RICE UNIVERSITY
The Absolute Motion of Trenches and Age of the Subducting
Slab
by
David C. Mathews
A THESIS SUBMITTED
IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE
Master of Science
APPROVED, THESIS COMMITTEE:
Richard G. Gordon, Chair
Keck Professor of Geophysics, Earth
Science Department Chair
Dale S. Sawyer
Professor, Earth Science
Fenglin Niu
Professor, Earth Science
HOUSTON, TEXAS
December 2014
ABSTRACT
The Absolute Motion of Trenches and Age of the Subducting Slab
by
David C. Mathews
Previous work proposes that many trenches advance, but inferred motions vary
considerably between different estimates of plate motion relative to hotspots. We remedy
this by using recent estimates of absolute plate motions inferred from seismic anisotropy,
incorporating the MORVEL relative plate angular velocities, and fully propagating the
uncertainties. Nearly half the trench velocities differ significantly from prior results, with
the greatest differences at the Kermadec, New Hebrides, and Marianas trenches. Trench
velocity ranges from retreat of 126 ± 20 mm a-1 to advance of 52 ± 14 mm a-1 with a
median of 9 mm a-1 of retreat. Out of 57 locations, trench advance is significant at only
five locations (along the Hikurangi, Marianas, and Izu-Bonin trenches), retreat is
significant at 23 locations, and trench motion differs insignificantly from zero at 29
locations. Trench advance increases with age and absolute velocity of subducting
lithosphere and with angle of subduction.
Acknowledgments
I recognize first my wife, Danielle, who has unflinchingly supported my
endeavors the last few years. She has persevered through multiple moves, expertly
raising three wonderful boys, and just generally holding everything together. Thank you
for everything you do every day that is not recognized with a certificate or award, I love
you so much!
I also recognize my mother and father who always pushed me to try, succeed, and
reach for more through my entire childhood and as an adult. Without your love and
guidance I would never have attempted something of this magnitude.
Thank you also to the entire Tectonophysics group, our leader and my advisor,
Richard G. Gordon who constantly pushed me to do my best work and leave no stone
unturned in preparing this thesis. Also every member of the group that has helped me
along the way, notably Lin Zheng who did most of the heavy lifting on the uncertainties,
and also Lily Seidman, my courier, and Tuo, Svetlana, Jay, Steven, and all the other Rice
Earth Science students along the way.
A big thank you is also in order for the staff of the Earth Science Department,
notably Mary Ann who always kept me ahead of the deadlines, and Soookie who just
keeps the whole place together and running so smoothly.
Contents
Acknowledgments ..................................................................................................... iii
Contents ................................................................................................................... iv
List of Figures ............................................................................................................. v
List of Tables ............................................................................................................. vi
Trench Advance, Slab Dip, and the Age and Absolute Velocity of Lithosphere Entering a
Trench ....................................................................................................................... 1
1.1. Introduction .............................................................................................................. 3
1.2. Methods and Input Angular Velocities ..................................................................... 5
1.2.1. Set of Angular Velocities Used Herein ............................................................... 5
1.2.1.1. Differences from SKS-MORVEL ................................................................... 6
1.2.1.2. Differences from the Assumed Plate Geometry and Angular Velocities of
Schellart [2008] ........................................................................................................ 8
1.2.2. Relative Plate Motion Uncertainties ............................................................... 10
1.2.3. Absolute Trench Velocities .............................................................................. 11
1.2.4. Comparisons .................................................................................................... 12
1.3. Results .................................................................................................................... 12
1.4. Discussion ............................................................................................................... 22
1.4.1. Distribution of Trench Velocities ..................................................................... 22
1.4.2. Trench Retreat and Distance from Slab Edge .................................................. 23
1.4.3. Convergence Rate ............................................................................................ 24
1.4.4. Trench-normal Absolute Velocity of the Subducting Plate ............................. 25
1.4.5. Age of the Subducting Plate ............................................................................ 25
1.4.6. Trench Advance and Dips of Slabs ................................................................... 26
1.5. Conclusions............................................................................................................. 28
References ............................................................................................................... 33
Appendix A .............................................................................................................. 40
List of Figures
Figure 1 - Trench locations considered herein………………………………………………………..7
Figure 2 – Map of trench velocities from this study and Schellart [2008]……….………13
Figure 3 – Scatterplot of trench velocities and uncertainties…………………………………14
Figure 4 – Histogram of trench velocities and statistics…………………………………………16
Figure 5 – Trench velocity versus distance to nearest slab edge…………………………….17
Figure 6 – Trench velocity versus plate convergence rate………………………………………18
Figure 7 – Trench velocity versus trench-normal subducting plate velocity……………19
Figure 8 – Trench velocity versus age of subducting plate……………………………………..20
Figure 9 – Trench-normal subducting plate velocity versus age of subducting plate.21
Figure 10- Northwest Pacific seismicity and cross sections across trench locations…27
List of Tables
Table 1 – Comparison of angular velocities in this study versus Schellart [2008]……..29
Table 2 – Trench locations, trench velocities, confidence intervals, and plate ages…32
Chapter 1
Trench Advance, Slab Dip, and the Age
and Absolute Velocity of Lithosphere
Entering a Trench
David C. Mathews1, Richard G. Gordon1, and Lin Zheng1
1
Department of Earth Science, Rice University, Houston, TX, 77005, USA
Submitted December 2014:
Journal of Geophysical Research
1
2
Summary
How fast and in what direction do trenches move relative to the deep mantle?
Although it has been proposed that trenches are stationary in the mantle or that they all
retreat, i.e., they migrate relative to the deep mantle seaward toward the subducting plate,
recent work indicates that many trenches instead advance, i.e., they migrate relative to the
deep mantle toward the overriding plate. Inferred trench advance depends on estimates
of plate motion relative to the hot spots, which vary considerably. Here we remedy this
shortcoming by using a recent estimate of absolute plate motions inferred not from hot
spots, but from seismic anisotropy. The new set of angular velocities incorporates the
MORVEL relative plate angular velocities augmented by six updated and fourteen
additional angular velocities for small plates. Trench-perpendicular motion ranges from
retreat of 126 ± 20 mm a-1 to advance of 52 ± 14 mm a-1 with a median of 9 mm a-1 of
retreat. Out of 57 locations along trenches, trench advance is significant at only five
locations (along the Hikurangi, Marianas, and Izu-Bonin trenches), retreat is significant at
23 locations, and trench motion differs insignificantly from zero at 29 locations.
Surprisingly, trench advance tends to increase (and trench retreat decreases) with age of
subducting lithosphere. Trench advance also tends to increase with the absolute velocity
of the subducting plate. Trench advance is thus uncommon, mainly occurs where the
Pacific plate subducts beneath the Philippine Sea plate, and occurs where subducting
slabs dip most steeply.
3
1.1. Introduction
Plate tectonics provides explanations for many of Earth's large-scale features
including the network of deep sea trenches located along many of the edges of the ocean
basins. The mega-thrusts associated with the trenches are where almost all great
earthquakes occur. In this paper, we analyze the kinematics of the trenches as viewed
from a perspective of global plate motions.
How fast and in what direction trenches move relative to the deep mantle has been
debated since the recognition of plate tectonics. Following Talwani‘s [1969] proposition
that the trenches are stationary, Francheteau and Sclater [1970] showed that all plate
boundaries are in relative motion and cannot form a fixed frame of reference. Later,
Hamilton [2003, 2007] argued that sinking of the underthrust oceanic lithosphere at
trenches implies that all trenches retreat, i.e., they migrate relative to the deep mantle
seaward toward the subducting plate. More recently, from estimates of plate motion
relative to hot spots, Faccenna et al. [2007] found instead that ≈50% of trenches advance,
i.e., they migrate relative to the deep mantle toward the overriding plate. Later, Schellart
[2008; Schellart et al., 2008] proposed that ≈25 to 40% of trenches advance, depending
on the choice of relative plate motions and realization of the hot spot reference frame. As
different estimates of current plate motions relative to the hot spots differ considerably,
how many trenches (if any) do indeed advance is unclear.
Here we take an alternative approach by using a recent estimate of absolute plate
motions inferred from seismic anisotropy [Zheng et al., 2014]. Unlike prior estimates,
which incorporate the NUVEL-1A [DeMets et al., 1994] set of relative angular velocities
4
for the major plates, the new set of angular velocities incorporates the MORVEL set of
relative plate angular velocities [DeMets et al., 2010]. Moreover, prior estimates largely
used the motion of small plates estimated by Bird [2003]; herein we augment or replace
some of these with six updated and fourteen additional angular velocities for small plates.
