We present a new global model of plate motions and strain rates in plate boundary zones constrained by horizontal geodetic velocities. This Global Strain Rate Model (GSRM v.2.1) is a vast improvement over its predecessor both in terms of amount of data input as in an increase in spatial model resolution by factor of $2.5 in areas with dense data coverage. We determined 6739 velocities from time series of (mostly) continuous GPS measurements; i.e., by far the largest global velocity solution to date. We transformed 15,772 velocities from 233 (mostly) published studies onto our core solution to obtain 22,511 velocities in the same reference frame. Care is taken to not use velocities from stations (or time periods) that are affected by transient phenomena; i.e., this data set consists of velocities best representing the interseismic plate velocity. About 14% of the Earth is allowed to deform in 145,086 deforming grid cells (0.25 longitude by 0.2 latitude in dimension). The remainder of the Earth's surface is modeled as rigid spherical caps representing 50 tectonic plates. For 36 plates we present new GPS-derived angular velocities. For all the plates that can be compared with the most recent geologic plate motion model, we find that the difference in angular velocity is significant. The rigid-body rotations are used as boundary conditions in the strain rate calculations. The strain rate field is modeled using the Haines and Holt method, which uses splines to obtain an self-consistent interpolated velocity gradient tensor field, from which strain rates, vorticity rates, and expected velocities are derived. We also present expected faulting orientations in areas with significant vorticity, and update the no-net rotation reference frame associated with our global velocity gradient field.Finally, we present a global map of recurrence times for M w 57.5 characteristic earthquakes.

SUMMARY In this paper we present a global model (GSRM‐1) of both horizontal velocities on the Earth's surface and horizontal strain rates for almost all deforming plate boundary zones. A model strain rate field is obtained jointly with a global velocity field in the process of solving for a global velocity gradient tensor field. In our model we perform a least‐squares fit between model velocities and observed geodetic velocities, as well as between model strain rates and observed geological strain rates. Model velocities and strain rates are interpolated over a spherical Earth using bi‐cubic Bessel splines. We include 3000 geodetic velocities from 50 different, mostly published, studies. Geological strain rates are obtained for central Asia only and they are inferred from Quaternary fault slip rates. For all areas where no geological information is included a priori constraints are placed on the style and direction (but not magnitude) of the model strain rate field. These constraints are taken from a seismic strain rate field inferred from (normalized) focal mechanisms of shallow earthquakes. We present a global solution of the second invariant of the model strain rate field as well as strain rate solutions for a few selected plate boundary zones. Generally, the strain rate tensor field is consistent with geological and seismological data. With the assumption of plate rigidity for all areas other than the plate boundary zones we also present relative angular velocities for most plate pairs. We find that in general there is a good agreement between the present‐day plate motions we obtain and long‐term plate motions, but a few significant differences exist. The rotation rates for the Indian, Arabian and Nubian plates relative to Eurasia are 30, 13 and 50 per cent slower than the NUVEL‐1A estimate, respectively, and the rotation rate for the Nazca Plate relative to South America is 17 per cent slower. On the other hand, Caribbean–North America motion is 76 per cent faster than the NUVEL‐1A estimate. While crustal blocks in the India–Eurasia collision zone move significantly and self‐consistently with respect to bounding plates, only a very small motion is predicted between the Nubian and Somalian plates. By integrating plate boundary zone deformation with the traditional modelling of angular velocities of rigid plates we have obtained a model that has already been proven valuable in, for instance, redefining a no‐net‐rotation model of surface motions and by confirming a global correlation between seismicity rates and tectonic moment rates along subduction zones and within zones of continental deformation.

Automatic estimation of velocities from GPS coordinate time series is becoming required to cope with the exponentially increasing flood of available data, but problems detectable to the human eye are often overlooked. This motivates us to find an automatic and accurate estimator of trend that is resistant to common problems such as step discontinuities, outliers, seasonality, skewness, and heteroscedasticity. Developed here, Median Interannual Difference Adjusted for Skewness (MIDAS) is a variant of the Theil‐Sen median trend estimator, for which the ordinary version is the median of slopes vij = (xj–xi)/(tj–ti) computed between all data pairs i > j. For normally distributed data, Theil‐Sen and least squares trend estimates are statistically identical, but unlike least squares, Theil‐Sen is resistant to undetected data problems. To mitigate both seasonality and step discontinuities, MIDAS selects data pairs separated by 1 year. This condition is relaxed for time series with gaps so that all data are used. Slopes from data pairs spanning a step function produce one‐sided outliers that can bias the median. To reduce bias, MIDAS removes outliers and recomputes the median. MIDAS also computes a robust and realistic estimate of trend uncertainty. Statistical tests using GPS data in the rigid North American plate interior show ±0.23 mm/yr root‐mean‐square (RMS) accuracy in horizontal velocity. In blind tests using synthetic data, MIDAS velocities have an RMS accuracy of ±0.33 mm/yr horizontal, ±1.1 mm/yr up, with a 5th percentile range smaller than all 20 automatic estimators tested. Considering its general nature, MIDAS has the potential for broader application in the geosciences.

