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Global Strain Rate Map Project:  Methodology
International Lithosphere Program         SUNY Stony Brook         Global Strain Rate Map Project

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The methodology adopted to estimate a global strain rate and velocity model has been presented in Kreemer et al. [2000a], but a brief overview is given here. 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 adopt the methodology by Haines and Holt [1993] to estimate the horizontal velocity gradient tensor field on a sphere. A bi-cubic Bessel interpolation is used instead of polynomials, however, to expand a model rotation vector function that is obtained by a least-squares minimization between model and geodetic velocities, and model and geologic strain rates. Geological strain rates are obtained through a summation of Quaternary fault slip rates using a variant of Kostrov's [1974] formula [Shen-Tu et al., 1999; Holt et al., 2000a]. This type of modeling has been presented in numerous papers concerning regional tectonics in zones of diffuse deformation; e.g., western United States [Shen-Tu et al., 1999], and central Asia [Holt et al., 2000a]. A comprehensive overview of the methodology can be found in Haines et al.[1998], Holt et al. [2000b], and Beavan and Haines [2001].

Our model grid is continuous in longitudinal direction and covers the globe between 80N and 80S. Each grid area is 0.6 by 0.5 in dimension. Whether an area is considered to be deforming or not is based primarily on seismicity occurrence (Engdahl et al. [1998] and the Harvard Centroid Moment Tensor (CMT) catalog [Dziewonski et al., 1981, 2000]). All oceanic ridge and transform zones are allowed to deform. Within oceanic and continental regions of diffuse deformation, where seismicity rates are often low, the designation of boundaries between deforming and plate-like regions was often subjective. Therefore, the geometry of deforming regions in this model should be viewed as approximate. About 25000 grid areas cover the Earth's deforming regions; all other areas are considered to be rigid. The rigid areas mimic 25 independent plates and blocks, including a number of relatively small entities such as the Rivera, Anatolia, Ochotsk, Caroline, Scotia, Sunda, Tarim, Amuria, and South China plates and blocks, among others.

In this model we currently perform a least-squares fit to 5170 geodetic velocities from 86 different studies (see Introduction for comparison with earlier GSRM versions). One of the main advantages of the methodology used for this model is that an unlimited number of geodetic studies may be combined. The original reference frame of each individual study does not need to be adopted and, in fact, can be left undefined, a priori, in the inversion; the reference frame is solved upon fitting geodetic velocities to one self-consistent velocity gradient tensor field. That is, implicit in our procedure is the assumption that a single rigid body rotation can be applied to velocity vectors from each individual study (one rotation vector for each study) such that the model velocity field provides a ' best-fit' to the observed vectors that have been rotated into a single model frame of reference. Besides geodetic velocities we also included Quaternary fault slip rate data from central Asia [England and Molnar, 1997; Holt et al., 2000a, and references therein]. We perform a smoothing of the geologic strain rates over an appropriate length scale (~50-100 km) such that geodetic and geologic strain rates compliment each other in reflecting the ongoing horizontal deformation in areas where the lateral dimension is several times larger than the elastic thickness. As a consequence of combining these different data sets, the resolution for the global strain rate model has a lower limit of ~50-100 km.

To accommodate the fact that not all plate boundary zones or areas within one single plate boundary zone strain with the same magnitude we constrain the magnitude of the a priori strain rate variance to vary globally. In order to do this all plate boundary zones are divided into 218 smaller areas. For each of these areas a value is assigned, depending on the expected magnitude of the strain rate for the area. For conformity the strain rate variance is chosen from a range of 4 values, depending on the expected strain rate; the highest a priori variance value is reserved for the zones that are expected to deform with the highest strain rate. A priori constraints on the expected lateral variation in strain rate are especially important for areas in which kinematics are ill-constrained due to a lack of observed velocities (e.g., Iran, East African Rift Valley, western Mediterranean, and central America).

