Strain Modeling at SUNY Stony Brook
Modeling Techniques
Regional Models
Global Strain Rate Models
Acknowledgements
References
Modeling Techniques
Outlined below you will find some information on the modeling done at SUNY Stony Brook. A variant of the method first introduced by Haines and Holt (1993) is used to estimate the horizontal velocity gradient tensor field using geodetic, seismological, and geologic observables (Haines et al., 1998). Bi-cubic Bessel interpolation on a curvilinear grid is used to extrapolate rotation vector function values in the process of simultaneously fitting geodetic velocities and observed strain rate tensors. From the obtained velocity gradient tensor field a model strain rate tensor field and velocity field can be inferred. Observed strain rates can be obtained from either Quaternary fault slip estimates or seismic moment tensors, using Kostrov's summation (1974). However, due to the brevity of the earthquake catalog seismic moment tensors can only be used to infer the style and direction of the seismic strain rate field, not the magnitude. A least-squares fit to the geodetic velocities is performed while observed strain rates are being matched by the model strain rate field. When no geologic strain rates are available the seismic moment tensor field, inferred from shallow events from the Harvard CMT catalog, is used to constrain the style and direction (not magnitude) of the model strain rate field in the process of fitting geodetic velocities. In the near future spreading rate information for oceanic ridges as well as ocean transform azimuths will also be implemented in the modeling.
Regional Models
To date modeling was mainly aimed at determining strain rate and velocity fields for regions of diffuse deformation such as the western U.S., and central, east, and southeast Asia. Modeling results for regional studies are shown below. Results for the western U.S. are from Shen-Tu et al. (1999), for central and east Asia from Holt et al. (2000), and for the Indonesia-Philippines region from Kreemer et al. (2000).
Figure 1. Strain rates inferred from Kostrov summation of Quaternary fault slip rates (white principal strain rate axes), and corresponding spatial averages of predicted strain rates (black principal strain rate axes) given by bi-cubic Bessel interpolation of fitted velocity values on a curvilinear grid. Fitted strain rate field is a self-consistent estimate determined in a least-squares inversion in which both strain rates and GPS velocities are matched by model strain rates and velocity fields, respectively. Amurian B. -Amurian Block, Ordos B. - Ordos Block, Sunda B. - Sunda Block, WSG - Weihe Shanxi Graben system. From (Holt et al.2000, JGR, in press).
Figure 2. Model velocity field relative to Eurasia obtained by bi-cubic Bessel interpolation of model rotation vector function values at the nodes in the grid shown on the figure of strain rates (above). Both GPS velocities and Quaternary strain rates are matched in the inversion procedure. Error ellipses are 95% confidence. WSG - Weihe Shanxi Graben system. From (Holt et al., 2000, JGR, in press).
Figure 3. A) Principal axes (red axes are compressional and open axes are extensional) of the model strain rate tensor field obtained by the least-squares fit of model velocities with 93 observed GPS velocities, using bi-cubic Bessel interpolation on a curvilinear grid. In the process of fitting geodetic velocities the direction and style (not magnitude) of the model strain rate field is constrained, a priori, by the seismic strain rate field inferred from a Kostrov summation of moment tensors from shallow events with Mw<7.3 from the Harvard CMT catalog. B) Model velocity field relative to Australia associated with model presented in A. Error ellipses represent 1-sigma standard deviation. Open arrows are NUVEL-1A estimates. From Kreemer et al. (2000).
Figure 4. Contour map of minimum strain rates for the Western U.S. This strain and the corresponding velocity solution (Figure 5, below) are from a joint-inversion of geological and GPS/VLBI data. All strain rate and velocity values are calculated at positions with 0.05-degree interval (From B. Shentu, 2000).
Figure 5. Velocities corresponding to the strain model solution in figure 4 (From B. Shentu, 2000).
Global Strain Rate Models
Recently the same methodology is adopted to estimate the strain rate tensor field for all of the Earth's deforming zones in one global model. For the global model ~1600 geodetic velocities are currently used. These velocities comprise mainly of GPS, but velocities from the SLR, VLBI and DORIS techniques are also used. To date Quaternary fault slip data has not been used yet (in part due to the lack of a consistent global data set), instead seismic moment tensors from the Harvard CMT catalog are taken to infer a seismic strain rate field, which is used as an a priori constraint on the style and direction (not the magnitude) of the model strain rate field in the process of fitting geodetic velocities. The model will soon be expanded to include fault orientations, fault slip observations, spreading rates, and ocean transform azimuths.
Figure 6. Grid used in global model, covering most of the Earth's deforming regions. The grid is continuous in longitudinal direction and bounded by 80°N and -80°S. Each grid cell measures 0.6°x0.5?in dimension (too small to be seen on figure !!); the total grid contains ~23000 cells. All areas that are not defined as a deformation zone are constrained to be rigid; currently the model mimics 25 independent plates and blocks.
Figure 7. Site locations of the geodetic velocities used in this study. Orange squares are from IGS, upright green triangles are VLBI (Ma and Ryan, 1998), blue diamonds are SLR (Smith et al., 1994; Robbins et al., 1994), yellow hexagonals are GPS from the United Sates Geologic Survey (USGS), and red circles are from campaign style GPS (list of references can be acquired through the authors).
Figure 8. Contours of the second invariant of the model strain rate tensor field obtained by a least squares fit to a large set of world-wide geodetic velocities and fault slip rate in Asia. Where no fault slip rate data is used the style and direction (but not magnitude) of the model strain rate field were constrained, a priori, using the seismic moment tensors of all shallow events in the CMT catalog.
References
Crétaux, J.-F., L. Soudarin, A. Cazenave, and F. Bouille, Present-day tectonic plate motions and crustal deformations from the DORIS space system, J. Geophys. Res., 103, 30,167-30,181, 1998.
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, 12,057-12,082, 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, and J. Ren, The velocity field in Asia inferred from Quaternary fault slip rates and GPS observations, J. Geophys. Res., in revision, 2000.
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., 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, 2000.
Ma, C., and J.W. Ryan, NASA Space Geodesy Program - GSFC DATA Analysis-1998, VLBI Geodetic Results 1979-1998, August, 1998.
Robbins, J.W., P.J. Dunn, M.H. Torrence, and D.E. Smith, Deformation in the eastern Mediterranean, in Proceedings of the First International Symposium on Deformation in Turkey, ed. M. Sahin and P.A. Cross, 1994.
Shen-Tu, B., W.E. Holt, and A.J. Haines, The kinematics of the western United States estimated from Quaternary rates of slip and space geodetic data, J. Geophys. Res., 104, 28,927-28,955, 1999.
Smith, D.E., R. Kolenkiewicz, R.S. Nerem, P.J. Dunn, M.H. Torrence, J.W. Robbins, S.M. Klosko, R.G. Williamson and E.C. Pavlis, Contemporary global horizontal crustal motion, Geophys. J. Int., 119, 511-520, 1994.
Acknowledgements
Boudewijn Ambrosius, Rick Bennett, Jean-Francois Crétaux, Jeff Freymueller, Brad Hager, Teruyuki Kato for providing unpublished GPS results.
For more information on this paper, please contact:
wholt
horizon.ess.sunysb.edu">Dr. William Holt
Related Pages:
Strain Rate Model Archive
Global Strain Rate Map Project
Comments or questions about this page? Send e-mail to Chuck Meertens (chuckmunavco.org).
Last modified Friday, 28-Jan-2011 21:10:28 UTC