make the assumption that the lithosphere in plate boundary zones
behaves as a continuum. This is a reasonable approximation when
considering large-scale deformation for areas that have horizontal
dimensions several times the thickness of the brittle elastic layer
. We use the method of Haines and Holt [e.g.,
Haines and Holt,
to model the strain rate field. This method uses bi-cubic splines to
obtain a continuous velocity gradient tensor field in the plate
boundary zones. The rigid-body rotations listed above are applied as
boundary conditions, relative to the Pacific plate, which is the
reference plate in the model.
model grid is continuous in longitudinal direction and covers the
globe between 87.5 N and 87.5 S. Each grid area is 0.25 degrees by 0.2 degrees
in longitudinal and latitudinal dimension. There are 145,086
deforming grid cells, comprising ~14% of the globe. Whether an area
is considered to be deforming or not is decided based on the plate
tectonic maps of Bird  (PB2002) and Chanot-Rooke and Rabaute
, with additional modifications made by us, if so desired based
on the GPS data.
areas that are not allowed to deform comprise of 50 different rigid
plates and blocks. A number of blocks defined in PB2002 were allowed
to deform in our model, typically in areas of diffuse deformation
such as Southeast Asia or the Andes. The rationale for this is that
these blocks are typically in areas of large and complex deformation.
If the blocks are covered by GPS stations, their velocities do often
not reflect long-term motion because of elastic strain build-up along
its margin (e.g., the Altiplano block) or, if they have no GPS
coverage, the motion defined in PB2002 may not be compatible with
nearby GPS data, causing spurious strain rates along the blocks'
edges. This is not to say that no rigid blocks exist in continental
but that it is not possible to properly model the surface deformation
(i.e., rigid block motion with localized high strain rates along its
edges) without correcting/modelling for elastic strain accumulation.
added a number of blocks that were not in PB2002. All these
additional blocks have been shown to exist in the literature and,
with two exceptions (Capricorn and Lwandle), we were able to
constrain their rigid-body rotations by the GPS data. The new blocks
are listed below with references arguing for their existence:
Mackey et al.,
Umhoefer and Dorsey,
Royer and Gordon,
Mann et al.,
Salamon et al.,
Haines and Holt method requires us to assign a
strain rate (co-)variances to each deforming grid cell. In order to
properly fit the velocity gradient field in areas of high and low
strain rates, and to avoid under- or over-fitting the geodetic
velocities, respectively, we prefer to assign a
variances that reflect the actual expected strain rates. To
accomplish this, we decided on a two-step approach, modelling the
strain rate field twice. In the first step, we assign the same
standard deviations of 10-8/yr
to each cell, with zero covariances (i.e., assumed isotropy). We made
one exception to this, discussed in the next paragraph. In the second
step, we took the modelled strain rate field from the first step and
used them to constrain the a
deviations. For this, we did not take-over the style or covariances
but set the a
standard deviation of εxx
equal to the second invariant of the tensor modeled in step 1
and εxy set to
the second invariant divided by the square-root of 2.
step 1, if we would assign the same a
errors to each grid cell, we would create some erroneous results in
the diffuse oceanic areas. For instance, we can safely assume that in
the Indian Ocean most of the deformation occurs along the spreading
centres and not in the diffuse zone between the India, Capricorn and
Australian plates. If we assign the same a
variances to all grid cells, strain rate due to the relative plate
motions will spread into the diffuse zone. To remedy this, we give
all cells with transform and ridge segments very large a
values. We do the same for the part of the Sunda subduction zone that
borders the Indian Ocean diffuse deformation area. We follow a
similar approach for the diffuse oceanic areas between the New
Hebrides and Fiji, the one the North and South America plates, and in
the “armpit” of the easternmost Aleutian/Alaska subduction zone.
For the diffuse boundary between Africa and Eurasia, southwest of
Portugal (as defined by Chamot-Rooke
), the PB2002 boundary segments run through the middle of the
diffuse zone and we set very high variances for the cells containing
the PB2002 boundary segments.
Beavan, J., and J. Haines
(2001), Contemporary horizontal velocity and strain rate fields of
the Pacific-Australian plate boundary zone through New Zealand, J.
Geophys. Res. Solid Earth,
P. (2003), An updated digital model of plate boundaries,
B., C. DeMets, B. Tikoff, P. Williams, L. Brown, and M.
Wiggins-Grandison (2012), Seismic hazard along the southern boundary
of the Gônave microplate: block modelling of GPS velocities from
Jamaica and nearby islands, northern Caribbean, Geophys.
B. A., M. Bevis, R. S. Jr, E. Kendrick, R. Manceda, E. Lauría, R.
Maturana, and M. Araujo (2003), Crustal motion in the Southern Andes
(26°–36°S): Do the Andes behave like a microplate?, Geochem.
