Skip to main content
SpringerLink
Log in

A Comprehensive Study of Gridding Methods for GPS Horizontal Velocity Fields

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

Abstract

Four gridding methods for GPS velocities are compared in terms of their precision, applicability and robustness by analyzing simulated data with uncertainties from 0.0 to ±3.0 mm/a. When the input data are 1° × 1° grid sampled and the uncertainty of the additional error is greater than ±1.0 mm/a, the gridding results show that the least-squares collocation method is highly robust while the robustness of the Kriging method is low. In contrast, the spherical harmonics and the multi-surface function are moderately robust, and the regional singular values for the multi-surface function method and the edge effects for the spherical harmonics method become more significant with increasing uncertainty of the input data. When the input data (with additional errors of ±2.0 mm/a) are decimated by 50% from the 1° × 1° grid data and then erased in three 6° × 12° regions, the gridding results in these three regions indicate that the least-squares collocation and the spherical harmonics methods have good performances, while the multi-surface function and the Kriging methods may lead to singular values. The gridding techniques are also applied to GPS horizontal velocities with an average error of ±0.8 mm/a over the Chinese mainland and the surrounding areas, and the results show that the least-squares collocation method has the best performance, followed by the Kriging and multi-surface function methods. Furthermore, the edge effects of the spherical harmonics method are significantly affected by the sparseness and geometric distribution of the input data. In general, the least-squares collocation method is superior in terms of its robustness, edge effect, error distribution and stability, while the other methods have several positive features.

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

Similar content being viewed by others

References

  • Adrakhmatov, K. Y., Aldazhanov, S. A., Hager, B. H., Hamburger, M. W., Herring, T. A., & Kalabaev, K. B. (1996). Relatively recent construction of the Tien Shan inferred from GPS measurements of present-day crustal deformation rates. Nature, 384(6608), 450–453.

    Article  Google Scholar 

  • Ann, S. P., Jean, C., & Riad, H. (2003). 3D mechanical modeling of the GPS velocity field along the North Anatolian fault. Earth Planetary Science Letters, 209, 361–377. doi:10.1016/S0012-821X(03)00099-2.

    Article  Google Scholar 

  • Anzidei, M., Baldi, P., Casula, G., Galvani, A., Riguzzi, F., & Zanutta, A. (1998). Evidence of active crustal deformation of the Colli Albani volcanic area (central Italy) by GPS surveys. Journal of Volcanology and Geothermal Research, 80, 55–65. doi:10.1016/S0377-0273(97)00044-9.

    Article  Google Scholar 

  • Bilham, R., Larson, K., & Freymueller, J. (1997). GPS measurements of present-day convergence across the Nepal Himalaya. Nature, 386(6620), 61–64.

    Article  Google Scholar 

  • Cao, J. L., Shi, Y. L., Zhang, H., & Wang, H. (2009). Numerical simulation of GPS observed clockwise rotation around the eastern Himalayan syntax in the Tibetan Plateau. Chinese Science Bulletin, 54(8), 1398–1410.

    Google Scholar 

  • Caporali, A., Martin, S., & Massironi, M. (2003). Average strain rate in the Italian crust inferred from a permanent GPS network—II. Strain rate versus seismicity and structural geology. Geophysical Journal International, 155, 254–268.

    Article  Google Scholar 

  • Chiles, J. P. Delfiner, P. G. (1999). Modeling Spatial Uncertainty, Wiley Series in Probability and Statistics.

  • David, J. W., Thomas, H. H., & Hudnut, K. W. (1996). The slip history of the 1994 Northridge, California, earthquake determined from strong-motion, teleseismic, GPS, and leveling data. Bulletin of the Seismological Society of America, 86(1B), 49–70.

    Google Scholar 

  • Desmond, D., & John, B. (2001). Evidence from GPS measurements for contemporary interplate coupling on the southern Hikurangi subduction thrust and for partitioning of strain in the upper plate. Journal of Geophysical Research Atmospheres, 106(B12), 30881–30892. doi:10.1029/2000JB000023.