We use the resulting set of absolute angular velocities to estimate trench velocities and
uncertainties at 57 locations. Over 40% of the trench velocities differ significantly from
prior results (i.e., those of Schellart [2008]), with the greatest differences along the
Kermadec, New Hebrides, and Marianas trenches [Wallace et al., 2005; Power et al.,
2012]. The median trench velocity is 9 mm a-1 of retreat (i.e. the trench moves seaward
towards the plate being subducted) with a 25th percentile of 3 mm a-1 of advance and a
75th percentile of 24 mm a-1 of retreat. This median velocity is the same sign as, but
lower in magnitude than, the preferred results of Schellart et al. [2008], who found a
mean rate of retreat of 21 mm a-1. Uncertainties in our individual estimated trench
velocities range from ±9 to ±43 mm a-1 (95% confidence level).
The trench velocity differs insignificantly from zero at 29 locations, indicates
significant retreat at 23 locations, and indicates significant advance at only five locations
(along the Hikurangi, Marianas, and Izu-Bonin trenches). Trench advance is thus
uncommon and mainly occurs where the Pacific plate subducts beneath the Philippine
Sea plate. The median rate of trench retreat suggest that the relative velocities of trenches
of opposite polarity is typically ≈20 mm a-1, which is a factor of ≈3–10 times as fast as
the nominal relative velocities of hot spots of 2–6 mm a-1 [Koivisto et al., 2014].
Consistent with prior work (Schellart et al. [2007, 2011]), we find that all retreat
faster than 40 mm a-1 occurs within 1500 km of a slab edge, but also note that 50 of our
5
57 trench locations are within 1500 km of a slab edge. We find that trench retreat and
convergence rate correlate significantly, but note that this might be expected because
convergence rate is the sum of the velocity of the lithosphere about to be subducted
(herein referred to as the subducting plate) and trench retreat. We confirm that trench
velocity correlates negatively with trench-normal subducting plate velocity and that
trench velocity correlates significantly negatively with age of the subducting plate
[Faccenna et al., 2007; Lallemand et al., 2008].
1.2. Methods and Input Angular Velocities
1.2.1. Set of Angular Velocities Used Herein
Zheng et al. [2014] estimated absolute plate motion from seismic anisotropy inferred
from shear-wave splitting (SKS) data compiled by Kreemer [2009]. To do so, they
assumed that the fast direction of upper mantle anisotropy parallels the direction of recent
absolute plate motion [Savage, 1999; Becker, 2008]. To avoid including data affected by
active tectonics, Kreemer [2009] excluded data from plate boundaries and limited
continental data to stable plate interiors. Zheng et al. [2014] accounted for the correlated
errors in these data and determined absolute plate motion constrained to consistency with
the MORVEL relative plate angular velocities [DeMets et al., 2010]. Zheng et al. [2014]
further incorporated the relative angular velocities of an additional 31 small plates [Argus
et al., 2011] (drawn from the work of Bird [2003]), and thus determine SKS-MORVEL, a
set of absolute angular velocities for 56 plates.
6
1.2.1.1. Differences from SKS-MORVEL
Since the work of Bird [2003], however, the existence of several other small plates
has been proposed, many inferred from GPS velocities [Reilinger et al., 2006; Galgana et
al., 2007; Loveless and Meade, 2010; Serpelloni et al., 2010; Nishimura, 2011; Power et
al., 2012; Wallace et al., 2012; McCaffrey et al., 2013; Métois et al., 2014; Nocquet et al.,
2014]. Thus, we add to SKS-MORVEL fourteen recently proposed angular velocities of
small plates relative to the leading edge of the overriding plate at several trenches and
remove the New Hebrides (NH) and Okinawa (ON) plates from the set of angular
velocities. Additionally, we replace the six angular velocities of the Aegean Sea (AS),
Anatolia (AT), Kermadec (KE), Marianas (MA), South Bismarck (SB), and Tonga (TO)
plates in SKS-MORVEL with those determined more recently from geodetic data
[Wallace et al., 2004a, 2005; Reilinger et al., 2006; Power et al., 2012] (Figure 1, Table
1).
Along the southern Kermadec trench, we take the overriding plate to be the Hikurangi
plate (HK) [Wallace et al., 2012], which is distinct from the Kermadec plate (KE) farther
north [Bird, 2003]. Along the New Hebrides trench, we assume that the overriding plates
are the Central Vanuatu plate (CV) north of 17°S and the South Vanuatu plate (SV) south
of 17°S [Wallace et al., 2005; Power et al., 2012; L. Wallace, personal communication,
2014] and thus we have no New Hebrides plate (NH) [Bird, 2003]. Along the Izu-Bonin
trench, we take the overriding plate to be the Izu Arc plate (IA) [Nishimura, 2011], which
is distinct from the Philippine Sea plate (PS).
Along the Cascadia trench, we assume that the overriding plates are the Olympic
Peninsula plate (OL) north of 47°N and the South Oregon Coastal Range plate (OR)
7
Figure 1. Trench locations considered herein. Hollow blue circles: locations where the
SKS-MORVEL [Zheng et al., 2014] set of angular velocities are used. Filled blue
circles: locations where updated or new (since SKS-MORVEL) relative angular
velocities are used. Gray curves: MORVEL56 plate boundaries [Argus et al., 2011] (as
modified from Bird [2003]). Thick black curves with barbs on overriding plate side:
trenches considered herein.
8
south of 47°N [McCaffrey et al., 2013], which are distinct from the North America
plate (NA). Along the Peru-Chile trench, we take the overriding plates to be the Inca
plate (IC) from 5°S to 15°S [Nocquet et al., 2014] and the Andes plate (AD) from 22°S to
40°S [Métois et al., 2014], which are distinct from the South America plate (SA).
In the Mediterranean region, we assume that the overriding plates are the Calabria
plate (CB) at the Calabria trench [Serpelloni et al., 2010] and the Lut plate (LT) at the
Makran trench [Reilinger et al., 2006], which are distinct from the Eurasia plate.
Along the Manila trench, we assume that the overriding plate is the Luzon plate (LU),
which is distinct from the Philippine Sea plate (PS) [Galgana et al., 2007]. Along the
Ryukyu and Nankai trenches, we adopt the model of Loveless and Meade [2010]. We
assume that the Okinawa plate (ON) of Bird [2003] instead consists of three new plates:
(1) the Southwest Ryukyu plate (RY) west of 126°E, (2) the Okinawa plate (ON) from
126°E to 130°E, and (3) the Nankai plate (NK), which consists of the remaining part of
the old Okinawa plate east of 130°E together with the southeastern tip of the Amur plate
(AM).
1.2.1.2. Differences from the Assumed Plate Geometry and Angular Velocities of
Schellart [2008]
Because of the availability of a new global set of plate angular velocities [DeMets et
al., 2010] and many new GPS data sets and analyses [e.g., Loveless and Meade, 2010;
Wallace et al., 2012; Power et al., 2012], the set of angular velocities presented herein
has many significant differences from those adopted by Schellart [2008] (Table 1).
Whereas Schellart [2008] used the relative angular velocities of most large plates
9
from NUVEL-1A [DeMets et al., 1994] and of the Amur (AM), Okhotsk (OK), Yangtze
(YZ), Sunda (SU), and Caribbean (CA) plates from Kreemer et al. [2003], we use the
more recently determined MORVEL relative angular velocities [DeMets et al., 2010].
Whereas Schellart [2008] uses fourteen angular velocities of small plates from Bird
[2003] (AS, AT, AP, BH, BU, KE, MA, MS, NH, ND, PM, SB, TO, and WL), we replace
six of these (AS, AT, KE, MA, SB, and TO) with new angular velocities from newer data
sets and analyses [Wallace et al., 2004a, 2005; Reilinger et al., 2006; Power et al., 2012],
and consider the overriding plate along the New Hebrides trench to be not one New
Hebrides plate (NH) but two new plates (Central Vanuatu (CV) and Southern Vanuatu
(SV)) [Wallace et al., 2005; Power et al., 2012; L. Wallace, personal
communication,2014].
