The angular velocities of the plates and the velocity of Earth's centre from space geodesy
01 Mar 2010-Geophysical Journal International (Oxford University Press)-Vol. 180, Iss: 3, pp 913-960
TL;DR: In this article, a set of relative plate angular velocities, called GEODVEL (for GEODesy VELocity) is presented, which is based on the estimation of the position of the Earth's center and the assignment of sites to plates.
Abstract: SUMMARY
Using space geodetic observations from four techniques (GPS, VLBI, SLR and DORIS), we simultaneously estimate the angular velocities of 11 major plates and the velocity of Earth's centre. We call this set of relative plate angular velocities GEODVEL (for GEODesy VELocity).
Plate angular velocities depend on the estimate of the velocity of Earth's centre and on the assignment of sites to plates. Most geodetic estimates of the angular velocities of the plates are determined assuming that Earth's centre is fixed in an International Terrestrial Reference Frame (ITRF), and are therefore subject to errors in the estimate of the velocity of Earth's centre. In ITRF2005 and ITRF2000, Earth's centre is the centre of mass of Earth, oceans and atmosphere (CM); the velocity of CM is estimated by SLR observation of LAGEOS's orbit. Herein we define Earth's centre to be the centre of mass of solid Earth (CE); we determine the velocity of CE by assuming that the portions of plate interiors not near the late Pleistocene ice sheets move laterally as if they were part of a rigid spherical cap. The GEODVEL estimate of the velocity of CE is likely nearer the true velocity of CM than are the ITRF2005 and ITRF2000 estimates because (1) no phenomena can sustain a significant velocity between CM and CE, (2) the plates are indeed nearly rigid (aside from vertical motion) and (3) the velocity of CM differs between ITRF2005 and ITRF2000 by an unacceptably large speed of 1.8 mm yr−1. The velocity of Earth's centre in GEODVEL lies between that of ITRF2000 and that of ITRF2005, with the distance from ITRF2005 being about twice that from ITRF2000. Because the GEODVEL estimates of uncertainties in plate angular velocities account for uncertainty in the velocity of Earth's centre, they are more realistic than prior estimates of uncertainties.
GEODVEL differs significantly from all prior global sets of relative plate angular velocities determined from space geodesy. For example, the 95 per cent confidence limits for the angular velocities of GEODVEL exclude those of REVEL (Sella et al.) for 34 of the 36 plate pairs that can be formed between any two of the nine plates with the best-constrained motion. The median angular velocity vector difference between GEODVEL and REVEL is 0.028° Myr−1, which is up to 3.1 mm yr−1 on Earth's surface. GEODVEL differs the least from the geodetic angular velocities that Altamimi et al. determine from ITRF2005. GEODVEL's 95 per cent confidence limits exclude 11 of 36 angular velocities of Altamimi et al., and the median difference is 0.015° Myr−1.
GEODVEL differs significantly from nearly all relative plate angular velocities averaged over the past few million years, including those of NUVEL-1A. The difference of GEODVEL from updated 3.2 Myr angular velocities is statistically significant for all but two of 36 angular velocities with a median difference of 0.063° Myr−1. Across spreading centres, eight have slowed down while only two have sped up. We conclude that plate angular velocities over the past few decades differ significantly from the corresponding angular velocity averaged over the past 3.2 Myr.
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TL;DR: MORVEL as discussed by the authors is a new closure-enforced set of angular velocities for the geologically current motions of 25 tectonic plates that collectively occupy 97 per cent of Earth's surface.
Abstract: SUMMARY
We describe best-fitting angular velocities and MORVEL, a new closure-enforced set of angular velocities for the geologically current motions of 25 tectonic plates that collectively occupy 97 per cent of Earth's surface. Seafloor spreading rates and fault azimuths are used to determine the motions of 19 plates bordered by mid-ocean ridges, including all the major plates. Six smaller plates with little or no connection to the mid-ocean ridges are linked to MORVEL with GPS station velocities and azimuthal data. By design, almost no kinematic information is exchanged between the geologically determined and geodetically constrained subsets of the global circuit—MORVEL thus averages motion over geological intervals for all the major plates. Plate geometry changes relative to NUVEL-1A include the incorporation of Nubia, Lwandle and Somalia plates for the former Africa plate, Capricorn, Australia and Macquarie plates for the former Australia plate, and Sur and South America plates for the former South America plate. MORVEL also includes Amur, Philippine Sea, Sundaland and Yangtze plates, making it more useful than NUVEL-1A for studies of deformation in Asia and the western Pacific. Seafloor spreading rates are estimated over the past 0.78 Myr for intermediate and fast spreading centres and since 3.16 Ma for slow and ultraslow spreading centres. Rates are adjusted downward by 0.6–2.6 mm yr−1 to compensate for the several kilometre width of magnetic reversal zones. Nearly all the NUVEL-1A angular velocities differ significantly from the MORVEL angular velocities. The many new data, revised plate geometries, and correction for outward displacement thus significantly modify our knowledge of geologically current plate motions. MORVEL indicates significantly slower 0.78-Myr-average motion across the Nazca–Antarctic and Nazca–Pacific boundaries than does NUVEL-1A, consistent with a progressive slowdown in the eastward component of Nazca plate motion since 3.16 Ma. It also indicates that