    Article  Google Scholar 

  • Eric, C., Yves, M., Bernard, M. L., Paul, M., Glen, M., & Pamela, J. (2002). Strain partitioning and fault slip rates in the northeastern Caribbean from GPS measurements. Geophysical Research Letters, 29(18), 31–34. doi:10.1029/2002GL015397.

    Article  Google Scholar 

  • Fernández, J., Yu, T. T., Rodrìguez, V. G., González, M. J., Romero, R., Rodrìguez, G., et al. (2003). New geodetic monitoring system in the volcanic island of Tenerife, Canaries, Spain. Combination of InSAR and GPS techniques. Journal of Volcanology and Geothermal Research, 124(03), 241–253. doi:10.1016/S0377-0273(03)00073-8.

    Article  Google Scholar 

  • Flerit, F., Armijo, R., King, G. P., Meyer, B., & Barka, A. (2003). Slip partitioning in the Sea of Marmara pull-apart determined from GPS velocity vectors. Geophysical Journal International, 154(1), 1–7. doi:10.1046/j.1365-246X.2003.01899.x.

    Article  Google Scholar 

  • Frederic, M., Mohammad, A., Yahya, D., Andrea, W., Farokh, T., Marc, D., et al. (2007). Large-scale velocity field and strain tensor in Iran inferred from GPS measurements: new insight for the present-day deformation pattern within NE Iran. Geophysical Journal International, 170(1), 436–440. doi:10.1111/j.1365-246X.2007.03477.x.

    Article  Google Scholar 

  • Gabriele, B., Flavio, B., & Marco, U. (2000). Levelling and GPS networks to monitor ground subsidence in the Southern Po Valley. Journal of Geodynamics, 30(3), 355–369. doi:10.1016/S0264-3707(99)00071-X.

    Article  Google Scholar 

  • Hardy, R. L. (1978). The application of Multi-quadric equations and point mass anomaly models to crustal movement studies. NOAA Technical Report NGS 76 NGS 11.

  • Hasanuddin, Z. A., Andreas, H., Rochman, D., Dudy, D., & Gamal, M. (2008). Land subsidence characteristics of Jakarta between 1997 and 2005, as estimated using GPS surveys. GPS Solutions, 12(1), 23–32. doi:10.1007/s10291-007-0061-0.

    Article  Google Scholar 

  • Hastaoglu, K. O., & Sanli, D. U. (2011). Monitoring Koyulhisar landslide using rapid static GPS: a strategy to remove biases from vertical velocities. Natural Hazards, 58(3), 1275–1294. doi:10.1007/s11069-011-9728-5.

    Article  Google Scholar 

  • Heiskanen, W. A., & Moritz, H. (1967). Physical geodesy. San Francisco CA: W. H. Freeman and Co., Ltd.

    Google Scholar 

  • Herring, T. A., King, R. W., McClusky, S. C. (2010a). GAMIT Reference Manual. GPS Analysis at MIT. Release 10.4. Massachussetts Institute Technology. http://www-gpsg.mit.edu/~simon/gtgk/index.htm, (last accessed 5 Oct 2011).

  • Herring, T. A., King, R. W., McClusky, S. C. (2010b). GLOBK Reference Manual. Global Kalman filter VLBI and GPS analysis program. Release 10.4. Massachussetts Institute Technology. http://www-gpsg.mit.edu/~simon/gtgk/index.htm (last accessed 5 Oct 2011).

  • John, P. L., & Brendan, J. M. (2010). Geodetic imaging of plate motions, slip rates, and partitioning of deformation in Japan. Journal of Geophysical Research Atmospheres, 115(B2), 178–189. doi:10.1029/2008JB006248.

    Google Scholar 

  • Johnson, K. M., Hsu, Y. J., Segall, P., & Yu, S. B. (2001). Fault geometry and slip distribution of the 1999 Chi-Chi, Taiwan Earthquake imaged from inversion of GPS data. Geophysical Research Letters, 28(1), 2285–2288. doi:10.1029/2000GL012761.

    Article  Google Scholar 

  • Josep, A. G., Jordi, C., & Joan, R. (2000). Using global positioning system techniques in landslide monitoring. Engineering Geology, 55(3), 167–192. doi:10.1016/S0013-7952(99)00127-1.