Whereas Schellart [2008] included angular velocities for the Okinawa (ON), Scotia
(SC), and Sandwich (SW) plates, we assume a new geometry and angular velocity for the
ON plate [Loveless and Meade, 2010], and use the SKS-MORVEL [Zheng et al., 2014]
angular velocities for the SC and SW plates. Whereas Schellart [2008] included angular
velocities for five small plates not included by Bird [2003] for the Central Hikurangi
(HK), Luzon (LU), Southern Oregon Coastal Range (OR), Olympic Peninsula (OL), and
Tokai South Kanto (TK) plates, we replace four of these angular velocities (HK, LU, OR,
OL) with new angular velocities [Galgana et al., 2007; Wallace et al., 2012; McCaffrey et
al., 2013] and assume a new geometry and angular velocity for the previous TK plate
[Loveless and Meade, 2010]. Whereas Schellart [2008] included a linear velocity from
GPS studies for the overriding block at each of the Calabria, Makran, South Shetland,
and Betic-Rif trenches, we replace two of these with new plates (Calabria plate (CB) at
10
the Calabria trench [Serpelloni et al., 2010]; Lut plate (LT) at the Makran trench
[Reilinger et al., 2006]), and use the angular velocity of the Shetland plate (SL) from
SKS-MORVEL at the South Shetland trench. We exclude the Betic-Rif trench used in
prior work because recent analysis images a vertical slab beneath the Gibraltar arc that
does not appear to be subducting [Thurner et al., 2014]. We also exclude the Puysegur
and Trobriand trenches due to few deep seismic events recorded along these trenches
[Wallace et al., 2004a; Benz et al., 2010].
We add five plates not considered by Schellart [2008] (Andean Sliver (AD), Izu Arc
(IA), Inca Sliver (IC), Nankai (NK), and Southwest Ryukyu (RY) [Loveless and Meade,
2010; Métois et al., 2014; Nocquet et al., 2014]), along with the previously mentioned
CV and SV plates.
1.2.2. Relative Plate Motion Uncertainties
For the 25 large-plate (MORVEL) angular velocities from SKS-MORVEL used in
this study, we use the three-by-three covariance matrix [table 4 of Zheng et al., 2014] to
determine plate velocity uncertainties. Argus et al. [2011] estimate uncertainties for each
of the 31 small-plate angular velocities from the work of Bird [2003]. We use 23 of these
31 angular velocities and for those we add the SKS-MORVEL three-by-three covariance
matrix [Zheng et al., 2014, table 4] to each of the 23 small-plate angular velocity
covariance matrices [Argus et al., 2011, table S2] to determine absolute plate angular
velocity uncertainties.
For the remaining eight angular velocities, we herein update six angular velocities
with newer published angular velocities, and do not use the remaining two angular
11
velocities. For these six, as well as for the fourteen angular velocities of new small plates
relative to large plates used in this study, we determine a new three-by-three covariance
matrix from (in most cases) published uncertainty ellipse parameters (rotation rate
uncertainty, lengths of the semimajor and semiminor axes, and azimuth of the semimajor
axis). For some plates (Andes (AD), Aegean Sea (AS), Anatolia (AT), Izu Arc (IA), Lut
(LT), Nankai (NK), Okinawa (ON), and Ryukyu (RY)) only the standard error of the
latitude and longitude of the pole location and standard error of the rotation rate are
available [Reilinger et al., 2006; Loveless and Meade, 2010; Nishimura, 2011; Métois et
al., 2014]. In the absence of information on the covariances, for these relative angular
velocities we assume that the covariances are zero, which corresponds to uncertainty
ellipse axes with principal axes that are oriented north-south, east-west, and up-down.
We then add the SKS-MORVEL three-by-three covariance matrix [Zheng et al., 2014,
table 4] to each newly determined three-by-three covariance matrix.
The resulting three-by-three covariance matrix of each angular velocity is used to
determine the one-dimensional (trench-normal component) linear plate velocity
uncertainties, which range from ±9 to ±43 mm a-1 (95% confidence level) (Table 2).
1.2.3. Absolute Trench Velocities
At 57 globally distributed trench locations, which sample all the plate pairs we
consider (Figure 1), linear velocities are determined from the appropriate angular
velocities. We assume that the trench velocity is the same as the velocity of the
overriding plate and neglect any trench erosion or accretion. We assign a positive value
to a trench-normal component of trench velocity away from the overriding plate and term
12
this motion trench retreat, and assign a negative value to a trench-normal component of
trench velocity toward the overriding plate and term this motion trench advance.
1.2.4. Comparisons
Absolute trench velocities are compared with distance to the slab edge, plate
convergence rates, and the age and trench-normal velocity of the subducting plate. The
edges of slabs are the same as those used by Schellart et al. [2011], and lithosphere ages
are from Müller et al. [2008]. If ages were unavailable at trench locations, the nearest
available age of subducting lithosphere was used. We exclude lithosphere where the
Nubia plate (NU) subducts beneath the Eurasia plate (EU) in the Mediterranean Sea
where ages are poorly constrained.
1.3. Results
At 51% (29 of 57) of locations, the trench velocity differs insignificantly from zero
and the trench could be stationary, retreating, or advancing (Table 2, Figures 2−3). At
72% (41) of locations the trench is nominally retreating, with significant retreat at 40%
(23) locations (along the Tonga, New Hebrides, San Cristobal, New Britain, Cascadia,
Mexico, Central America, Colombia, Peru, Chile, Scotia, Hellenic, Andaman, North
Sulawesi, Halmahera, Manila, and Ryukyu trenches). At 28% (16) of locations the trench
is nominally advancing, with significant advance at 9% (5) locations (one along the
Hikurangi trench, two of three locations along the Marianas trench, and both locations
13
Figure 2. Trench-perpendicular component of velocities relative to the lower mantle
(blue arrows, this paper; red arrows, Schellart [2008]). Thin black error bars at end of
blue arrows: one-dimensional 95% confidence interval of our velocities. Gray curves:
MORVEL56 plate boundaries [Argus et al., 2011] (as modified from Bird [2003]).
Thick black curves with barbs on overriding plate side: trenches considered herein.
14
Figure 3 Trench-normal component of trench velocity in mm a-1 (blue squares) with
one-dimensional 95% confidence intervals at each of the 57 trench locations. The order
of trenches from left to right is clockwise around the Pacific Ocean starting in the
southwest, then across the Eurasia-Nubia plate boundary, then around the Sunda plate and
up the west side of the Philippine Sea plate.
15
along the Izu-Bonin trench).
The median trench velocity is retreat at 9 mm a-1 (± 13 mm a-1) and the mean is 14
mm a-1 with a population standard deviation of 34 mm a-1. The 25th percentile is –3 mm
a-1 (i.e., modestly advancing) and the 75th percentile is 24 mm a-1 (i.e., retreating). The
most rapid retreat occurs along the northern Tonga trench at 126 ± 20 mm a-1 and the
most rapid advance occurs along the southern Izu-Bonin trench at –52 ± 14 mm a-1
(Figure 4).
Nominal differences from trench velocities estimated by Schellart [2008] range from
0 to 51 mm a-1, with the greatest nominal differences along the Kermadec trench (37–51
mm a-1), New Hebrides trench (36–45 mm a-1), and Marianas trench (29–36 mm a-1).
Twenty four of 57 (42%) of trench velocities (along the Hikurangi, Kermadec, New
Hebrides, San Cristobal, New Britain, Marianas, Izu-Bonin, Kamchatka, Mexico, Central
America, Puerto Rico, Peru, Bolivia, Calabria, Hellenic, Andaman, Java, North Sulawesi,
Halmahera, and Manila trenches) differ significantly from those of Schellart [2008]
(Figure 2).
In Figures 5 to 8, the trench-perpendicular component of trench velocity is plotted
respectively against distance to the nearest slab edge, plate convergence rate, trenchnormal velocity of the subducting plate, and age of the subducting plate. Figure 9 shows
the trench-normal component of absolute velocity of the lithosphere about to be
subducted versus age of the lithosphere; trench velocity is indicated by symbol color. In
each of Figures 5 to 9, the best-fitting straight line fit to the data has a slope that differs
significantly from zero.
16
Figure 4. Number of trench location (out of 57) for velocities in 10 mm a-1 bins (blue
bars). Red line, mean trench velocity (14.2 mm a-1); green line, median trench velocity
(8.7 mm a-1); cyan lines, 25th (–3 mm a-1) and 75th (24 mm a-1) percentiles of trench
velocities.