motions across the Caribbean–North America and Caribbean–South America plate boundaries are twice as fast as given by NUVEL-1A. Summed, least-squares differences between angular velocities estimated from GPS and those for MORVEL, NUVEL-1 and NUVEL-1A are, respectively, 260 per cent larger for NUVEL-1 and 50 per cent larger for NUVEL-1A than for MORVEL, suggesting that MORVEL more accurately describes historically current plate motions. Significant differences between geological and GPS estimates of Nazca plate motion and Arabia–Eurasia and India–Eurasia motion are reduced but not eliminated when using MORVEL instead of NUVEL-1A, possibly indicating that changes have occurred in those plate motions since 3.16 Ma. The MORVEL and GPS estimates of Pacific–North America plate motion in western North America differ by only 2.6 ± 1.7 mm yr−1, ≈25 per cent smaller than for NUVEL-1A. The remaining difference for this plate pair, assuming there are no unrecognized systematic errors and no measurable change in Pacific–North America motion over the past 1–3 Myr, indicates deformation of one or more plates in the global circuit. Tests for closure of six three-plate circuits indicate that two, Pacific–Cocos–Nazca and Sur–Nubia–Antarctic, fail closure, with respective linear velocities of non-closure of 14 ± 5 and 3 ± 1 mm yr−1 (95 per cent confidence limits) at their triple junctions. We conclude that the rigid plate approximation continues to be tremendously useful, but—absent any unrecognized systematic errors—the plates deform measurably, possibly by thermal contraction and wide plate boundaries with deformation rates near or beneath the level of noise in plate kinematic data.
2,089 citations
TL;DR: In this paper, a new type of global plate motion model consisting of a set of continuously-closing topological plate polygons with associated plate boundaries and plate velocities since the break-up of the supercontinent Pangea is presented.
1,519 citations
Cites background from "The angular velocities of the plate..."
...…(1) “Geologically current” models based on present day plate motions from GPS measurements (Argus and Heflin, 1995), space geodesy e.g. GEODVEL (Argus et al., 2010) or a combination of spreading rates, fault azimuths and GPS measurements e.g. NUVEL-1 (DeMets et al., 1990, 2010) and MORVEL…...
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...Currently, plate reconstructions fall into three main categories: (1) “Geologically current” models based on present day plate motions from GPS measurements (Argus and Heflin, 1995), space geodesy e.g. GEODVEL (Argus et al., 2010) or a combination of spreading rates, fault azimuths and GPS measurements e.g. NUVEL-1 (DeMets et al., 1990, 2010) and MORVEL (DeMets et al., 2010); (2) Traditional plate tectonicmodels based on the interpretation of the seafloor spreading record and/or paleomagnetic data to reconstruct the ocean basins, continents and terranes within an absolute reference framework (Scotese et al., 1988; Scotese, 1991; Golonka and Ford, 2000; Schettino and Scotese, 2005; Golonka, 2007; Müller et al., 2008b); (3) Coupled geodynamic–plate models, whichmodel plate boundary locations andmantle density heterogeneity to predict past and/or present plate motions (Hager and O'Connell, 1981; Lithgow-Bertelloni and Richards, 1998; Conrad and Lithgow-Bertelloni, 2002; Stadler et al., 2010)....
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...GEODVEL (Argus et al., 2010) or a combination of spreading rates, fault azimuths and GPS measurements e....
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TL;DR: In this paper, a new model of the last deglaciation event of the Late Quaternary ice age is described and denoted as ICE-6G_C (VM5a), which has been explicitly refined by applying all of the available Global Positioning System (GPS) measurements of vertical motion of the crust that may be brought to bear to constrain the thickness of local ice cover as well as the timing of its removal.
Abstract: A new model of the last deglaciation event of the Late Quaternary ice age is here described and denoted as ICE-6G_C (VM5a). It differs from previously published models in this sequence in that it has been explicitly refined by applying all of the available Global Positioning System (GPS) measurements of vertical motion of the crust that may be brought to bear to constrain the thickness of local ice cover as well as the timing of its removal. Additional space geodetic constraints have also been applied to specify the reference frame within which the GPS data are described. The focus of the paper is upon the three main regions of Last Glacial Maximum ice cover, namely, North America, Northwestern Europe/Eurasia, and Antarctica, although Greenland and the British Isles will also be included, if peripherally, in the discussion. In each of the three major regions, the model predictions of the time rate of change of the gravitational field are also compared to that being measured by the Gravity Recovery and Climate Experiment satellites as an independent means of verifying the improvement of the model achieved by applying the GPS constraints. Several aspects of the global characteristics of this new model are also discussed, including the nature of relative sea level history predictions at far-field locations, in particular the Caribbean island of Barbados, from which especially high-quality records of postglacial sea level change are available but which records were not employed in the development of the model. Although ICE-6G_C (VM5a) is a significant improvement insofar as the most recently available GPS observations are concerned, comparison of model predictions with such far-field relative sea level histories enables us to identify a series of additional improvements that should follow from a further stage of model iteration.
