicentral Locations and Focal Mechanisms of the Earthquakes
Id
Date year-month-day
Latitude (°)
Longitude (°)
Depth (km)
Strike (°)
Dip (°)
Slip (°)
Azimuth of slip
vector projected (°)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1948-12-04a
1976-02-09b
1982-12-08
1989-01-31
1989-12-08c
1991-04-01
1995-10-09
1995-10-18
1999-03-12
2000-12-08
2001-04-29
2001-11-13
2003-01-22
2003-02-17
2007-02-11
2007-09-06
21.6
21.63
22.71
22.28
19.25
22.37
19.11
19.42
22.27
22.72
18.76
22.38
18.94
18.88
21.41
19.54
–106.7
–106.59
–106.82
–107.30
–105.14
–107.00
–104.20
–104.93
–107.35
–107.55
–104.58
–106.95
–104.30
–104.96
–106.27
–105.02
0d
11 ± 2
62
20.3
15
10
42.3
51.6
6.6
4.6
29
17.7
45.7
11.1
47.3
63.4
316
276
160
276
13
303
302
273
274
89
292
321
299
282
314
310
54
36
90
74
22
10
9
25
83
87
18
78
23
34
29
25
116
93
180
173
162
132
92
49
–179
178
77
–169
85
64
114
96
20 ± 4
3±2
340
283
31
351
30
44
273
271
35
310
34
38
20
34
a
JARAMILLO and SUAREZ (2011)
b
GOFF et al. (1987)
c
Global Centroidal Moment Tensor (CMT)
d
ISS
Vol. 170, (2013)
Relative Motion Between the Rivera and North American Plates
The database also includes the largest instrumental earthquake on the TME. This event, which took
place on 4 December 1948, had a magnitude Ms 6.9;
Mw 6.4 (JARAMILLO and SUAREZ 2011). The focal
mechanism of the 1948 earthquake indicates high
angle reverse faulting on NW to SE oriented nodal
planes (Fig. 2).
3.2. Grid Search for the Best Fitting Euler Pole
In order to determine the Euler pole that best
describes the relative motion between the Rivera and
North American plates, a grid search was conducted. At
each point of the grid, the direction of relative motion
was estimated and compared with the slip direction of
the focal mechanisms of the earthquakes on the RIVNAM plate boundaries. A grid spacing of 0.2° was
selected. This value is consistent with the estimated
errors in the epicentral locations of most of the
earthquakes used in the analysis. Furthermore, the
locations of the existing, best-fitting Euler poles describing the motion of this plate pair have error estimates that
are far greater than the proposed grid spacing.
The focal mechanisms used in the grid search are:
(1) Events that occur along the MAT reflecting
Rivera plate subduction; (2) Earthquakes that take
place beneath the TME; (3) Events with epicenters
2167
that lie in the vicinity to the TFZ (Fig. 2; Table 1).
The process followed in the grid search analysis is
summarized as follows:
1. A grid was generated from 21° to 22.4°N and 107°
to 108.4°W, with a spacing of 0.2°. This area
yields 64 potential Euler poles.
2. For each point on the grid, a velocity vector was
calculated for all earthquakes on the RIV-NAM
plate boundaries (Table 1). The velocity vector is
defined as the horizontal projection of the slip
vector of all published focal mechanisms.
3. The differences between the slip vectors of the
earthquakes and the direction of motion predicted
by each point on the grid were computed.
4. A root mean square value (RMS) was calculated
of the difference between the predicted and the
observed slip direction for each potential Euler
pole of the grid.
4. The Best-Fitting RIV–NAM Euler Pole
Before analyzing which is the best-fitting pole, it
is illustrative to compare independently the errors in
each of the three segments of the RIV-NAM plate
boundary (Fig. 3).
Figure 3
The graph shows the RMS errors between the observed and estimated direction of slip for the 64 poles on the grid. RMS errors are shown
separately for earthquakes along the subduction zone (MAT) (set 1); the TME (set 2), and the TFZ (set 3) (see inset)
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G. Suárez et al.
The errors between observed and predicted slip
directions in the MAT subduction zone are the
smallest. On this plate boundary, the RMS errors are
relatively constant and are the smaller of the three
plate boundaries. In contrast, the TME and the TFZ
show consistently larger errors. For all poles, the
errors are larger on the TFZ than on the TME
(Fig. 3). In the case of the TME, minima in RMS
errors are observed for poles 20–40. The errors rise
sharply for poles 41–64. For the rest of the poles, the
RMS errors on the TME plate boundary show large
variations and local minima (Fig. 3).
