Skip to main content
SpringerLink
Log in

Analysis of GPS Measurements in Eastern Canada Using Principal Component Analysis

  • Published:
Pure and Applied Geophysics Aims and scope Submit manuscript

Abstract

Continuous Global Positioning System (CGPS) position time series from eastern North America constrain the pattern and magnitude of regional crustal deformation. Initial analysis delineates consistent uplift patterns, as expected from glacial isostatic adjustment (GIA) predictions, but the associated horizontal deformation is not definitive, in part due to the short time periods for a significant number of the available stations. We employ an eigenpattern decomposition in order to define a unique, finite set of deformation patterns for this continuous GPS data. Similar in nature to the empirical orthogonal functions historically employed in the analysis of atmospheric and oceanographic phenomena, the method derives the eigenvalues and eigenstates from the diagonalization of the correlation matrix using a Karhunen–Loeve expansion (KLE). The KLE technique is used to identify the important modes in both time and space for the CGPS data, modes that potentially include signals such as horizontal and vertical GIA, tectonic strain, and seasonal effects. Here we filter both the vertical and horizontal velocity patterns on different spatiotemporal scales in order to study the potential geophysical sources, after the removal of correlated and random noise. The method is successful in disaggregating the linear vertical signal from more variable and less spatially correlated signals. The vertical and horizontal results are compared to the predictions of the ICE-3G GIA loading model with a number of plausible mantle viscosity profiles. The horizontal velocity analysis allows for qualitative differentiation between several potential GIA models and suggests that, with longer time series, this technique can be employed to remove correlated noise and improve estimates of crustal strain patterns and their sources.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  • Adams, J. and P. W. Basham (1991), The seismicity and seismotectonics of eastern Canada, in Neotectonics of North America,

  • Adams, J., and S. Halchuk (2003), Fourth generation seismic hazard maps of Canada: Values for over 650 Canadian localities intended for the 2005 Building Code of Canada, Geol. Surv. Can. Open File, 4459, 155 pp.

  • Adams, J., P. W. Basham, and S. Halchuk (1995), Northeastern North America earthquake potential—New challenges for seismic hazard mapping Geol. Surv. Can. Current Res., 1995-D, 91–99.

  • Altamimi, Z., P. Sillard, and C. Boucher (2002), ITRF2000: a new release of the International Terrestrial Reference Frame for earth science applications, J. Geophys. Res., 107(B10), 2214, doi:10.1029/2001JB000561.

  • Anghel, M. and Y. Ben-Zion (2001), Nonlinear system identification and forecasting of earthquake fault dynamics using artificial neural networks, EOS Trans., AGU, 82, F571.

  • Anghel, M., Y. Ben-Zion, and R.R. Martinez (2004), Dynamical system analysis and forecasting of deformation produced by an earthquake fault, Pure and Applied Geophysics, 161, doi:10.1007/s00024-004-2547-9.

  • Aubrey, D. G., and K. O. Emery, Eigenanalysis of recent United States sea levels, Cont. Shelf Res., 2, 21–33, 1983.

  • Bawden, G.W., W., Thatcher, R.S., Stein, K.W. Hudnut, and G. Peltzer (2001), Tectonic contraction across Los Angeles after removal of groundwater pumping affects, Nature, 412, 812–815.

  • Bevis M, D. Alsdorf, E. Kendrick, L.P., Fortes, B. Forsberg, R. Smalley, J. Becker (2005), Seasonal fluctuations in the mass of the Amazon River system and Earth’s elastic response. Geophys. Res. Ltrs., 32, L16308.

  • Calais, E., J.Y. Han, C. DeMets, and J.M. Nocquet (2006), Deformation of the North American plate interior from a decade of continuous GPS measurements J. Geophys. Res., 111, B06402, doi:10.1029/2005JB004253.

  • Conroy, J.L., J.T. Overpeck, J.E. Cole and M. Steinitz-Kannan (2009), Variable oceanic influences on western North American drought over the last 1200 years, GRL, 36, L17703, doi:10.1029/2009GL039558.