The present kinematics in the eastern Mediterranean and Middle East is now well constrained by GPS measurements and dominated by a circular counterclockwise motion. While Arabia rotates rigidly, the rotational velocities increase from the Levant to Aegea, causing extension in western Anatolia. We place the present pattern in light of the post–Middle Miocene geological history and propose that in addition to the effects of the Hellenic subduction and Zagros collision-subduction zones on driving the surface motion, an underlying asthenospheric flow is also required. This counterclockwise toroidal flow is expected to exist around the eastern edge of the African slab owing to subduction rollback, and it helps explain the initiation of the North Anatolia Fault, the extrusion and uplift of Anatolia, and the Mid-Miocene to Recent volcanism in eastern Anatolia. The Afar plume had a similar effect on the acceleration of Arabia at 40 Mya.

Here we describe the new Sub-Saharan Africa Geodetic Strain Rate Model v.1.0 (SSA-GSRM v.1.0), which provides fundamental constraints on long-term tectonic deformation in the region and an improved seismic hazards assessment in Sub-Saharan Africa. Sub-Saharan Africa encompasses the East African Rift System, the active divergent plate boundary between the Nubian and Somalian plates, where strain is largely accommodated along the boundaries of three subplates. We develop an improved geodetic strain rate field for sub-Saharan Africa that incorporates 1) an expanded geodetic velocity field, 2) redefined regions of deforming zones guided by seismicity distribution, and 3) updated constraints on block rotations. SSA-GSRM v.1.0 spans longitudes 22° to 55.5° and latitudes −52° to 20° with 0.25° (longitude) by 0.2° (latitude) spacing. For plates/sub-plates, we assign rigid block rotations as constraints on the strain rate calculation that is determined by fitting bicubic Bessel splines to a new geodetic velocity solution for an interpolated velocity gradient tensor field. We derive strain rates, velocities, and vorticity rates from the velocity gradient tensor field. A comparison with the Global Geodetic Strain Rate model v2.1 reveals regions of previously unresolved spatial heterogeneities in geodetic strain rate distribution, which indicates zones of elevated seismic risk.

[1] We infer rates of crustal deformation in the northern Walker Lane (NWL) and western Basin and Range using data from the Mobile Array of GPS for Nevada transtension, and other continuous GPS networks including the EarthScope Plate Boundary Observatory. We present 224 new GPS velocities, correct them for the effects of viscoelastic postseismic relaxation, and use them to constrain a block model to estimate fault slip rates. The data segregate the NWL into domains based on differences in deformation rate, pattern, and style. Deformation is transtensional, with highest rates near the western and eastern edges of the NWL. Some basins, e.g., Tahoe, experience shear deformation and extension. Normal slip is distributed throughout the NWL and Basin and Range, where 11 subparallel range-bounding normal fault systems have an average horizontal extension rate of 0.1 mm/yr. Comparison between geologic and geodetic slip rates indicates that out of 12 published geologic rates, 10 agree with geodetic rates to within uncertainties. This suggests that smaller crustal blocks move steadily, similar to larger lithospheric plates, and that geodetic measurements of slip rates are reliable in zones of complex crustal deformation. For the two slip rates that disagree, geologic rates are greater. The vertical axis rotation rate of the Carson domain is −1.3 ± 0.1°/My clockwise, lower than the 3°to 6°/My obtained in paleomagnetic measurements. This suggests that vertical axis rotation rates may have decreased over the last 9-13 My as the role of faulting has increased at the expense of rigid rotations.

[1] The 26 December 2004 Sumatra earthquake (M w 9.2-9.3) generated the most deadly tsunami in history. Yet within the first hour, the true danger of a major oceanwide tsunami was not indicated by seismic magnitude estimates, which were far too low (M w 8.0-8.5). This problem relates to the inherent saturation of early seismicwave methods. Here we show that the earthquake's true size and tsunami potential can be determined using Global Positioning System (GPS) data up to only 15 min after earthquake initiation, by tracking the mean displacement of the Earth's surface associated with the arrival of seismic waves. Within minutes, displacements of >10 mm are detectable as far away as India, consistent with results using weeks of data after the event. These displacements imply M w 9.0 ± 0.1, indicating a high tsunami potential. This suggests existing GPS infrastructure could be developed into an effective component of tsunami warning systems.

We introduce Global Positioning System (GPS) Imaging, a new technique for robust estimation of the vertical velocity field of the Earth's surface, and apply it to the Sierra Nevada Mountain range in the western United States. Starting with vertical position time series from Global Positioning System (GPS) stations, we first estimate vertical velocities using the MIDAS robust trend estimator, which is insensitive to undocumented steps, outliers, seasonality, and heteroscedasticity. Using the Delaunay triangulation of station locations, we then apply a weighted median spatial filter to remove velocity outliers and enhance signals common to multiple stations. Finally, we interpolate the data using weighted median estimation on a grid. The resulting velocity field is temporally and spatially robust and edges in the field remain sharp. Results from data spanning 5–20 years show that the Sierra Nevada is the most rapid and extensive uplift feature in the western United States, rising up to 2 mm/yr along most of the range. The uplift is juxtaposed against domains of subsidence attributable to groundwater withdrawal in California's Central Valley. The uplift boundary is consistently stationary, although uplift is faster over the 2011–2016 period of drought. Uplift patterns are consistent with groundwater extraction and concomitant elastic bedrock uplift, plus slower background tectonic uplift. A discontinuity in the velocity field across the southeastern edge of the Sierra Nevada reveals a contrast in lithospheric strength, suggesting a relationship between late Cenozoic uplift of the southern Sierra Nevada and evolution of the southern Walker Lane.