Interpolation of horizontal GPS velocity field in the oblique collision zone of Arabia-Eurasia tectonic plates using Green’s functions

Document Type : Research Article

Author

Assistant Professor, Department of Surveying, Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran

Abstract

One way of gridding two dimensional vector data is gridding each component separately. Alternatively, using Green’s functions we can grid two components simultaneously in a way that couples them through elastic deformation theory. This is particularly suited, though not exclusive, to data that represent elastic/semi-elastic deformation, like horizontal GPS velocity fields. Measurements made on the surface of the Earth are often sparse and unevenly distributed. For example, GPS displacement measurements are limited by the availability of ground stations and airborne geophysical measurements are highly sampled along flight lines but there is often a large gap between lines. Many data processing methods require data distributed on a uniform regular grid, particularly methods involving the Fourier transform or the computation of directional derivatives. Hence, the interpolation of sparse measurements onto a regular grid (known as gridding) is a prominent problem in the Earth Sciences.
In this research, sparse two-dimensional vector data of the horizontal GPS velocity field are interpolated using Green’s functions derived from elastic constraints. The method is based on the Green’s functions of an elastic body subjected to in-plane forces. This approach ensures elastic coupling between the two components of the interpolation. Users may adjust the coupling by varying Poisson’s ratio. Smoothing can be achieved by ignoring the smallest eigenvalues in the matrix solution for the strengths of the unknown body forces. The study area is the oblique collision zone of Arabia-Eurasia tectonic plates, which has a GPS velocity field with sparse distribution.
Since the Green’s functions developed for the half-space environment, the Mercator map projection used to create the half-space for interpolation and gridding. Data split into a training and testing set. We will fit the gridder on the training set and use the testing set to evaluate how well the gridder is performing. The vector gridding was done using the Poisson's ratio 0.5 to couple the two horizontal components. Then score on the testing data. The best possible score is 1, meaning a perfect prediction of the test data. By calculating the mean square deviation ratio (MSDR) to evaluate the gridding accuracy, the score of 0.86 obtained for this statistic.
While this method is not new, it provides some insight into the behavior of the coupled interpolation for a wide range of Poisson’s ratio. This approach provides improved interpolation of sparse vector data when the physics of the deforming material follows elasticity equations.
We interpolated our horizontal GPS velocities onto a regular geographic grid with 1 arc second spacing and masked the data that were far from the observation points and finally the residuals between the predictions and the original input data were calculated. Interpolation of horizontal GPS velocity fields of local geodynamic networks were proposed to obtain an estimate for Poisson's ratio values in the best case for gridding validation.
In this study, two dimensional GPS data were interpolated. Three dimensional GPS data gridding can also be done using the Green’s functions provided by Uieda et al., (2018). It is also recommended to use different Green’s functions to grid different types of spatial data.