  • Dragert, H., K. Wang, and T. James (2001), A silent slip event on the deeper Cascadia subduction interface, Science, 292, 1525–1528.

  • Dong, D., P. Fang, Y. Bock, M. K. Cheng, and S. Miyazaki (2002), Anatomy of apparent seasonal variations from GPS-derived site position time series, J. Geophys. Res., 107(B4), 2075, doi:10.1029/2001JB000573.

  • Dong, D., P. Fang, Y. Bock, F. Webb, L. Prawirodirdjo, S. Kedar, and P. Jamason (2006), Spatiotemporal filtering using principal component analysis and Karhunen-Loeve expansion approaches for regional GPS network analysis, J. Geophys. Res. 111, doi:10.1029/2005JB003806.

  • Dyke, A. S. (2004), An outline of North American deglaciationwith emphasis on central and northern Canada, in Quaternary Glaciations—Extent and Chronology, Part 2, North America, Dev. Quat. Sci., vol. 2b, edited by J. Ehlers and P. L. Gibbard, pp. 373–424, Elsevier, New York.

  • Fancourt C.L. and J. C. Principe (1998), Competitive Principal Component Analysis for Locally Stationary Time Series, IEEE Trans. Signal Proc., 46, 3068–3081.

  • Faure, S., A. Tremblay, and J. Angelier (1996), Alleghanian paleostress reconstruction in the northern Appalachians: Intraplate deformation between Laurentia and Gondwana, Geol. Soc. Am. Bull., 108, 1467–1480.

  • Fukunaga, K. (1970), Introduction to Statistical Pattern Recognition, Academic, San Diego, Calif.

  • Hanrahan, J.L., S.V. Kravtsov, P.J. Roebber (2010), Connecting past and present climate variability to the water levels of Lakes Michigan and Huron, Geophys. Res. Ltrs., 37, L01701, doi:10.1029/2009GL041707.

  • Henton, J. A., M. R. Craymer, R. Ferland, H. Dragert, S. Mazzotti, and D. L. Forbes (2006), Crustal motion and deformation monitoring of the Canadian landmass, Geomatica, 60, 173–191.

  • Hill, E.M., J.L. Davis, P. Elo′segui, B.P. Wernicke, E. Malikowski, and N.A. Niemi, (2009) Characterization of site-specific GPS errors using a short-baseline network of braced monuments at Yucca Mountain, southern Nevada, J. Geophys. Res., doi:10.1029/2008JB006027.

  • Hoerling, M., X.-W. Quan, J. Eischeid, (2009), Distinct causes for two principal US droughts of the 20th century, GRL, 36, L19708, doi:10.1029/2009GL039860.

  • Holmes, P., J. L. Lumley, and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge Univ. Press, New York, 1996.

  • Hotelling, H. (1933), Analysis of a complex of statistical variables into principal components, J. Educ. Psych., 24, 417–520.

  • Hugentobler, U., S. Schaer, and P. Fridez (Eds.) (2001), Documentation of the Bernese GPS software version 4.2, 511 pp., Astron. Inst., Univ. of Bern, Bern.

  • Hudnut, K. W., Z. Shen, M. Murray, S. McClusky, R. King, T. Herring, B. Hager, Y. Feng, P. Fang, A. Donnellan (1996), Co-seismic displacements of the 1994 Northridge, California, earthquake, Bull. Seismol. Soc. Am., 86, s19–s36.

  • James, T. S., and A. L. Bent (1994), A comparison of eastern North America seismic strain rates to postglacial rebound strain rates, Geophys. Res. Lett., 21, 2127–2130.

  • James, T. S., and A. Lambert (1993), A comparison of VLBI data with the ICE-3G glacial rebound model, Geophys. Res. Lett., 20, 871–874.

  • Johansson, J. M., et al. (2002), Continuous GPS measurements of postglacialadjustment in Fennoscandia: 1. Geodetic results, J. Geophys. Res., 107(B8), 2157, doi:10.1029/2001JB000400.

