Pure and Applied Geophysics

, Volume 173, Issue 3, pp 937–944 | Cite as

Defining Geodetic Reference Frame using Matlab®: PlatEMotion 2.0

  • Flavio CannavòEmail author
  • Mimmo Palano


We describe the main features of the developed software tool, namely PlatE-Motion 2.0 (PEM2), which allows inferring the Euler pole parameters by inverting the observed velocities at a set of sites located on a rigid block (inverse problem). PEM2 allows also calculating the expected velocity value for any point located on the Earth providing an Euler pole (direct problem). PEM2 is the updated version of a previous software tool initially developed for easy-to-use file exchange with the GAMIT/GLOBK software package. The software tool is developed in Matlab® framework and, as the previous version, includes a set of MATLAB functions (m-files), GUIs (fig-files), map data files (mat-files) and user’s manual as well as some example input files. New changes in PEM2 include (1) some bugs fixed, (2) improvements in the code, (3) improvements in statistical analysis, (4) new input/output file formats. In addition, PEM2 can be now run under the majority of operating systems. The tool is open source and freely available for the scientific community.


Euler pole matlab geodetic reference frame 



We thank the Guest Editor, María Charco, and three anonymous reviewers for their critical reviews, constructive suggestions and useful comments that improved the paper.


  1. Anderson, G. M. (1976). Error propagation by the Monte Carlo method in geochemical calculations. Geochimica et Cosmochimica Acta, 40(12), 1533–1538, doi: 10.1016/0016-7037(76)90092-2.
  2. Altamimi, Z., Metivier, L. and Collilieux, X. (2012). ITRF2008 plate motion model. J. Geophys. Res., 117, B07402, doi: 10.1029/2011JB008930.
  3. Bird, P. (2003). An updated digital model of plate boundaries. Geochemistry Geophysics Geosystems, 4(3), 1027, doi: 10.1029/2001GC000252.
  4. Bullard, E. C., Everett, J. E. and Smith, A. G. (1965). Fit of continents around the atlantic. Roy. Soc. London, Phil. Trans. Ser. A, V., 258.Google Scholar
  5. Bowring, B. R. (1976). Transformation from spatial to geographical coordinates. Survey review, 23(181), 323–327.Google Scholar
  6. Bowring, B. R. (1985). The accuracy of geodetic latitude and height equations. Survey Review, 28(218), 202–206.Google Scholar
  7. Cannavó, F. (2012). Sensitivity analysis for volcanic source modeling quality assessment and model selection. Computers & Geosciences, 44, 52–59, doi: 10.1016/j.cageo.2012.03.008.
  8. Cannavó, F. and Palano, M. (2011). PlatEMotion: a Matlab ® Tool for geodetic reference frame definition. Rapporti Tecnici INGV, 201, 1–12.Google Scholar
  9. Cannavó, F., Arena A. and Monaco, C. (2015). Local geodetic and seismic energy balance for shallow earthquake prediction. J. Seismol. 19(1), 1–8.Google Scholar
  10. DeMets, C., Gordon, R. G., Argus, D. F. and Stein, S. (1990). Current plate motions. Geophys. J. Int., 101, 425–478.Google Scholar
  11. Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2010). F (Variance Ratio) or FisherSnedecor Distribution, in Statistical Distributions, Fourth Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi:  10.1002/9780470627242.ch20.
  12. Greiner, B. (1999). Euler rotations in plate-tectonic reconstructions. Computers & Geosciences, 25(3), 209–216.Google Scholar
  13. Gripp, A. E. and Gordon, R. G. (1990). Current plate velocities relative to the hotspots incorporating NUVEL-1 global plate motion. Geophys. Res. Lett., 17, 1109–1112, doi: 10.1029/GL017i008p01109.
  14. Herring, T.A., King, R.W. and Mcclusky, S.C. (2010). Introduction to GAMIT/GLOBK, Release 10.4, Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
  15. Leick, A. (2004). GPS Satellite Surveying. John Wiley & Sons, ISBN 0471059307.Google Scholar
  16. Marques F.O., Catalao J.C., DeMets C., Costa A.C.G. and Hildenbrand A. (2013). GPS and tectonic evidence for a diffuse plate boundary at the Azores Triple Junction. Earth Planet. Sci. Lett. 381, 177–187, doi: 10.1016/j.epsl.2013.08.051.
  17. Minster, J.B. and Jordan T.H. (1978). Present-day plate motions. J. Geophys. Res. 83(11), 53, doi:  10.1029/JB083iB11p05331.
  18. Mulargia, F. and Gasperini, P. (1995). Evaluation of the applicability of the time and slip-predictable earthquake recurrence models to Italian seismicity. Geophys. J. Int., 120, 453–473, doi: 10.1111/j.1365-246X.1995.tb01832.x.
  19. Nocquet, J.-M., Calais, E, Altamimi, Z, Sillard, P. and Boucher, C. (2001). Intraplate deformation in the western Europe deduced from an analysis of the International Terestrial Reference Frame 1997 (ITRF97) velocity field. J. Geophys. Res., 106, B6, 11239–11257, doi: 10.1029/2000JB900410.
  20. Nocquet, J.-M., Calais, E. and Parsons, B. (2005). Geodetic constraints on glacial isostatic adjustment in Europe. Geophys. Res. Lett., 32, L06308, doi: 10.1029/2004GL022174.
  21. Palais, B., and Palais, R. (2007). Euler’s fixed point theorem: The axis of a rotation. Journal of Fixed Point Theory and Applications, 2(2), 215–220.Google Scholar
  22. Palano, M., González, P. J. and Fernández, J. (2013a). Strain and stress fields along the Gibraltar Orogenic Arc: Constraints on active geodynamics. Gondwana Research, 23(2), 1071–1088, doi: 10.1016/
  23. Palano, M., Imprescia, P. and Gresta, S. (2013b). Current stress and strain-rate fields across the Dead Sea Fault System: Constraints from seismological data and GPS observations. Earth and Planetary Science Letters 369370, 305–316, doi: 10.1016/j.epsl.2013.03.043.
  24. Palano, M. (2015). On the present-day crustal stress, strain-rate fields and mantle anisotropy pattern of Italy. Geophys. J. Int., 200(2), 969–985, doi: 10.1093/gji/ggu451.
  25. Sella, G.F., Dixon, T.H. and Mao, A. (2002). REVEL: A model for recent plate velocity from space geodesy. J. Geophys. Res., 107, doi: 10.1029/2000JB000033.
  26. Snedecor, G.W. and Cochran, W.G. (1989). Statistical Methods, Eighth Edition. Iowa State University Press.Google Scholar
  27. Tarantola, A. and Vallette, B. (1982). Generalized nonlinear inverse problems solved using the least squares criterion. Rev. Geophys. Space Phys., 20, 219–232, doi: 10.1029/RG020i002p00219.
  28. Vermeille, H. (2002). Direct Transformation from Geocentric to Geodetic Coordinates. J. Geod. 76(8), 451–454, doi: 10.1007/s00190-002-0273-6.
  29. Vine, F.J. (1966). Spreading of the ocean floor: new evidence. Science, 154, 1405–1415, doi:  10.1126/science.154.3755.1405.
  30. Wegener, A. (1927). Die geophysikalischen Grundlagen der Theorie der Kontinentverschiebung. Scientia, Milan, 41, 103–116.Google Scholar
  31. Wessel, P. and Smith, W.H.F. (1998). New improved version of the Generic Mapping Tools released. EOS Trans. AGU, 79, 579, doi: 10.1029/98EO00426.

Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Istituto Nazionale di Geofisica e VulcanologiaCataniaItaly

Personalised recommendations