In the TFZ, not only are the errors larger compared to the other two segments, but they also show a
large variability, which makes it difficult to estimate
a minimum. On average, poles numbers 0–19 show
the largest errors (Fig. 3). The relatively large RMS
errors in the TFZ may be due to the fact that this plate
Pure Appl. Geophys.
boundary is probably a broad zone of deformation
and not a discrete fault accommodating the relative
plate motion here. In a zone of diffuse deformation, a
single pole would not fit all earthquakes.
Pole number 28 is at the center of a broad minimum and shows the smallest RMS value when the
three plate boundaries are considered jointly. This
point was selected as the best fitting Euler pole
(21.8°N, 107.6°W). The locations of the poles and
their associated RMS errors are shown on Fig. 4. In
plane view, pole number 28 clearly shows that the
errors increase for all poles that are farther away from
this point (Fig. 4). It is worth noting that the location
of the best-fitting Euler pole determined from the grid
search lies about 20 km to the east of the Euler pole
suggested by LONSDALE (1995) (Fig. 4). Statistically,
the slip predicted by the points inside the contour with
a value of RMS \ 20 have a 95 % confidence level.
Figure 4
Map view of the grid points used in the search of the best-fitting RIV-NAM Euler pole. The grid points are colored according to the observed
RMS values obtained from the difference between observed and predicted slip directions. The best-fitting Euler pole (blue point) lies in the
center of the minimum of the RMS errors. Errors increase away from this minimum. Other Euler poles proposed are shown as: square
(DEMETS and STEIN 1990); a pentagon (MINTER and JORDAN 1979); black circles (BANDY and PARDO 1994); a triangle (DEMETS et al. 1994); a
star (LONSDALE 1995); a diamond (BANDY et al. 1997); an asterisk (DEMETS and WILSON 1997); and an inverse triangle (DEMETS et al. 2010).
Red arrows represent the direction of slip predicted by the best fitting Euler pole and the green arrows the observed direction of slip of the
focal mechanisms. The bathymetry of the TME is shown in the inset from SANDWELL and SMITH (1997)
Vol. 170, (2013)
Relative Motion Between the Rivera and North American Plates
The analysis presented here allows determining
only the geographic location of the best-fitting Euler
pole. It is not possible, however, to estimate the rate
of rotation of the estimated Euler vector. In order to
estimate the angular velocity of the pole, a calculation is made following the approach of BANDY et al.
(1997). These authors propose that a lower bound of
the slip rate of the Rivera plate beneath the North
American plate may be obtained by summing the slip
observed during the most recent earthquake cycle in
this segment of the subduction zone. Summing the
slip of the 3 and 18 June 1932 and the 9 October 1995
great earthquakes, an angular velocity of rotation of
5.3°/year is determined.
5. Discussion of Results
The rate and direction of motion predicted by
the best fitting Euler pole indicate that south of
2169
approximately 20°N subduction of the Rivera plate
beneath the North America takes place in a direction
N30°E–N50°E, at a rate of approximately 4.31
cm/year. This direction is almost perpendicular to the
trench and agrees with the slip direction of the focal
mechanisms of the major earthquakes in the area
(Fig. 5).
North of 20°N, the convergence becomes oblique
to the subduction zone and the rate of relative motion
decreases sharply to about 1.9 cm/year (Fig. 5). This
change in direction of relative motion and the slower
slip rate may explain the decrease in the rate of
seismicity observed here (Fig. 1). RUTZ-LÓPEZ and
NUÑEZ-CORNÚ (2004) on the basis of locally recorded
earthquakes, suggested a subduction direction that is
oblique to the trench in agreement with the direction
of slip suggested here.