  • Karlstrom, K. E., K. I. Ahall, S. S. Harlan, M. L. Williams, J. McLelland, and J. W. Geissman (2001), Long-lived (1.8– 1.0 Ga) convergent orogen in southern Laurentia, its extensions to Australia and Baltica, and implications for refining Rodinia, Precambrian Res., 111, 5–30.

  • Kedar, S., G. A. Hajj, B. D. Wilson, and M. B. Heflin (2003), The effect of the second order GPS ionospheric correction on receiver positions, Geophys. Res. Lett., 30(16), 1829, doi:10.1029/2003GL017639.

  • Kumarapeli, P. S. (1985), Vestiges of Iapetan rifting in the craton west of the northern Appalachians, Geosci. Can., 12, 54–59.

  • Lambert, A., N. Courtier, G. S. Sasagawa, F. Klopping, D. Winester, T. S. James, and J. O. Liard (2001), New constraints on Laurentide postglacial rebound from absolute gravity measurements, Geophys. Res. Lett., 28, 109–112.

  • Langbein, J. (2008), Noise in GPS displacement measurements from Southern California and Southern Nevada, J. Geophys. Res., doi:10.1029/2007JB005247.

  • Langbein, J. and H. Johnson (1997), Correlated errors in geodetic time series: Implications for time-dependent deformation, J. Geophys. Res., 102, 591–603.

  • Lemieux, Y., A. Tremblay, and D. Lavois (2003), Structural analysis of supracrustal faults in the Charlevoix area, Québec: Relation to impact cratering and the St-Laurent fault system, Can. J. Earth Sci., 40, 221–235.

  • Main, I.G., L. Li, K. J. Heffer, O. Papasouliotis, and T. Leonard (2006), Long-range, critical-point dynamics in oil field flow rate data, Geophys. Res. Lett., 33, L18308, doi:10.1029/2006GL027357.

  • Mainville, A., and M. Craymer (2005), Present-day tilting of the Great Lakes region based on water level gauges, Geol. Soc. Am. Bull., 117, 1070–1080.

  • Márquez-Azúa, B., and C. DeMets (2003), Crustal velocity field of Mexico from continuous GPS measurements, 1993 to June 2001: Implications for the neotectonics of Mexico, J. Geophys. Res., 108(B9), 2450, doi:10.1029/2002JB002241.

  • Mazzotti, S., and J. Adams (2005), Rates and uncertainties on seismic moment and deformation in eastern Canada, J. Geophys. Res., 110, B09301, doi:10.1029/2004JB003510.

  • Mazzotti, S., H. Dragert, J. Henton, M. Schmidt, R. Hyndman, T. James, Y. Lu, and M. Craymer (2003), Current tectonics of northern Cascadia from a decade of GPS measurements, J. Geophys. Res., 108(B12),2554, doi:10.1029/2003JB002653.

  • Mazzotti, S., T.S. James, J. Henton, and J. Adams (2005), GPS crustal strain, postglacial rebound, and seismic hazard in eastern North America: The Saint Lawrence valley example, J. Geophys. Res., 110, B11301, doi:10.1029/2004JB003590.

  • Mazzotti, S. (2007), Geodynamic models for earthquake studies in intraplate North America, in Stein, S., and Mazzotti, S., eds., Continental Intraplate Earthquakes: Science, Hazard, and Policy Issues, Geol. Soc. Amer. Special Paper 425, p. 17–33, doi:10.1130/2007.2425(02).

  • Moghaddam, B., W. Wahid, and A. Pentland, Beyond eigenfaces: Probabilistic matching for face recognition, paper presented at Third IEEE International Conference on Automatic Face and Gesture Recognition, Nara, Japan, 14–16 April 1998.

  • Park, K., R. S. Nerem, J. L. Davis, M. S. Schenewerk, G. A. Milne, and J. X. Mitrovica (2002), Investigation of glacial isostatic adjustment in the northeast US using GPS measurements, Geophys. Res. Lett., 29(11), 1509, doi:10.1029/2001GL013782.

