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Methodology

We 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 [1982]. 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 a priori boundary conditions, relative to the Pacific plate, which is the reference plate in the model.

Our 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 [2003] (PB2002) and Chanot-Rooke and Rabaute [2006], with additional modifications made by us, if so desired based on the GPS data.

All 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.

We 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]

Puerto 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]

The Haines and Holt method requires us to assign a priori 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 priori 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 for εxx and εyy, and 1/2 10^-8/yr for εxy 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 priori standard deviations. For this, we did not take-over the style or covariances but set the a priori standard deviation of εxx and εyy 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.

For step 1, if we would assign the same a priori 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 priori 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 priori 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 [2006]), 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, 106(B1), 741–770, https://doi.org/10.1029/2000JB900302.

Bird, P. (2003), An updated digital model of plate boundaries, Geochemistry, Geophysics, Geosystems, 4(3), 1027, https://doi.org/10.1029/2001GC000252.

Benford, 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. J. Int., 190(1), 59–74, https://doi.org/10.1111/j.1365-246X.2012.05493.x.

Brooks, 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. Geophys. Geosystems, 4(10), 1085, https://doi.org/10.1029/2003GC000505.

Calais, E., C. Ebinger, C. Hartnady, and J.-M. Nocquet (2006), Kinematics of the East African rift from GPS and earthquake slip vector data, in The Afar Volcanic Province within the East African Rift System, vol. 259, edited by C. J. Ebinger, G. Yirgu, and P. K. . Maguire, pp. 9–22.

Chlieh, 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. Geophys. Res., 116(B12), B12405, https://doi.org/10.1029/2010JB008166.

Conder, 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., 188(1), 91–105, https://doi.org/10.1016/S0012-821X(01)00326-0.

Cross, 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. Geophys. Res., 113(B7), B07405, https://doi.org/10.1029/2007JB005136.

England, P.C., and D.P. McKenzie (1982), A thin viscous sheet model for continental deformation, Geophys. J. Royal Astron. Soc., 70, 295-321.

Haines, 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. Geophys. Res., 98(B7), 12057–12082, https://doi.org/10.1029/93JB00892.

Hartnady, C. J. H. (2002), Earthquake hazard in Africa: perspectives on the Nubia-Somalia boundary, South Afr. J. Sci., 98(9-10), 425–428.

Holt, 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 Monograph Series, 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.

Horner-Johnson, 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. Geophys. Res., 112(B5), B05418, https://doi.org/10.1029/2006JB004519.

Jansma, 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, 19(6), 1021–1037, https://doi.org/10.1029/1999TC001170.

Mackey, 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, 25(11), 979–982, https://doi.org/10.1130/0091-7613(1997)025<0979:SOTBSR>2.3.CO;2.

Mahmoud, 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., 238(1–2), 217–224, https://doi.org/10.1016/j.epsl.2005.06.063.

Manaker, 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, Geophys. J. Int., 174(3), 889–903.

Mann, 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, 246(1–3), 1–69, https://doi.org/10.1016/0040-1951(94)00268-E.

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., 118, https://doi.org/10.1029/2012JB009473.

McCann, W. R. (1985), On the earthquake hazards of Puerto Rico and the Virgin Islands, Bull. Seism. Soc. Am., 75(1), 251–262.

McClusky, S. et al. (2010), Kinematics of the southern Red Sea–Afar Triple Junction and implications for plate dynamics, Geophys. Res. Lett., 37(5), L05301, https://doi.org/10.1029/2009GL041127.

Nishimura, 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., 142(3–4), 185–203, https://doi.org/10.1016/j.pepi.2003.12.014.

Plattner, 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. Int., 170(3), 1373–1380, https://doi.org/10.1111/j.1365-246X.2007.03494.x.

Royer, J.-Y., and R. G. Gordon (1997), The motion and boundary between the Capricorn and Australian plates, Science, 277(5330), 1268–1274, https://doi.org/10.1126/science.277.5330.1268.

Salamon, A., A. Hofstetter, Z. Garfunkel, and H. Ron (2003), Seismotectonics of the Sinai subplate – the eastern Mediterranean region, Geophys. J. Int., 155(1), 149–173, https://doi.org/10.1046/j.1365-246X.2003.02017.x.

Umhoefer, P. J., and R. J. Dorsey (1997), Translation of terranes: Lessons from central Baja California, Mexico, Geology, 25(11), 1007–1010, doi:doi: 10.1130/0091-7613(1997)​025<1007:TOTLFC>​2.3.CO;2.

Wallace, L. M., J. Beavan, R. McCaffrey, and D. Darby (2004), Subduction zone coupling and tectonic block rotations in the North Island, New Zealand, J. Geophys. Res., 109(B12), B12406, https://doi.org/10.1029/2004JB003241.