17
Figure 5. Trench-normal component of absolute trench velocity versus distance to
nearest slab edge. Solid line: least squares best-fitting straight line (with slope of –0.014
± 0.012 mm a-1 km-1 [95% confidence limits]). Abbreviations: Cy, Cypress; Ry, Ryukyu;
Ha, Halmahera; Cb, Calabria;; Hk, Hikurangi; Mn, Manila; To, Tonga; Sc, Scotia; Mk,
Makran; Hb, New Hebrides; Mr, Marianas; Jv, Java; Ke, Kermadec; Ad, Andaman; Co,
Colombia; At, Aleutian; Cr, San Cristobal; Am, Central America; Sm, Sumatra; Iz, IzuBonin; Jp, Japan; Pe, Peru; Ch-Chile, Bl, Bolivia.
18
Figure 6. Trench-normal component of trench absolute velocity versus plate
convergence rate. Solid line: least squares best-fitting straight line (with slope of 0.51 ±
0.19 [95% confidence limits]). Abbreviations: Ad, Andaman; Mr, Marianas; Iz, IzuBonin; Hk, Hikurangi; Hl, Hellenic; Ke, Kermadec; Sc, Scotia; Mn, Manila; Ry,
Ryukyu; Cr, San Cristobal; Ha, Halmahera; Br, New Britain; Hb, New Hebrides; To,
Tonga.
19
Figure 7. Trench-normal component of trench absolute velocity versus trench-normal
component of absolute velocity of the subducting plate at the trench. Solid line: least
squares best-fitting straight line (with slope of -0.35 ± 0.27 [95% confidence limits]).
Abbreviations: Ad, Andaman; Ve-Venezuela, Ch-Chile, Me-Mexico, Ha, Halmahera; Mn,
Manila; Sc, Scotia; Cr, San Cristobal; Hb, New Hebrides; Mr, Marianas; Ry, Ryukyu;
Hk, Hikurangi; Br, New Britain; Ke, Kermadec; Iz, Izu-Bonin; To, Tonga; Jp, Japan.
20
Figure 8. Trench-normal component of absolute trench velocity versus age of the
subducting plate. Plate ages and horizontal error bars from Müller et al. [2008]. Solid
line: least squares best-fitting straight line (with slope of –0.35 ± 0.20 mm a-1 Ma-1 [95%
confidence limits]). We exclude locations where the Nubia plate (NU) subducts beneath
the Eurasia plate (EU) in the Mediterranean Sea where ages are poorly constrained (along
the Calabria, Hellenic, and Cyprus trenches). Trench abbreviations: Cs, Cascadia; Me,
Mexico; Ch, Chile; Am, Central America; Hb, New Hebrides; Mn, Manila; Sc, Scotia; Cr,
San Cristobal; Mk, Makran; Ha, Halmahera; An, Lesser Antilles; To, Tonga; Ke,
Kermadec; Ku, Kuril; Hk, Hikurangi; Jp, Japan; Jv, Java; Ve, Venezuela; Iz, Izu-Bonin;
Mr, Marianas.
21
Figure 9. Trench-normal component of velocity of the subducting plate versus age of the
subducting plate at the trench. Color represents trench-perpendicular component of
velocity. Warm colors are trench advance and cool colors are trench retreat. Solid line:
least squares best-fitting straight line (with slope of 0.39 ± 0.17 mm a-1 Ma-1 [95%
confidence limits]). Abbreviations: Ad-Andaman, Am-Central America, An-Lesser
Antilles, Br-New Britain, Ch-Chile, Co-Colombia, Cr-San Cristobal, Cs-Cascadia, HaHalmahera, Hb-New Hebrides, Hk-Hikurangi, Iz-Izu-Bonin, Jp-Japan, Jv-Java, KaKamchatka, Ke-Kermadec, Me-Mexico, Mk-Makran, Mn-Manila, Mr-Marianas, NaNankai, Pr-Puerto Rico, Ry-Ryukyu, Sc-Scotia, Sh-South Shetland, Sl-North Sulawesi,
Sm-Somalia, To-Tonga.
22
1.4. Discussion
1.4.1. Distribution of Trench Velocities
The distributions of trench velocities found in prior studies are inferred from different
realizations of the hot spot frame of reference. For example, Heuret and Lallemand
[2005], using the plate-hot spot angular velocities of Gripp and Gordon [2002], found
that 53% of trenches advance and 47% retreat. Significant trench advance is a surprising
result as some modeling studies indicate that trenches are expected to retreat but not to
advance [Royden and Husson, 2006; Cizkova and Bina, 2013]. Schellart et al. [2008]
considered a wide range of realizations of the hot spot frame of reference and found that
the percentage of trenches advancing varied from 22% to 38%, much less than the 53%
found by Heuret and Lallemand [2005]. From the multiple realizations of the hot spot
reference frame that they considered, they chose the one that best met several criteria
including minimizing the number of trenches that advance, minimizing the trench
migration velocity in the center of wide subduction zones, minimizing the cumulative
trench-normal trench velocity globally, and minimizing upper mantle toroidal volume
flux. In their preferred realization of the hot spot frame, the percentage of trenches that
advance is 25%.
Although Schellart et al. [2008] considered different realizations of the hot spot
frame, they did not consider the uncertainties, which are substantial and may explain
some of the differences between different realizations. Herein we fully consider the
uncertainties in absolute plate motions inferred from seismic anisotropy as well as the
uncertainties in relative plate motion. We find that nominally 28% of trenches advance,
23
which is similar to Schellart et al.’s [2008] preferred value. When uncertainties are
considered, however, as few as 9% and as many as 60% of trenches may be advancing
(Table 2).
Similarly, while nominally 72% of trenches retreat, the range is 40% to 91%
considering uncertainties. Furthermore, the trench-normal component of velocities of
51% (29) of the trenches differs insignificantly from zero.
1.4.2. Trench Retreat and Distance from Slab Edge
Analog and numerical three-dimensional models of plate motion and subduction
suggest that trench retreat should be faster near (<1500 km) the lateral edges of the
subducting slab than far (>1500 km) from those edges because mantle may flow around
the lateral edges to accommodate retreat, while mantle far from these edges can only flow
around bottom edge of a subducting slab [Stegman et al., 2006]. Schellart et al. [2011]
found on Earth that trench-normal trench velocity is always low (≤17 mm a-1) in the
center of a subduction zones (i.e., >2200 km from the slab edge) and that only near the
(<1000 km) slab edge can the trench velocity exceed 60 mm a-1. Schellart et al. [2011]
also present detailed results of numerical models that agree qualitatively with their results
for Earth.
Our results roughly agree in some ways with their models (and estimates for Earth),
but in other ways differ significantly. In agreement with their models, the four highest
values we find for trench retreat occur within 500 km of a slab edge. We also find a
small but formally significant negative correlation (–0.014 ± 0.012 mm a-1 km-1 (95%
confidence limits)) between the trench velocity and the distance of a site from the nearest
24
slab edge (Figure 5). We note, however, that the 95% confidence limits include slopes as
small as 0.002 mm a-1 km-1. Moreover, the uncertainties in slope depend on the implicit
assumption that the estimates of trench velocity in different locations are uncorrelated,
which is unlikely to be true in many cases. Thus, realistic uncertainties would almost
surely indicate that this correlation is not significant.
Only 7% (4 of 57) of our sites lie more than 2200 km from a slab edge. Among these
four sites, none retreats quickly, but one of the five advances at 37 mm a-1.
The models of Schellart et al. [2011] indicate that trenches rarely advance, and when
they do so, it is at only a few mm a-1, and then only for trench locations more than 2500
km from a slab edge. In contrast, we find rates of advance up to 52 ± 14 mm a-1 and
significant advance as near as ≈1000 km from a slab edge. We conclude that distance
from slab edge only explains a small part of the variation in observed trench-normal
trench velocities.
1.4.3. Convergence Rate
There is an apparently strong correlation between trench velocity and convergence
rate with a slope of 0.51 ± 0.19 (95% confidence limits; Figure 6). We interpret this
relation cautiously, however, as convergence rate is the sum of trench-normal trench
velocity and the trench-normal subducting plate velocity [Schellart et al., 2011]. Thus,
Figure 6 compares trench-normal trench velocity with itself summed with something else,
so it probably should not be surprising that we find a significant positive correlation
(Figure 6). Below we discuss our finding that trench-normal trench velocity decreases
significantly (–0.35 ± 0.27) with the trench-normal subducting plate velocity (Figure 7)
25
(that is, high velocity of the subducting plate favors advance over retreat). The positive
slope of trench velocity versus convergence rate thus appears to arise from a combination
of the positive (unity) slope of trench velocity with itself, on the one hand, with the
negative correlation of trench velocity and absolute velocity of the subducting plate.