    Article  Google Scholar 

  • Jyr, C. H., Jacques, A., & Shui-Beih, Y. (1997). An interpretation of the active deformation of southern Taiwan based on numerical simulation and GPS studies. Tectonophysics, 274, 145–169. doi:10.1016/S0040-1951(96)00302-2.

    Article  Google Scholar 

  • Krige, D. G. (1951). A statistical approach to some mine valuations and allied problems on the Witwatersrand, Unpubl., Masters thesis. University of Witwatersrand.

  • LaFemina, P. C., Dixon, T. H., Malservisi, R., Arnadottir, T., Sturkell, E., Sigmundsson, F., Elinarsson, P. (2005). Geodetic GPS measurements in south Iceland: Strain accumulation and partitioning in a propagating ridge system, Journal of Geophysical Research 110(B11). doi:10.1029/2005JB003675.

  • Lennardo, S., & Arnaud, P. (1998). Strain partitioning along the Himalayan arc and the Nanga Parbat antiform. Geology, 26(9), 791–794.

    Article  Google Scholar 

  • Liu, M., & Yang, Y. (2003). Extensional collapse of the Tibetan Plateau: results of three-dimensional finite element modeling. Journal of Geophysical Research, 108(8), 2361. doi:10.1029/2002JB002248.

    Article  Google Scholar 

  • Mahdi, M., Yahya, D., Thomas, R. W., Hans-Ulrich, W., Jochen, Z., & Siavash, A. (2007). Land subsidence in Mashhad Valley, northeast Iran: results from InSAR, levelling and GPS. Geophysical Journal International, 168(2), 518–526. doi:10.1111/j.1365-246X.2006.03246.x.

    Article  Google Scholar 

  • Manaker, D. M., Calais, E., Freed, A. M., Ali, S. T., Przybylski, P., Mattioli, G., et al. (2008). Interseismic plate coupling and strain partitioning in the Northeastern Caribbean. Geophysical Journal International, 174(3), 889–903. doi:10.1111/j.1365-246X.2008.03819.x.

    Article  Google Scholar 

  • Marcos, M., Matthias, R., & Onno, O. (2010). Maule earthquake slip correlates with pre-seismic locking of Andean subduction zone. Nature, 467, 198–202. doi:10.1038/nature09349.

    Article  Google Scholar 

  • Mariko, S., Tadashi, I., Naoto, U., Shigeru, Y., Masayuki, F., Masashi, M., et al. (2011). Displacement above the hypocenter of the 2011 Tohoku-Oki earthquake. Science, 332, 1395. doi:10.1126/science.1207401.

    Article  Google Scholar 

  • Mark, S., Yuri, F., & Luis, R. (2002). Coseismic deformation from the 1999 M w 7.1 hector mine, California, earthquake as inferred from InSAR and GPS observations. Bulletin of the Seismological Society of America, 92(4), 1390–1402. doi:10.1785/0120000933.

    Article  Google Scholar 

  • McCaffrey, R., Long, M. D., Goldfinger, C., Zwick, P. C., Nabelek, J. L., Johnson, C. K., et al. (2000). Rotation and plate locking at the southern Cascadia subduction zone. Geophysical Research Letters, 27(19), 3117–3120. doi:10.1029/2000GL011768.

    Article  Google Scholar 

  • Meade, B. J., & Hager, B. H. (2005). Block models of crustal motion in southern California constrained by GPS measurements. Journal of Geophysical Research, 110, B03403. doi:10.1029/2004JB003209.

    Article  Google Scholar 

  • Murray, J. R., Segall, P., Cervelli, P., Prescott, W., & Svarc, J. (2001). Inversion of GPS data for spatially variable slip-rate on the San Andreas Fault near Parkfield, CA. Geophysical Research Letters, 28(2), 359–362. doi:10.1029/2000GL011933.

    Article  Google Scholar 

  • Paul, S. (2002). Integrating geologic and geodetic estimates of slip rate on the San Andreas fault system. International Geology Review, 44(1), 62–82. doi:10.2747/0020-6814.44.1.62.

    Article  Google Scholar 

  • Robert, M., Anthony, I. Q., Robert, W. K., Ray, W., Giorgi, K., Charles, A. W., et al. (2007). Fault locking, block rotation and crustal deformation in the Pacific Northwest. Geophysical Journal International, 169(3), 1315–1340. doi:10.1111/j.1365-246X.2007.03371.x.