E., C. Ebinger, C. Hartnady, and J.-M. Nocquet (2006), Kinematics of
the East African rift from GPS and earthquake slip vector data, in
Afar Volcanic Province within the East African Rift System,
vol. 259, edited by C. J. Ebinger, G. Yirgu, and P. K. . Maguire, pp.
M., H. Perfettini, H. Tavera, J.-P. Avouac, D. Remy, J.-M. Nocquet,
F. Rolandone, F. Bondoux, G. Gabalda, and S. Bonvalot (2011),
Interseismic coupling and seismic potential along the Central Andes
subduction zone, J.
J. A., and D. W. Forsyth (2001), Seafloor spreading on the Southeast
Indian Ridge over the last one million years: a test of the Capricorn
plate hypothesis, Earth
Planet. Sci. Lett.,
R. S., and J. T. Freymueller (2008), Evidence for and implications of
a Bering plate based on geodetic measurements from the Aleutians and
western Alaska, J.
P.C., and D.P. McKenzie (1982), A thin viscous sheet model for
continental deformation, Geophys.
J. Royal Astron. Soc.,
A. J., and W. E. Holt (1993), A procedure for obtaining the complete
horizontal motions within zones of distributed deformation from the
inversion of strain rate data, J.
C. J. H. (2002), Earthquake hazard in Africa: perspectives on the
Nubia-Somalia boundary, South
Afr. J. Sci.,
W. E., B. Shen-Tu, J. Haines, and J. Jackson (2000), On the
determination of self-consistent strain rate fields within zones of
distributed continental deformation, in Geophysical
vol. 121, edited by M. A. Richards, R. G. Gordon, and R. D. van der
Hilst, pp. 113–141, American Geophysical Union, Washington, D. C.
B. C., R. G. Gordon, and D. F. Argus (2007), Plate kinematic evidence
for the existence of a distinct plate between the Nubian and Somalian
plates along the Southwest Indian Ridge, J.
P. E., G. S. Mattioli, A. Lopez, C. DeMets, T. H. Dixon, P. Mann, and
E. Calais (2000), Neotectonics of Puerto Rico and the Virgin Islands,
northeastern Caribbean, from GPS geodesy, Tectonics,
K. G., K. Fujita, L. V. Gunbina, V. N. Kovalev, V. S. Imaev, B. M.
Koz’min, and L. P. Imaeva (1997), Seismicity of the Bering Strait
region: Evidence for a Bering block, Geology,
S., R. Reilinger, S. McClusky, P. Vernant, and A. Tealeb (2005), GPS
evidence for northward motion of the Sinai Block: Implications for E.
Mediterranean tectonics, Earth
Planet. Sci. Lett.,
D. M., E. Calais, A. M. Freed, S. T. Ali, P. Przybylski, G. Mattioli,
P. Jansma, C. Petit, and J. B. de Chabalier (2008), Interseismic
plate coupling and strain partitioning in the Northeastern Caribbean,
P., F. W. Taylor, R. L. Edwards, and T.-L. Ku (1995), Actively
evolving microplate formation by oblique collision and sideways
motion along strike-slip faults: An example from the northeastern
Caribbean plate margin, Tectonophysics,
R., R. W. King, S. J. Payne, and M. Lancaster (2013), Active
tectonics of northwestern U.S. inferred from GPS-derived surface
W. R. (1985), On the earthquake hazards of Puerto Rico and the Virgin
Seism. Soc. Am.,
S. et al. (2010), Kinematics of the southern Red Sea–Afar Triple
Junction and implications for plate dynamics, Geophys.
S., M. Hashimoto, and M. Ando (2004), A rigid block rotation model
for the GPS derived velocity field along the Ryukyu arc, Phys.
Earth Planet. Inter.,
C., R. Malservisi, T. H. Dixon, P. LaFemina, G. F. Sella, J.
Fletcher, and F. Suarez-Vidal (2007), New constraints on relative
motion between the Pacific Plate and Baja California microplate
(Mexico) from GPS measurements, Geophys.
J.-Y., and R. G. Gordon (1997), The motion and boundary between the
Capricorn and Australian plates, Science,
A., A. Hofstetter, Z. Garfunkel, and H. Ron (2003), Seismotectonics
of the Sinai subplate – the eastern Mediterranean region, Geophys.
P. J., and R. J. Dorsey (1997), Translation of terranes: Lessons from
central Baja California, Mexico, Geology,
L. M., J. Beavan, R. McCaffrey, and D. Darby (2004), Subduction zone
coupling and tectonic block rotations in the North Island, New