1.4.4. Trench-normal Absolute Velocity of the Subducting Plate
Applying the plate-hot spot angular velocities of HS3-NUVEL1A [Gripp and
Gordon, 2002], previous studies found that the trench-normal component of trench
velocity and the trench-normal component of subducting plate velocity correlate strongly
with a slope of –0.60 [Faccenna et al., 2007; Lallemand et al., 2008]. These results were
thought to be due to the resistance of the subducting lithosphere to penetrate the upper
mantle [Faccenna et al., 2007].
Consistent with these results, we find that trench velocity decreases significantly (–
0.35 ± 0.27) with the trench-normal component of absolute velocity of the subducting
plate (Figure 7), that is, high absolute plate velocity of the subducting plate favors
advance over retreat. The negative slope suggests that the positive slope of trench
velocity versus convergence rate, discussed above, is some combination of the positive
correlation of trench velocity with itself, on the one hand, with the negative correlation of
trench velocity and absolute velocity of the subducting plate.
1.4.5. Age of the Subducting Plate
Lallemand et al. [2008], through an analysis of upper plate velocities and subducting
26
plate age and velocities at over 160 trench locations using the HS3-NUVEL1A set of
angular velocities [Gripp and Gordon, 2002], found that all advancing trenches are
characterized by a subducting plate older than 70 Ma. They also note that an old and fast
subducting plate is characteristic of an advancing upper plate, while a young and slow
subducting plate is characteristic of a retreating upper plate.
Consistent with the results of Lallemand et al. [2008], we find a significant negative
correlation (-0.35 ± 0.20 mm a-1 Ma-1 (95% confidence limits)) between trench velocity
and the age of the subducting plate (Figure 8). We also note that all of the five trenches
that advance significantly (red squares (excluding Ke) in Figure 9) are characterized by
an old (> 120 Ma) and fast (>70 mm a-1) subducting plate.
1.4.6. Trench Advance and Dips of Slabs
By constructing a global data set of subduction parameters (including slab depth, slab
length, and shallow and deep slab depth from tomography, and absolute velocities of the
subducting plate, trench/arc system, and upper plate) along almost 160 trench transects,
Lallemand et al. [2005] separated trenches into several classes based on deep slab (>125
km) dip. Deep slab dips from ~0º to 60º correlated with trenches that are retreating,
while dips greater than 60º correlated with trenches that are advancing (except for New
Hebrides trench with a dip greater than 60º but a slab that penetrates only ~300 km deep).
Thus, a negative correlation was seen between trench retreat and slab dip, and slabs that
penetrate the 670 km discontinuity tended to advance.
From a brief analysis of seismicity along trench locations in the west Pacific
(Marianas, Izu-Bonin, Japan, Kuril, and Kamchatka trenches) we find that trench advance
27
Figure 10. Left side of figure: topography, trenches (thick black curves with barbs on
overriding plate side), and USGS-reviewed earthquakes from 1900-2013 of magnitude
5.5 or greater (colored for focus depth) in the northwestern Pacific. Gray curves:
MORVEL56 plate boundaries [Argus et al., 2011] (as modified from Bird [2003]). Thick
black lines: transects along trench locations (blue squares) considered herein: AKamchatka trench, B-Kuril trench, C,D-Japan trench, E,F-Izu-Bonin trench, G,H,IMarianas trench. Right side of figure: cross sections along each transect with earthquake
focus depth plotted versus distance along transect with no vertical exaggeration. Thin
gray curves: topography with 10 times vertical exaggeration. Trench velocity at each
trench location: A. 4±16 mm a-1, B. 3±15 mm a-1, C. 2±15 mm a-1, D. -1±15 mm a-1, E. 37±14 mm a-1, F. -52±14 mm a-1, G. -50±33 mm a-1, H. -45±38 mm a-1, I. -15±43 mm a-1.
28
correlates with increasing slab dip (Figure 10), in agreement with previous results
[Lallemand et al., 2005].
1.5. Conclusions
(1) Out of 57 locations, five (along the Hikurangi, Marianas, and Izu-Bonin trenches)
advance significantly, 23 retreat significantly, and at 29 locations the trench velocity is
not significantly different from zero.
(2) Where the trench is advancing, the age of the subducting lithosphere exceeds 100
Ma, the trench-normal component of absolute velocity of the subducting plate exceeds 70
mm a-1, and convergence rates of the subducting and overriding plates are less than 60
mm a-1.
(3) Trench velocity correlates significantly negatively with distance to the slab edge,
trench-normal velocity of the subducting plate, and age of the subducting plate, generally
in agreement with previous studies while utilizing an objective (not hot spot based) frame
of reference.
(4) By considering the uncertainties of relative plate motions and the seismic
anisotropy reference frame, trench advance is possible at from 9% to 60% of trench
locations, which compared to other studies suggests a lower possible percentage of
advancing trenches but also encompasses results of most other studies.
(5) The main limitation to current results are the still poorly constrained estimates of
the motion of the leading edge of overlying plates relative to their stable plate interiors
including at the Kermadec and Marianas trenches.
29
Table 1. Our angular velocities (first row) compared with those of Schellart [2008] (second row)
at trenches where we added to or replaced angular velocities in SKS-MORVELa
trench
Hikurangi
Kermadec
Tonga
New Hebrides
New Hebrides
New Britain
Mariana
Izu-Bonin
Cascadia
Cascadia
Peru
N. Chile
Calabria
Hellenic
Cyprus
Makran
Manila
small
plateb
large
platec
HK
angular velocity of small plate
relative to large plated
°N
°E
° Ma-1
AU
-38.89
172.27
-2.9
HK
AU
-39.15
172.78
KE
AU
-35.14
KE
AU
TO
source
e
angular velocity of small plate
relative to the mantle
°N
°E
° Ma-1
1
35.94
3.11
3.3f
-2.99
2
38.64
0.99
3.46g
170.78
-0.988
3,4
28.55
14.28
1.481
-40
175
-1.8
5
39
7
2.3
PA
-29.23
182.33
-9.3
6,4
24.90
5.12
8.9
TO
PA
-28.81
182.26
-9.30
5
25.4
4.6
8.9
h
AU
-11.64
165.43
-6.002
3,4
12.21
-9.49
6.383
-1.2
-5.3
2.5
11.95
-10.57
8.164
-1.2
-5.3
2.5
5.15
-31.15
7.60
6.39
-31.57
8.06
CV
i
NH
AU
-8.7
164.5
2.14
5
SVh
AU
-11.49
165.47
-7.788
3,4
NH
AU
-8.7
164.5
2.14
5
SB
AU
-4.18
144.02
-7.45
6
i
i
SB
AU
-4.53
144.78
-7.89
5
MA
PA
26.1
148.9
2.56
7
7.3
142.3
2.60
MA
PA
43.8
149.2
1.28
5
10.6
139.4
1.24
h
IA
PS
26.5
140.7
-0.604
8
-44.8
-28.3
1.613
n/a
PS
9
-46.2
-34.3
0.94
OL
NA
46.6
-117.0
-0.23
10
-67.1
22.2
0.43
OL
NA
38.90
254.50
-0.126
11
-68.90
265.60
0.187
OR
NA
44.8
-117.2
-0.66
10
-57.0
48.7
0.83
OR
NA
45.16
240.99
-1.019
11
-55.38
55.82
0.993
ICh
SA
22.47
-63.76
0.092
12
-73.78
-40.19
0.228
n/a
SA
9
-50.12
201.67
0.177
13
-23.53
111.60
0.24
9
-50.12
201.67
0.177
14
-40.45
195.94
2.093
9
34.42
222.08
0.167
AD
h
SA
-39.22
-61.51
-0.25
n/a
SA
CBh
NU
n/a
EU
AS
EU
15.9
52.3
0.563
15
11.5
50.8
0.548
AS
EU
-27.8
95.2
0.3
5
-16.0
139.7
0.2
AT
EU
30.8
32.1
1.231
15
29.0
31.3
1.209
AT
EU
30.7
32.6
1.2
5
38.3
31.1
1.1
h
EU
26.1
83.2
-0.152
15
-36.9
267.1
0.186
n/a
EU
9
34.42
222.08
0.167
LU
PS
16
11.42
118.42
5.500
LT
38.73
18.44
13.02
122.56
-2.176
6.182
30
SW Ryukyu
Ryukyu
Nankai
a
LU
PS
17.6
122.1
6.0
17
12.5
119.2
5.3
RYh
EU
25.52
126.33
13.29
18
25.37
126.33
13.26
ON
EU
30.5
138.7
1.254
19,20
33.5
145.8
1.325
h
EU
37.61
143.14
1.25
18
36.35
143.43
1.21
ON
EU
30.5
138.7
1.254
19,20
33.5
145.8
1.325
NKh
EU
36.96
135.57
1.55
18
35.95
135.71
1.51
TK
EU
23.9
133.1
0.849
21,20
29.0
143.2
0.904
ON
This table is in addition to the many changes since the work of Bird [2003] incorporated into
SKS-MORVEL [Zheng et al., 2014]. Angular velocities of each small plate relative to the mantle
(columns 8-10) are determined from the sum of the angular velocity of each small plate relative to
the large plate (columns 4-6) and the angular velocity of each large plate relative to the mantlef,g.