In the TME, the relative motion RIV-NAM is
perpendicular to the sharp bathymetric escarpment
that delineates the TME (Figs. 4, 5). The subduction
Figure 5
The arrows on the map indicate the average direction of slip along the various RIV-NAM plate boundaries predicted by the best-fitting Euler
pole. The number indicates the predicted rate of motion. Solid contour indicates the value of RMS \ 20 for the best-fitting Euler pole
proposed here (black point). Dashed ellipses indicate 95 % confidence areas for previous poles proposed. Shaded zone indicates region of
diffuse deformation proposed by DEMETS and WILSON (1997) and the fractures zones proposed by LONSDALE (1995). Other symbols indicate
previous proposed poles as in Fig. 4
2170
G. Suárez et al.
seems to stop in this segment of the trench, giving
way to high-angle reverse faulting earthquakes with
compressional axes oriented NE–SW, such as the
1948 and 1976 quakes (GOFF et al. 1987; JARAMILLO
and SUAREZ 2011). The sharp bathymetric relief of the
TME coincides with the presence of reverse faulting
as shown by the focal mechanisms (Figs. 2, 4). The
convergence rate on this compressional boundary is
approximately 0.9 cm/yr. This rate of relative motion
is considerably lower than that predicted by
KOSTOGLODOV and BANDY (1995) (2.0–3.0 cm/year)
based on seismotectonic arguments. It is possible that
the rate of rotation used here based on a seismic cycle
of only a few tens of years is a lower bound for the rate
of relative motion. Nevertheless, it should be pointed
out that the low level of seismic activity observed in
the TME is more consistent with the slow convergence
rate observed from our best fitting Euler pole.
On the northwestern RIV-NAM plate boundary,
the best-fitting Euler pole lies within the zone of
apparent diffuse deformation and explains some of
the seismic and bathymetric features in this region.
The location of this Euler pole close to this diffuse
plate boundary explains why the deformation is very
slow here. The rate of relative motion predicted by
our best fitting Euler pole for this plate segment is
only 0.5–1.0 cm/year. In an area of slow deformation
the seismicity is low in both the number of earthquakes and in magnitude, as observed in this region
(Figs. 1, 5). Furthermore, the location of our best
fitting Euler pole explains the very complicated
bathymetry observed in this area. LONSDALE (1995)
mapped some east–west features that coming off the
East Pacific Rise that are sharply truncated to the
east. The termination of these features to the east
appears to be controlled by the location the proposed
Euler pole.
The focal mechanisms of earthquakes in the
vicinity of the TFZ show almost pure right-lateral,
strike-slip motion parallel to the general orientation
of the TFZ (Fig. 2). This is in agreement with the slip
vectors predicted by the proposed new Euler pole
(Figs. 4, 5). It is possible that the deformation here is
taken up by a series of en-echelon, right-lateral faults
on a relatively broad zone of deformation. The Euler
vector proposed here would predict that some of the
east–west features mapped by LONSDALE (1995) to be
Pure Appl. Geophys.
normal faults. However, there are no focal mechanisms showing this type of motion.
6. Summary
A new Euler vector describing the relative motion
between the Rivera and North American plates was
determined using the horizontal projection of the slip
vectors of all the published focal mechanisms along
its plate boundaries.
The best fitting Euler vector obtained by fitting
the horizontal direction of slip of the focal mechanisms determined along the RIV-NAM plate
boundaries explains the style of deformation and
relative rate of motion along the three segments of
this boundary. The decrease in the rate of seismicity
from south to north on the MAT is explained by the
gradual decrease of the rate of relative motion. Furthermore, the direction of relative motion becomes
more oblique in the northern segment of the MAT.
There is, however, no evidence of forearc deformation due to this oblique subduction.
On the TME, the reverse faulting mechanisms
shown by the earthquakes in this region, and predicted by our best fitting Euler vector, may explain
the sharp bathymetric step here. The relatively low
rate of deformation is explained by the decrease in
the relative rate of motion predicted by the Euler
pole.
The location of the preferred Euler pole describing the RIV-NAM motion on the northwestern
boundary of the Rivera helps to understand some of
the problems encountered by previous studies. The
northwestern boundary of the Rivera plate appears to
be a zone of slow and very diffuse deformation. The
location of our best fitting Euler pole predicts that the
relative motion here should be very slow and helps to
explain the complex bathymetric features mapped in
the region.
Acknowledgments
SHJ acknowledges support from the Sistema Nacional de Investigadores (SNI) for the completion of
this work as a research assistant. The paper was
Vol. 170, (2013)
Relative Motion Between the Rivera and North American Plates
improved thanks to the valuable comments of an
anonymous reviewer and A. Schettino. This work
was supported by the Consejo Nacional de Ciencia y
Tecnologı́a (CONACYT) through grant number
082821.
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(Received August 24, 2012, revised March 12, 2013, accepted March 14, 2013, Published online April 12, 2013)