  • Parker, J. W. (2001), Analysis and modeling of southern California deformation, in APEC Cooperation for Earthquake Simulation (ACES), 2nd ACES Workshop Proceedings, Univ. of Queensland, Brisbane, Australia.

  • Peltier, W. R. (1998), Postglacial variations in the level of the sea: Implications for climate dynamics and solid-Earth geophysics, Rev. Geophys., 36, 603–689.

  • Peltier, W. R. (2002), Global glacial isostatic adjustment: Palaeogeodetic and space-geodetic tests of the ICE-4G (VM2) model, J. Quat. Sc., 17, 491–510.

  • Peltier, W. R. and R. Drummond (2009), Rheological stratification of the lithosphere: A direct inference based upon the geodetically observed pattern of the glacial isostatic adjustment of the North American continent, Geophys. Res. Ltrs., doi:10.1029/2008GL034586.

  • Penland, C. (1989), Random forcing and forecasting using principal oscillation pattern analysis, Mon. Weather Rev., 117, 2165–2185.

  • Penland, C., and P. D. Sardeshmukh (1995), The optimal growth of tropical sea surface temperature anomalies, J. Clim., 8, 1999–2024.

  • Posadas, A.M., F. Vidal, F. DeMiguel, G. Alguacil, J. Pena, J.M. Ibanez, and J. Morales (1993), Spatial-temporal analysis of a seismic series using the principal components method—the Antequera series, Spain, 1989, J. Geophys. Res., 98, 1923–1932.

  • Preisendorfer, R. W., Principle Component Analysis in Meteorology and Oceanography, Elsevier Sci., New York, 1988.

  • Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vettering, (1992), Numerical Recipes in C, 2nd ed., Cambridge Univ. Press, New York.

  • Rondot, J. (1968), Nouvel impact meteoritique fossile? La structure semicirculaire de Charlevoix, Can. J. Earth Sci., 5, 1305–1317.

  • Savage, J. C. (1988), Principal component analysis of geodetically measured deformation in Long Valley caldera, eastern California, 1983–1987, J. Geophys. Res., 93, 13297–13305.

  • Savage, J.C., and J. Langbein (2008), Postearthquake relaxation after the 2004 M6 Parkfield, California, earthquake and rate-and-state friction, J. Geophys. Res., 113, B10407, doi:10.1029/2008JB005723.

  • Scherneck, H.-G., J. M. Johansson, and R. Haas (2000), BIFROST project: Studies of variations of absolute sea level in conjunction with postglacial rebound in Fennoscandia, in Towards an Integrated Global Geodetic Observing System (IGGOS), Int. Assoc. Geod. Symp., vol. 120, edited by R. Rammel et al., pp. 241–244, Springer, New York.

  • Sella, G.F., S. Stein, T.H. Dixon, M. Craymer, T.S. James, S. Mazzotti, and R.K. Dokka (2007), Observation of glacial isostatic adjustment in ‘‘stable’’ North America with GPS, Geophys. Res. Ltrs., 34, L02306, doi:10.1029/2006GL027081.

  • Sellinger, C.E., C.A. Stow, E.C. Lamon, and S.S. Qian (2008) Recent Water Level Declines in the Lake Michigan-Huron System, Environ. Sci. Technol., 42, 367–373.

  • Small, D., and S. Islam (2007), Decadal variability in the frequency of fall precipitation over the United States, GRL, 34, L02404, doi:10.1029/2006GL028610.

  • Smith, E.G.C., T.D. Williams, and D.J. Darby (2007), Principal component analysis and modeling of the subsidence of the shoreline of Lake Taupo, New Zealand, 1983–1999: Evidence for dewatering of a magmatic intrusion?, J. Geophys. Res., 112, B08406, doi:10.1029/2006JB004652.

  • Stow, C. (2009), Water Levels of the Great Lakes, NOAA Great Lakes Environmental Research Laboratory Brochure.