b
Plate abbreviations: HK – Central Hikurangi, KE – Kermadec, TO – Tonga, CV – Central
Vanuatu, NH – New Hebrides, SV – Southern Vanuatu, SB – South Bismarck, MA – Mariana, IA
– Izu Arc, OL – Olympic Peninsula, OR – South Oregon Coastal Ranges, IC – Inca Sliver, AD –
Andean Sliver, CB – Calabria, LT – Lut Block, LU – Luzon, RY – Southwest Ryukyu, ON –
Okinawa, NK – Nankai, TK – Tokai South Kanto.
c
Plate abbreviations: AU – Australia, PA – Pacific, PS – Philippine Sea, NA – North America, SA
– South America, NU – Nubia, EU – Eurasia, YZ – Yangtze, AM – Amur.
d
Positive rotation rate indicates counterclockwise rotation. n/a indicates where Schellart [2008]
did not use a small plate.
e
1-Wallace et al. [2012] 2-Wallace et al. [2004b] 3-Power et al. [2012] 4-L. Wallace, personal
communication, 2014 5-Bird [2003] 6-Wallace et al. [2004a] 7-Wallace et al. [2005] 8-Nishimura
[2011] 9-DeMets et al. [1994] 10-McCaffrey et al. [2013] 11-McCaffrey et al. [2007] 12-Nocquet
et al. [2014] 13-Métois et al. [2014] 14-Serpelloni et al. [2010] 15-Reilinger et al. [2006] 16Galgana et al. [2007] 17-Rangin et al. [1999] 18-Loveless and Meade [2010] 19-Nishimura et al.
[2004] 20-Kreemer et al. [2003] 21-Mazzotti et al. [2001].
f
We use herein the first row of angular velocities for each small plate relative to the mantle, which
are determined using the large plate angular velocities relative to the mantle from SKS-MORVEL
[Zheng et al., 2014, table 4].
g
Schellart [2008] uses the second row of angular velocities for each small plate relative to the
mantle, which are determined using most large plate angular velocities from NUVEL-1A
[DeMets et al., 1994] (except angular velocities of the YZ and AM plates are from Kreemer et al.
[2003]) combined with the hot spot-based mantle reference frame of O'Neill et al., [2005].
h
New plates used in this study not considered by Bird [2003] or Schellart [2008].
i
Determined using the NUVEL-1A relative angular velocities [DeMets et al., 1994].
31
Table 2. Trench locations, trench-normal component of velocities (vtp)a, confidence intervals
(C.I.), subducting plate ages
trench location
trenchb
Hikurangi
Kermadec
Kermadec
Kermadec
Tonga
Tonga
New Hebrides
New Hebrides
San Cristobal
San Cristobal
New Britain
Mariana
Mariana
Mariana
Izu Bonin
Izu Bonin
Japan
Japan
Kuril
Kamchatka
Aleutian
Aleutian
Alaska
Cascadia
Cascadia
Mexico
C. America
C. America
Venezuela
Lesser Antilles
Puerto Rico
Colombia
Colombia
Peru
Bolivia
Chile
Chile
Chile
latitude
(°N)
longitude
(°E)
-40.1
-35.0
-29.9
-26.0
-21.9
-17.9
-21.3
-16.1
-12.9
-10.6
-6.2
11.8
15.0
20.3
27.5
32.0
36.9
42.4
46.9
51.5
50.5
52.6
56.6
48.3
44.0
19.4
14.2
8.8
11.8
12.4
19.8
3.4
-1.1
-10.6
-21.3
-30.2
-39.8
-49.8
178.8
-178.6
-176.3
-175.4
-174.0
-172.5
168.9
166.4
165.9
160.4
151.5
144.2
147.5
147.2
143.2
142.1
143.4
146.7
154.7
160.6
-179.2
-165.4
-150.1
-126.7
-125.4
-105.9
-94.1
-84.7
-75.1
-57.5
-65.1
-78.7
-81.4
-80.0
-71.2
-72.6
-75.1
-77.0
upper
platec
HK1,e
KE2,3,f
KE2,3,f
KE2,3,f
TO4,3,f
TO4,3,f
SV2,3,e
CV2,3,e
PA
PA
SB5,f
MA4,f
MA4,f
MA4,f
IA6,e
IA6,e
OK
OK
OK
OK
NA
NA
NA
OL7,e
OR7,e
NA
NA
PM
ND
CA
CA
ND
ND
IC8,e
AP
AD9,e
AD9,e
SA
vtp
95% C.I.
(mm a-1) (±mm a-1)
-33
-31
-12
5
53
126
117
22
69
11
28
-15
-45
-50
-52
-37
-1
2
3
4
9
8
8
19
20
28
21
-3
11
-8
1
17
19
22
13
22
24
21
15
42
31
31
14
20
33
12
9
11
12
43
38
33
14
14
15
15
15
16
13
14
14
11
10
9
9
10
11
9
9
12
12
10
14
22
24
15
age of the
subducting
subducting
plated
platec
(Ma)
PA
PA
PA
PA
PA
PA
AU
AU
AU
AU
SS
PA
PA
PA
PA
PA
PA
PA
PA
PA
PA
PA
PA
JF
JF
RI
CO
CO
CA
SA
NA
NZ
NZ
NZ
NZ
NZ
NZ
AN
124
111
97
86
96
104
27
39
60
60
38
150
151
145
131
136
134
126
113
104
52
56
44
4
9
13
25
17
132
91
105
15
19
41
53
41
25
13
32
S. Shetland
Scotia
Calabria
Hellenic
Cyprus
Makran
Andaman
Andaman
Sumatra
Sumatra
Java
Java
N. Sulawesi
Halmahera
Manila
Ryukyu
Ryukyu
Ryukyu
-61.4
-58.2
38.3
35.7
35.0
24.1
15.4
8.7
0.1
-6.6
-10.1
-11.1
2.4
1.7
18.2
23.4
25.9
28.3
-60.7
-23.8
17.8
22.4
30.8
61.4
93.4
91.7
97.0
101.9
107.8
114.4
122.5
126.4
119.3
125.0
129.0
131.1
SL
SW
CB10,e
AS11,f
AT11,f
LT11,e
BU
BU
SU
SU
SU
SU
MS
BH
LU12,e
RY13,e
RY13,e
ON13,e
8
54
-4
35
7
-7
28
3
-6
-4
-1
0
23
89
71
31
38
24
10
12
10
15
15
16
10
13
11
10
9
9
11
14
12
21
41
14
AN
SR
NU
NU
NU
AR
IN
IN
CP
CP
AU
AU
SU
SU
SU
PS
PS
PS
29
34
243g
259g
256g
83
81
74
44
86
110
128
38
86
29
53
86
82
Nankai
32.3
135.0
NK13,e
6
13
PS
15
a
vtp is determined from the trench-perpendicular component of the overriding plate velocity
relative to the mantle at each trench location.
b
Trench names from Schellart [2008].
c
Plate name abbreviations from MORVEL56 [Argus et al., 2011], except all plates are upper case
with Nubia plate abbreviated as NU. Numbered references for new plates or updated angular
velocities: 1-Wallace et al. [2012] 2-Power et al. [2012] 3-L. Wallace, personal
communication, 2014 4-Wallace et al. [2005] 5-Wallace et al. [2004a] 6-Nishimura [2011] 7McCaffrey et al. [2013] 8-Nocquet et al. [2014] 9-Métois et al. [2014] 10-Serpelloni et al. [2010]
11-Reilinger et al. [2006] 12-Galgana et al. [2007] 13-Loveless and Meade [2010].
d
Plate ages from Müller et al. [2008].
e
New plates not included in SKS-MORVEL [Zheng et al., 2014].
f
Plates with angular velocities updated since SKS-MORVEL [Zheng et al., 2014].
g
Müller et al. [2008] gives ages at these three locations, but we do not use them here because no
data supports these ages.