902 citations
TL;DR: The Global Strain Rate Model (GSRM v.2.1) as mentioned in this paper is a new global model of plate motions and strain rates in plate boundary zones constrained by horizontal geodetic velocities.
Abstract: 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 Mw=7.5 characteristic earthquakes.
608 citations
Cites background or result from "The angular velocities of the plate..."
...The new model, commissioned by the Global Earthquake Model (GEM) foundation is named the GEM Strain Rate Model, and version 2.1 is presented here (v.2.0 was released to GEM in 2013)....
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...In order for the velocity gradient field inside the plate boundaries to be self-consistent with the rigid plate motions, our description of plate motion can differ from recent studies [Kogan and Steblov, 2008; Argus et al., 2010; Altamimi et al., 2012]....
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...We compare our angular velocities relative to the Pacific plate with previous geodetic estimates that provided a full covariance matrix (GEODVEL [Argus et al., 2010], ITRF2008 [Altamimi et al....
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...…as the center of mass of the Earth, oceans, and atmosphere as estimated by satellite laser ranging (SLR), which is not only uncertain but is also inconsistent with the idea that surface motions should be referenced relative to the center of mass of the solid Earth [Argus, 2007; Argus et al., 2010]....
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...A continuous velocity field v x̂ð Þ can then be written as: v x̂ð Þ5R _W x̂ð Þ3 x̂ (B1) where R is the Earth’s radius, and x̂ is a three-dimensional unit vector for any point on the Earth’s surface with latitude h and longitude u: x̂5 coshcosu; coshsinu; sinhð Þ (B2) If _W is constant over a given area, then (B1) gives the well-known formulation for a rigid body rotation....
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TL;DR: The NNR-MORVEL56 set of geologically current relative plate angular velocities is derived in this article, which is the first set of angular veloci measured relative to the unique reference frame in which there is no net rotation of the lithosphere.
Abstract: NNR-MORVEL56, which is a set of angular velocities of 56 plates relative to the unique reference frame in which there is no net rotation of the lithosphere, is determined. The relative angular velocities of 25 plates constitute the MORVEL set of geologically current relative plate angular velocities; the relative angular velocities of the other 31 plates are adapted from Bird (2003). NNR-MORVEL, a set of angular velocities of the 25 MORVEL plates relative to the no-net rotation reference frame, is also determined. Incorporating the 31 plates from Bird (2003), which constitute 2.8% of Earth's surface, changes the angular velocities of the MORVEL plates in the no-net-rotation frame only insignificantly, but provides a more complete description of globally distributed deformation and strain rate. NNR-MORVEL56 differs significantly from, and improves upon, NNR-NUVEL1A, our prior set of angular velocities of the plates relative to the no-net-rotation reference frame, partly due to differences in angular velocity at two essential links of the MORVEL plate circuit, Antarctica-Pacific and Nubia-Antarctica, and partly due to differences in the angular velocities of the Philippine Sea, Nazca, and Cocos plates relative to the Pacific plate. For example, the NNR-MORVEL56 Pacific angular velocity differs from the NNR-NUVEL1A angular velocity by a vector of length 0.039 ± 0.011° a−1 (95% confidence limits), resulting in a root-mean-square difference in velocity of 2.8 mm a−1. All 56 plates in NNR-MORVEL56 move significantly relative to the no-net-rotation reference frame with rotation rates ranging from 0.107° a−1 to 51.569° a−1.
458 citations
Cites background or methods from "The angular velocities of the plate..."
...…Antarctica, and South America plates has 10 of 13 decreased since 0.8 Ma ago [Tebbens and Cande, 1997; Angermann et al., 1999, Norabuena et al., 1999; Sella et al., 2002; Kendrick et al., 2003; Argus et al., 2010], the age of the magnetic reversal used to estimate Nazca‐Pacific motion in MORVEL....
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...The GPS site Magadan, on the Okhotsk plate, is moving relative to the North America plate toward the southwest at 1.8 mm a−1 [Argus et al., 2010], a velocity that differs 11 of 13 insignificantly from both zero and the MORVEL56 prediction....
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References
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01 Jun 1969
TL;DR: In this paper, Monte Carlo techniques are used to fit dependent and independent variables least squares fit to a polynomial least-squares fit to an arbitrary function fitting composite peaks direct application of the maximum likelihood.
Abstract: Uncertainties in measurements probability distributions error analysis estimates of means and errors Monte Carlo techniques dependent and independent variables least-squares fit to a polynomial least-squares fit to an arbitrary function fitting composite peaks direct application of the maximum likelihood. Appendices: numerical methods matrices graphs and tables histograms and graphs computer routines in Pascal.
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TL;DR: Numerical methods matrices graphs and tables histograms and graphs computer routines in Pascal and Monte Carlo techniques dependent and independent variables least-squares fit to a polynomial least-square fit to an arbitrary function fitting composite peaks direct application of the maximum likelihood.
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