  • Tiampo, K.F., J.B. Rundle, S.J. Gross, S. McGinnis, W. Klein (2002), Eigenpatterns in southern California seismicity, Journal of Geophysical Research, 107, 2354, doi:10.1029/2001JB000562.

  • Tiampo, K.F., J.B. Rundle, W. Klein, Y. Ben-Zion, S. McGinnis, (2004), Using eigenpattern analysis to constrain seasonal signals in southern California, Pure and Applied Geophysics, 1991–2003.

  • Tremblay, A., B. Long, and U. Glasmacher (2001), Supracrustal faults of the St Lawrence Rift system, Quebec: Kinematics and geometry as revealed by field mapping and marine seismic reflection data, Geol. Soc. Am. Abstr. Programs, 33, A-210.

  • Tushingham, A. M., and W. R. Peltier (1991), ICE-3G: A new global model of late Pleistocene deglaciation based upon geophysical predictions of postglacial relative sea level change, J. Geophys. Res., 96, 4497–4523.

  • Vautard, R., and M. Ghil (1989), Singular spectrum analysis in nonlinear dynamics, with applications to paleodynamic time series, Physica D, 35, 395–424.

  • Watson, K. M., Y. Bock, and D.T. Sandwell (2002), Satellite interferometric observations of displacements associated with seasonal groundwater in the Los Angeles basin, J. Geophys. Res., 107(B4), 2074, doi:10.1029/2001JB000470.

  • Wdowinski, S., Y. Bock, J. Zhang, P. Fang, and J. Genrich (1997), Southern California permanent GPS geodetic array: Spatial filtering of daily positions for estimating coseismic and postseismic displacements induced by the 1992 Landers earthquake, J. Geophys. Res., 102, 18,057–18,070.

  • Wheeler, R. L. (1995), Earthquakes and the cratonward limit of Iapetan faulting in eastern North America, Geology, 23, 105–108.

  • Wheeler, R. L., and A. C. Johnson (1992), Geological implications of earthquake source parameters in central and eastern North America, Seismol. Res. Lett., 63, 491–514.

  • Williams, H. (1979), Appalachian orogen in Canada, Can. J. Earth Sci., 16, 792–807.

  • Williams, S. D. P., Y. Bock, P. Fang, P. Jamason, R. M. Nikolaidis, L. Prawirodirdjo, M. Miller, and D. J. Johnson (2004), Error analysis of continuous GPS position time series, J. Geophys. Res., 109, B03412, doi:10.1029/2003JB002741.

  • Zerbini, S., Raicich, F., Richter, B., Gorini, V., Errico, M. (2010), Hydrological signals in height and gravity in northeastern Italy inferred from principal components analysis, J. Geodynamics, doi:10.1016/j.jog.2009.11.001.

Download references

Acknowledgments

Research by KFT was funded by an NSERC Discovery Grant. The GPS data used in this study were provided by the National Geodetic Survey (USA) Continuously Operating Reference Stations (CORS), Natural Resources Canada (NRCan) Geodetic Survey Division (GSD), and the Province of Quebec Ministère des Resources Naturelles et Forêts (MRNF). GPS data archiving and processing was supported by the NRCan Canadian Crustal Deformation Service (CCDS). This is ESS contribution number 20110184. Images were plotted with the help of GMT software developed and supported by Paul Wessel and Walter H.F. Smith.

Author information

Authors and Affiliations

  1. Department of Earth Sciences, University of Western Ontario, London, ON, Canada

    K. F. Tiampo

  2. Geological Survey of Canada, Natural Resources Canada, Sidney, BC, Canada

    S. Mazzotti & T. S. James

Authors
  1. K. F. Tiampo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Mazzotti
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. S. James
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. F. Tiampo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tiampo, K.F., Mazzotti, S. & James, T.S. Analysis of GPS Measurements in Eastern Canada Using Principal Component Analysis. Pure Appl. Geophys. 169, 1483–1506 (2012). https://doi.org/10.1007/s00024-011-0420-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00024-011-0420-1

Keywords

Search

Navigation