33
References
Argus, D. F., R. G. Gordon, and C. DeMets (2011), Geologically current motion of 56
plates relative to the no-net-rotation reference frame, Geochem. Geophys. Geosyst.,
12(11), Q11001, doi:10.1029/2011GC003751.
Becker, T. W. (2008), Azimuthal seismic anisotropy constrains net rotation of the
lithosphere, Geophys. Res. Lett. 35 (L05303), doi:10.1029/2007GL032928
Benz, H. M., M. Herman, A. C. Tarr, G. P. Hayes, K. P. Furlong, A. Villaseñor, R. L. Dart,
and S. Rhea, (2011), Seismicity of the Earth 1900–2010 eastern margin of the
Australia plate: U.S. Geological Survey Open-File Report 2010–1083-I, scale
1:8,000,000.
Bird, P. (2003), An updated digital model of plate boundaries, Geochem. Geophys.
Geosyst., 4(3), 1027, doi:10.1029/2001GC000252.
Cizkova, H., and C. R. Bina (2013), Effects of mantle and subduction-interface
rheologies on slab stagnation and trench rollback, Earth and Planetary Science
Letters, 379, 95-103, doi:10.1016/j.epsl.2013.08.011.
DeMets, C., R. G. Gordon, D. F. Argus, and S. Stein (1994), Effect of recent revisions to
the geomagnetic reversal time scale on estimates of current plate motions, Geophys.
Res. Lett., 21, 2191–2194, doi:10.1029/94GL02118.
DeMets, C., R. G. Gordon, and D. F. Argus (2010), Geologically current plate motions,
Geophys. J. Int., 181, 1-80, doi:10.1111/j.1365-246X.2009.04491.x.
Faccenna, C., A. Heuret, F. Funiciello, S. Lallemand, and T. W. Becker (2007), Predicting
trench and plate motion from the dynamics of a strong slab, Earth and Planetary
34
Science Letters, 257, 29-36, doi:10.1016/j.epsl.2007.02.016.
Francheteau, J., and J. G. Sclater (1970), Comments on Paper by E, Irving and W. A.
Robertson, ‘Test for Polar Wandering and Some Possible Implication’, J. Geophys.
Res., 75(5), 1023-1027.
Galgana, G., M. Hamburger, R. McCaffrey, E. Corpuz, and Q. Chen (2007), Analysis of
crustal deformation in Luzon, Philippines using geodetic observations and earthquake
focal mechanisms, Tectonophysics,432, 63-87, doi:10.1016/j.tecto.2006.12.001.
Gripp, A. E., and R. G. Gordon (2002), Young tracks of hotspots and current plate
velocities, Geophys. J. Int., 150, 321-361, doi:10.1046/j.1365-246X.2002.01627.x.
Hamilton, W. B. (2003), An Alternative Earth, GSA Today, 13(11), 4-12.
Hamilton, W. B. (2007), Driving mechanism and 3-D circulation of plate tectonics,
Geological Society of America Special Papers, 433, 1-25,
doi:10.1130/2007.2433(01).
Heuret, A., and S. Lallemand (2005), Plate motions, slab dynamics and back-arc
deformation, Physics of the Earth and Planetary Interiors, 149, 31-51,
doi:10.1016/j.pepi.2004.08.022.
Koivisto, E. A., D. L. Andrews, and R. G. Gordon (2014), Tests of fixity of the IndoAtlantic hot spots relative to Pacific hot spots, J. Geophys. Res. Solid Earth, 119,
661–675, doi:10.1002/2013JB010413.
Kreemer, C. (2009), Absolute plate motions constrained by shear wave splitting
orientations with implications for hot spot motions and mantle flow, J. Geophys.
Res., 114, B10405, doi:10.1029/2009JB006416.
35
Kreemer, C., W. E. Holt, and A. J. Haines (2003), An integrated global model of presentday plate motions and plate boundary deformation, Geophys. J. Int., 154, 8-34,
doi:10.1046/j.1365-246x.2003.01917.x.
Lallemand, S., A. Heuret, and D. Boutelier (2005), On the relationships between slab dip,
back-arc stress, upper plate absolute motion, and crustal nature in subduction zones,
Geochem. Geophys. Geosyst., 6 Q09006, doi:10.1029/2005GC000917.
Lallemand, S., A. Heuret, C. Faccenna, and F. Funiciello (2008), Tectonics, 27, TC3014,
doi:10.1029/2007TC002212.
Loveless, J. P., and B. J. Meade (2010), Geodetic imaging of plate motions, slip rates,
and partitioning of deformation in Japan, J. Geophys. Res., 115, B02410,
doi:10.1029/2008JB006248.
Mazzotti, S., P. Henry, and X. Le Pichon (2001), Transient and permanent deformation of
central Japan estimated by GPS 2. Strain partitioning and arc-arc collision, Earth and
Planetary Science Letters, 184, 455-469 doi:10.1016/S0012-821X(00)00336-8.
McCaffrey, R., A. I. Qamar, R. W. King, R. Wells, G. Khazaradze, C. A. Williams, C.
W. Stevens, J. J. Vollick, and P. C. Zwick (2007), Fault locking, block rotation and
crustal deformation in the Pacific Northwest, Geophys. J. Int., 169, 1315-1340,
doi:10.1111/j.1365-246X.2007.03371.x.
McCaffrey, R., R. W. King, S. J. Payne, and M. Lancaster (2013), Active tectonics of
northwestern U.S. inferred from GPS-derived surface velocities, J. Geophys. Res.
Solid Earth, 118, doi:10.1029/2012JB009473.
Métois, M., C. Vigny, A. Socquet, A. Delorme, S. Morvan, I. Ortega, and C.-M ValderasBermejo (2014), GPS-derived interseismic coupling on the subduction and seismic
36
hazards in the Atacama region, Chile, Geophys. J. Int., 196, 644-655,
doi:10.1093/gji/ggt418.
Müller, R.D., M. Sdrolias, C. Gaina, and W.R. Roest (2008), Age, spreading rates and
spreading symmetry of the world's ocean crust, Geochem. Geophys. Geosyst., 9,
Q04006, doi:10.1029/2007GC001743.
Nishimura, S., M. Hashimoto, and M. Ando (2004), A rigid block rotation model for the
GPS derived velocity field along the Ryukyu arc, Physics of the Earth and Planetary
Interiors, 142, 185-203, doi:10.1016/j.pepi.2003.12.014.
Nishimura, T. (2011), Back-arc spreading of the northern Izu-Ogasawara (Bonin) Islands
arc clarified by GPS data, Tectonophysics, 512, 60-67,
doi:10.1016/j.tecto.2011.09.022.
Nocquet, J-M., J. C. Villegas-Lanza, M. Chlieh, P. A. Mothes, F. Rolandone, P. Jarrin, D.
Cisneros, A. Alvarado, L. Audin, F. Bondoux, X. Martin, Y. Font, M. Régnier, M.
Vallée, T. Tran, C. Beauval, J. M. Maguiña Mendoza, W. Martinez, H. Tavera, and
H. Yepes, (2014), Nature Geoscience, 7, 287–291, doi:10.1038/ngeo2099.
O'Neill, C., D. Muller, and B. Steinberger (2005), On the uncertainties in hot spot
reconstructions and the significance of moving hot spot reference frames, Geochem.
Geophys. Geosyst., 6(4), Q04003, doi:10.1029/2004GC000784.
Power, W., L. Wallace, X. Wang, and M. Reyners (2012), Tsunami Hazard Posed to New
Zealand by the Kermadec and Southern New Hebrides Subduction Margins: An
Assessment Based on Plate Boundary Kinematics, Interseismic Coupling, and
Historical Seismicity, Pure Appl. Geophys., 169, 1-36, doi:10.1007/s00024-0110299-x.