For regions that are not densely sampled with geodetic observations, the interpolation of geodetic velocities can be highly non-unique in describing the regional strain rate field [Kreemer et al., 2000b; Beavan and Haines, 2001]. However, the design of the strain rate covariance matrix can place a priori constraints on the style and direction of the model strain rate field. The constraint on the direction of the principal axes of the model strain rate field involves an uncertainty of 10. Information about the style and direction of expected strain rate is inferred from the principal axes of the seismic strain rate field, which is obtained through a Kostrov [1974] summation of seismic moment tensors in each grid area. Seismic moment tensors are used only from shallow events (less or equal 40 km) in the Harvard CMT catalog (January 1977 - November 2002) and from Pondrelli et al. [2002] for the Mediterranean (January 1997 - December 2000). For this purpose all events are weighted equally in the Kostrov summation. This approach is adopted here, except for areas where Quaternary fault slip rate data are used to infer geologic strain rate estimates (currently only for central Asia). It should be noted that only the style and direction of the model strain rate field is constrained using the direction and style of the seismic strain rate field, not the magnitude. Also, constraints on the style and direction of the model strain rate field do not significantly affect the fit of the model velocities to the observed velocities. Moreover, including constraints on the style and direction of the model strain rate field results in a solution that is as consistent as possible with regional seismotectonics, while providing more stability in the model strain rate field from one grid area to another [Kreemer et al., 2000b].


Beavan, J., and J. Haines, Contemporary horizontal velocity and strain rate fields of the Pacific-Australian plate boundary zone through New Zealand, J. Geophys. Res., 106, 741-770, 2001.

Dziewonski, A.M., T.-A. Chou, and J.H. Woodhouse, Determination of earthquake source parameters from waveform data for studies of global and regional seismicity, J. Geophys. Res., 86, 2825-2852, 1981.

Dziewonski, A.M., G. Ekström, and N.N. Maternovskaya, Centroid-moment tensor solutions for July-September, 1999, Phys. Earth Planet. Int., 119, 311-319, 2000.

Engdahl, E.R., R. van der Hilst, and R. Buland, Global teleseismic relocation with improved travel times and procedures for depth determination, Bull. Seismol. Soc. Am., 88, 722-743, 1998.

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

England, P.C., and P. Molnar, The field of crustal velocity in Asia calculated from Quaternary rates of slip on faults, Geophys J. Int., 130, 551-582, 1997.

Haines, A.J., and W.E. Holt, A procedure for obtaining the complete horizontal motions within zones of distributed deformation from the inversion of strain rate data, J. Geophys. Res., 98, 12057-12082, 1993.

Haines, A.J., J.A. Jackson, W.E. Holt, and D.C. Agnew, Representing distributed deformation by continuous velocity fields, Sci. Rept. 98/5, Inst. of Geol. and Nucl. Sci., Wellington, New Zealand, 1998.

Holt, W.E., N. Chamot-Rooke, X. LePichon, A.J. Haines, B. Shen-Tu, and J. Ren, The velocity field in Asia inferred from Quaternary fault slip rates and GPS observations, J. Geophys. Res., 105, 19185-19210, 2000a.

Holt, W.E., B. Shen-Tu, A.J. Haines, J. Jackson, On the determination of self-consistent strain rate fields within zones of distributed continental deformation, in The History and Dynamics of Global Plate Motions, eds. M.A. Richards, R.G. Gordon, and R.D. van der Hilst, AGU, Washington, D.C., 2000b.

Kostrov V.V., Seismic moment and energy of earthquakes, and seismic flow of rocks, Izv. Acad. Sci. USSR Phys. Solid Earth, 1, Eng. Transl., 23-44, 1974.

Kreemer, C., J. Haines, W.E. Holt, G. Blewitt, and D. Lavallée, On the determination of a global strain rate model, Earth Planets Space, 52, 765-770, 2000a.

Kreemer, C., W.E. Holt, S. Goes, and R. Govers, Active deformation in eastern Indonesia and the Philippines from GPS and seismicity data, J. Geophys. Res., 105, 663-680, 2000b.

Pondrelli, S., A. Morelli, G. Ekström, S. Mazza, E. Boschi, and A.M. Dziewonski, European-Mediterranean regional centroid-moment tensors: 1997-2000, Phys. Earth Planet. Int., 130, 71-101, 2002.

Shen-Tu, B., W.E. Holt, and A.J. Haines, Deformation kinematics in the western United States determined from Quaternary fault slip rates and recent geodetic data, J. Geophys. Res., 104, 28927-28955, 1999.


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