Keywords

Main Subjects

References

حسنی­پاک، ع. ا.، 1389، زمین آمار (ژئواستاتیستیک)، انتشارات دانشگاه تهران، تهران، 314 ص.
غفاری رزین، م. ر. و وثوقی، ب.، 1395، برآورد میدان سرعت پوسته زمین با استفاده از شبکه عصبی مصنوعی و درون­یابی کرِیجینگ فراگیر (منطقه موردمطالعه: شبکه ژئودینامیک کشور ایران)، مجله فیزیک زمین و فضا، 42(1)، 89-98.
Bogusz, J., Klos, A., Grzempowski, P. and Kontny, B., 2013, Modelling the velocity field in a regular grid in the area of poland on the basis of the velocities of European permanent stations, Pure and Applied Geophysics, doi: 10.1007/s00024- 013-0645-2.
Briggs, I. C., 1974, Machine contouring using minimum curvature, Geophysics, 39(1), 39–48.
Frohling, E. and Szeliga, W., 2016, GPS constraints on interpolate locking within Makran subduction zone, Geophys. J. Int., 205, 67–76.
Franke, R., 1982, Smooth interpolation of scattered data by local thin plate splines. Computers & Mathematics with Applications, 8(4), 273–281. doi:10.1016/0898- 1221(82)90009-8.
Ghaffari Razin, M. R. and Mohammadzadeh, A., 2015, 3-D crustal deformation analysis using isoparametric method and multi-layer artificial neural networks (Case Study: Iran), Engineering Journal of Geospatial Information Technolog, 2 (4), 1-15.
Ghods, A., Shabanian, E., Bergman, E., Faridi, M., Donner, S., Mortezanejad, G. and Aziz Zanjani, A., 2015, The Varzaghan–Ahar, Iran, Earthquake Doublet (Mw 6.4, 6.2): implications for the geodynamics of northwest Iran. Geophys. J. Int., 203, 522–540.
Gullu, M., Yilmaz, I., Yilmaz, M. and Turgut, B., 2011, An alternative method for estimating densification point velocity based on back propagation artificial neural networks, Studia Geophysica et Geodaetica, 55(1), 73-86.
Hackl, M., Malservaisi, R. and Wdowinski, S., 2009, Strain pattern from dense GPS networks, Nat. Hazards Earth Syst., 9, 1177–1187.
Haines, A. J. and Holt, W. E., 1993, 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, doi:10.1029/93JB00892.
Haines, A. J., Dimitrova, L. L., Wallace, L. M. and Williams, C. A., 2015, Enhanced Surface Imaging of Crustal Deformation: Obtaining Tectonic Force Fields Using GPS Data, 99 pp., Springer Int. Publ., New York, doi:10.1007/978-3-319-21578-5.
Hearn, E., Johnson, K., Sandwell, D. and Thatcher, W., 2010, SCEC UCERF workshop report. [Available at http://www.scec.org/workshops/ 2010/gps-ucerf3/FinalReport_GPS UCERF3Workshop.pdf.]
Hessami, K., Jamali, F. and Tabassi, H., 2003, Major Active Faults of Iran (map), Ministry of Science, Research and Technology, International Institute of Earthquake Engineering and Seismology.
Khorrami, F., Vernant, P., Masson, F., Nilfouroushan, F., Mousavi, Z., Nankali, H., Saadat, S. A., Walpersdorf, A., Hosseini, S., Tavakoli, P., Aghamohammadi, A. and Alijanzade, M., 2019, An up-to-date crustal deformation map of Iran using integrated campaign-mode and permanent GPS velocities. Geophys. J. Int., 217, 832–843.
McCaffrey, R., King, R. W., Payne, S. J. and Lancaster, M., 2013, Active tectonics of northwestern US inferred from GPS-derived surface velocities, J. Geophys. Res. Solid Earth, 118, 709–723, doi:10.1029/2012JB009473.
Moghtased-Azar, K. and Zaletnyik, P., 2009, Crustal velocity field modeling with neural network and polynomials, in: Sideris, M.G., (Ed.), Observing our changing Earth, International Association of Geodesy Symposia, 133, 809-816.
Okada, Y., 1985, Surface deformation due to shear and tensile faults in a half-space: Bulletin of the Seismological Society of America, 75, 4, 1135-1154.
Oliver, M. A. and Webster, R., 2015, Basic steps in Geostatistics: The Variogram and Kriging, Springer, 106 pp.
Raeesi, M., Zarifi, Z., Nilfouroushan, F., Boroujeni S. and Tiampo, K., 2017, Quantitative Analysis of Seismicity in Iran. Pure Appl. Geophys., 174, 793-833.
Reilinger, R., McClusky, S., Vernant, P., Lawrence, S., Ergintav, S., Cakmak, R., Ozener, H., Kadirov, F., Guliev, I., Stepanyan, R., Nadariya, M., Hahubia, G., Mahmoud, S., Sakr, K., ArRajehi, A., Paradissis, D., Al-Aydrus, A., Prilepin, M., Guseva, T., Evren, E., Dmitrotsa, A., Filikov, S.V., Gomez, F., Al-Ghazzi, R. and Karam, G., 2006, GPS constraints on continental deformation in the Africa–Arabia–Eurasia continental collision zone and implications for the dynamics of plate interactions, J. geophys. Res., 111, doi:10.1029/2005JB004051.
Sandwell, D. T. and Wessel P., 2016, Interpolation of 2-D vector data using constraints from elasticity, Geophys. Res. Lett., 43, 10, 703–10,709, doi:10.1002/2016GL070340.
Sandwell, D. T., 1987, Biharmonic spline interpolation of GEOS-3 and SEASAT altimeter data, Geophys. Res. Lett., 14, 139–142, doi:10.1029/GL014i002p00139.
Shen, Z. K., Wang, M., Zeng, Y. and Wang, F., 2015, Optimal interpolation of spatially discretized geodetic data, Bull. Seismol. Soc. Am., 105(4), 2117–2127, doi:10.1785/0120140247.
Smith, B. and Sandwell, D., 2003, Coulomb stress accumulation along the San Andreas Fault system, J. Geophys. Res., 108(B6), 2296, doi:10.1029/2002JB002136.
Smith, W. H. F. and Wessel, P., 1990, Gridding with continuous curvature splines in tension, Geophysics, 55(3), 293–305, doi:10.1190/ 1.1442837.
Swain, C. J., 1976, A FORTRAN IV program for interpolating irregularly spaced data using the difference equations for minimum curvature, Comput. Geosci., 1(4), 231–240.
Talebian, M., Ghorashi, M. and Nazari, H., 2013, Seismotectonic map of the Central Alborz, Research Institute for Earth Sciences, Geological Survey of Iran.
Uieda, L., 2018, Verde: Processing and gridding spatial data using Green’s functions. Journal of Open Source Software, 3(30), 957. https://doi.org/10.21105/joss.00957.
Uieda, L., Sandwell, D. and Wessel, P., 2018, Presentation: Joint Interpolation of 3-component GPS Velocities Constrained by Elasticity. figshare. doi:10.6084/m9.figshare.6387467.
VanGorp, S., Masson, F. and Chéry, J., 2006, The use of Kriging to interpolate GPS velocity field and its application to the Arabia-Eurasia collision zone, Geophysical Research Abstracts, 8, 02120.
Wessel, P. and Bercovici, D., 1998, Interpolation with splines in tension: A Green’s function approach, Math. Geol., 30(1), 77–93, doi:10.1023/ A:1021713421882.
Journal of the Earth and Space Physics
Volume 48, Issue 3
online publication date: 6 December 2022
December 2022
Pages 611-621

Files

Share

How to cite

Statistics