37
Rangin, C., X. L. Pichon, S. Mazzotti, M. Pubellier, N. Chamot-Rooke, M. Aurelio, A.
Walpersdorf, and R. Quebral (1999), Plate convergence measured by GPS across the
Sundaland/Philippine Sea Plate deformed boundary: the Philippines and eastern
Indonesia, Geophys. J. Int., 139, 296-316, doi:10.1046/j.1365-246x.1999.00969.x.
Reilinger, R., S. McClusky, P. Vernant, S. Lawrence, S. Ergintav, R. Cakmak, H. Ozener,
F. Kadirov, I. Guliev, R. Stepanyan, M. Nadariya, G. Hahubia, S. Mahmoud, K. Sakr,
A. ArRajehi, D. Paradissis, A. Al-Aydrus, M. Prilepin, T. Guseva, E. Evren, A.
Dmitrotsa, S. V. Filikov, F. Gomez, R. Al-Ghazzi, and G. Karam (2006), GPS
constraints on continental deformation in the Africa-Arabia-Eurasia continental
collision zone and implications for the dynamics of plate interactions, J. Geophys.
Res.,111, B05411, doi:10.1029/2005JB004051.
Royden, L. H., and L. Husson (2006), Trench motion, slab geometry and viscous stresses
in subduction systems, Geophys. J. Int., 167, 881-905, doi:10.1111/j.1365246X.2006.03079.x.
Savage, M. K. (1999), Seismic anisotropy and mantle deformation: What have we
learned from shear-wave-splitting? Rev. Geophys., 37, 65-106.
doi:10.1029/98RG02075.
Schellart, W. P. (2008), Overriding plate shortening and extension above subduction
zones: A parametric study to explain formation of the Andes Mountains, Geological
Society of America Bulletin, 120, 1441-1454, doi:10.1130/B26360.1.
Schellart, W. P., J. Freeman, D. R. Stegman, L. Moresi, and D. May (2007), Evolution
and diversity of subduction zones controlled by slab width, Nature, 446, 308-311,
doi:10.1038/nature05615.
38
Schellart, W. P., D. R. Stegman, and J. Freeman (2008), Global trench migration
velocities and slab migration induced upper mantle volume fluxes: Constraints to find
an Earth reference frame based on minimizing viscous dissipation, Earth-Science
Reviews, 88, 118-144, doi:10.1016/j.earscirev.2008.01.005.
Schellart, W. P., D. R. Stegman, R. J. Farrington, and L. Moresi (2011), Influence of
lateral slab edge distance on plate velocity, trench velocity, and subduction
partitioning, J. Geophys. Res., 116, B10408, doi:10.1029/2011JB008535.
Serpelloni, E., R. Bürgmann, M. Anzidei, P. Baldi, B. Mastrolembo Ventura, and E.
Boschi (2010), Strain accumulation across the Messina Straits and kinematics of
Sicily and Calabria from GPS data and dislocation modeling, Earth and Planetary
Science Letters, 298, 347-360,doi:10.1016/j.epsl.2010.08.005.
Stegman, D. R., J. Freeman, W. P. Schellart, L. Moresi, and D. May (2006), Influecnce of
trench width on subduction hinge retreat rates in 3-D models of slab rollback,
Geochem. Geophys. Geosyst., 7, Q03012, doi:10.1029/2005GC001056.
Talwani, M. (1969), Plate tectonics and deep sea trenches (abstract), Trans. Am.
Geophys. Union, 50, 180.
Thurner, S., I. Palomeras, A. Levander, R. Carbonell, and C.-T. Lee (2014), Ongoing
lithospheric removal in the western Mediterranean: Evidence from Ps receiver
functions and thermobarometry of Neogene basalts (PICASSO project), Geochem.
Geophys. Geosyst., 15(4), 1113-1127, doi:10.1002/2013GC005124.
Wallace, L. M., C. Stevens, E. Silver, R. McCaffrey, W. Loratung, S. Hasiata, R.
Stanaway, R. Curley, R. Rosa, and J. Taugaloidi (2004a), GPS and seismological
constraints on active tectonics and arc-continent collision in Papua New Guinea:
39
Implications for mechanics of microplate rotations in a plate boundary zone, J.
Geophys. Res., 109, B05404, doi:10.1029/2003JB002481.
Wallace, L. M., J. Beavan, R. McCaffrey, and D. Darby (2004b), Subduction zone
coupling and tectonic block rotations in the North Island, New Zealand, J. Geophys.
Res., 109, B12406, doi:10.1029/2004JB003241.
Wallace, L. M., R. McCaffrey, J. Beavan, and S. Ellis (2005), Rapid microplate rotations
and backarc rifting at the transition between collision and subduction, Geology, 33,
857-860, doi:10.1130/G21834.1.
Wallace, L. M., P. Bames, J. Beavan, R. Van Dissen, N. Litchfield, J. Mountjoy, R.
Langridge, G. Lamarche, and N. Pondard (2012), The kinematics of a transition from
subduction to strike-slip: An example from the central New Zealand plate boundary, J.
Geophys. Res., 117, B02405, doi:10.1029/2011JB008640.
Zheng, L., R. G. Gordon, and C. Kreemer (2014), Absolute plate velocities from seismic
anisotropy: Importance of correlated errors, J. Geophys. Res. Solid Earth, 119,
doi:10.1002/2013JB010902.
40
Appendix A
SUPPLEMENTAL FIGURES
Figure S1. Overriding plate velocity (hollow arrows) and trench-perpendicular
component velocity (solid arrows) relative to the mantle at trench locations along the
Kermadec and Hikurangi trenches. Blue arrows: velocity or component of velocity
41
determined using our new set of angular velocities. Black error bars: one-dimensional
95% confidence interval of trench-perpendicular component of velocity. Red arrows:
velocity or component of velocity determined using Schellart's [2008] set of angular
velocities. To determine velocities at the three northern trench locations, two different
angular velocities of the Kermadec (KE) plate are used. Blue star labeled “KE-mantle”:
pole of rotation for the sum of the angular velocity of the KE plate relative to the
Australia (AU) plate [Power et al., 2012] and the angular velocity of the AU plate
relative to the mantle from SKS-MORVEL [Zheng et al., 2014]. Red star: pole of
rotation for the sum of the angular velocity of the KE plate relative to the AU plate [Bird,
2003] and the angular velocity of the AU plate relative to the mantle from Schellart
[2008]. To determine velocities at the southern trench location, two different angular
velocities of the Central Hikurangi (HK) plate are used. Blue diamond labeled “HKmantle”: pole of rotation for the sum of the angular velocity of the HK plate relative to
the AU plate [Wallace et al., 2012] and the angular velocity of the AU plate relative to the
mantle from SKS-MORVEL [Zheng et al., 2014]. Red diamond: pole of rotation for the
sum of the location of the angular velocity of the HK plate relative to the AU plate
[Wallace et al., 2004b] and the angular velocity of the AU plate relative to the mantle
from Schellart [2008]. Arrows around poles indicate rotation direction. Gray and black
curves follow conventions of Figure 1. PA is Pacific plate.
42
Figure S2. Overriding plate velocity (hollow arrows) and trench-perpendicular
component velocity (solid arrows) relative to the mantle at trench locations along the
Marianas and Izu-Bonin trenches. Arrow, ellipse, and label conventions as in Figure 10.
43
Blue star labeled “MA-mantle”: pole of rotation for the sum of the angular velocity of the
Marianas (MA) plate relative to the Pacific (PA) plate [Wallace et al., 2005] and the
angular velocity of the PA plate relative to the mantle from SKS-MORVEL [Zheng et al.,
2014]. Red star: pole of rotation for the sum of the angular velocity of the MA plate
relative to the Philippine Sea (PS) plate [Bird, 2003] and the angular velocity of the PS
plate relative to the mantle from Schellart [2008]. Blue diamond labeled “IA-mantle”:
pole of rotation for the sum of the angular velocity of the Izu Arc (IA) plate relative to the
Philippine Sea (PS) plate [Nishimura, 2011] and the angular velocity of the PS plate
relative to the mantle from SKS-MORVEL [Zheng et al., 2014]. Red diamond labeled
“PS-mantle”: pole of rotation for PS plate relative to the mantle from Schellart [2008].