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 [e.g., England
and McKenzie . We use the method of Haines and Holt [e.g., Haines and Holt, 1993; Holt et al., 2000; Beavan
and Haines, 2001]
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
back-arcs [Brooks et al., 2003; Wallace et al., 2004; Chlieh et al., 2011; McCaffrey et al., 2013], 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:
Bering [e.g., Mackey et al., 1997; Cross
and Freymueller, 2008]
Baja California [e.g., Umhoefer and Dorsey, 1997; Plattner et al., 2007]
Capricorn [e.g., Royer and Gordon, 1997; Conder
and Forsyth, 2001]
Danakil [McClusky et al., 2010]
Gônave [e.g., Mann et al., 1995; Benford et al., 2012]
Lwandle [e.g., Hartnady, 2002; Horner-Johnson et al., 2007]
Rico [e.g., McCann, 1985; Jansma et al., 2000; Manaker et al., 2008]
Rovuma [e.g., Hartnady, 2002; Calais et al., 2006b]
Sakishima [Nishimura et al., 2004]
Satunam [Nishimura et al., 2004]
Sinai [e.g., Salamon et al., 2003; Mahmoud et al., 2005]
Victoria [e.g., Hartnady, 2002; Calais et al., 2006b]
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
and εyy, and 1/2
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
(sqrt(εxx^2+εyy^2+2εxy^2)), 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
and Rabaute ), 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.
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