    Article  Google Scholar 

  • Satoshi, M., Sadato, U., Toshiya, S., Kenji, T., & Hiroyuki, H. (2000). Crustal deformation associated with the 1998 seismo-volcanic crisis of Iwate Volcano, Northeastern Japan, as observed by a dense GPS network. Earth, Planets and Space, 52(11), 1003–1008. doi:10.1186/BF03352321.

    Article  Google Scholar 

  • Satoshi, M., Toshiya, S., Akira, H., Yoko, S., Kenji, T., & Satoshi, Y. (2004). Strain concentration zone along the volcanic front derived by GPS observations in NE Japan arc. Earth, Planets and Space, 56(12), 1347–1355. doi:10.1186/BF03353360.

    Article  Google Scholar 

  • Shimada, S., Fujinawa, Y., Sekiguchi, S., Ohmi, S., & Eguchi, T. (1990). Detection of a volcanic fracture opening in Japan using global positioning system measurements. Nature, 343, 631–633. doi:10.1038/343631a0.

    Article  Google Scholar 

  • Sigurjón, J., Páll, E., & Freysteinn, S. (1997). Extension across a divergent plate boundary, the Eastern Volcanic Rift Zone, south Iceland, 1967–1994, observed with GPS and electronic distance measurements. Journal of Geophysical Research Atmospheres, 1021(B6), 11913–11930. doi:10.1029/96JB03893.

    Google Scholar 

  • Socquet, A., Vigny, C., Chamot-Rooke, N., Simons, W., Rangin, C., & Ambrosius, B. (2006). India and Sunda plates motion and deformation along their boundary in Myanmar determined by GPS. Journal of Geophysical Research, 111, B05406. doi:10.1029/2005JB003877.

    Google Scholar 

  • Stein, M. L. (1999). Interpolation of spatial data: Some theory for Kriging. New York: Springer.

    Book  Google Scholar 

  • Stéphane, M., Xavier, L. P., Pierre, H., & Shin-Ichi, M. (2012). Full interseismic locking of the Nankai and Japan-west Kurile subduction zones: an analysis of uniform elastic strain accumulation in Japan constrained by permanent GPS. Journal of Geophysical Research Solid Earth, 105(B6), 13159–13177. doi:10.1029/2000JB900060.

    Google Scholar 

  • Takeshi, S., Shin’ichi, M., & Takashi, T. (2000). Continuous GPS array and present-day crustal deformation of Japan. Pure Appl. Geoph, 157(11–12), 2303–2322. doi:10.1007/978-3-0348-7695-7_26.

    Google Scholar 

  • Thorsten, W. B., Jeanne, L. H., & Greg, A. (2005). Constraints on fault slip rates of the southern California plate boundary from GPS velocity and stress inversions. Geophysical Journal International, 160(2), 634–650. doi:10.1111/j.1365-246X.2004.02528.x.

    Article  Google Scholar 

  • Vigny, C., Simons, W. J. F., Abu, S., Ronnachai, B., Chalermchon, S., Nithiwatthn, C., et al. (2005). Insight into the 2004 Sumatra-Andaman earthquake from GPS measurements in southeast Asia. Nature, 436, 201–206. doi:10.1038/nature03937.

    Article  Google Scholar 

  • Wang, J., Ye, Z. R., & He, J. K. (2008). Three-dimensional mechanical modeling of large-scale crustal deformation in China constrained by the GPS velocity fleld. Tectonophysics, 446, 51–60.

    Article  Google Scholar 

  • Wang, Q., Zhang, P. Z., & Freymuller, J. T. (2001). Present day crustal deformation in China constrained by Global Positioning System measurements. Science, 294(5542), 574–577.

    Article  Google Scholar 

  • Wessel, P., Smith, W. H. (2006). The generic mapping tools. http://gmt.soest.hawaii.edu/.

  • Wu, Y. Q., Jiang, Z. S., Yang, G. H., Wei, W. X., & Liu, X. X. (2011). Comparison of GPS strain rate computing methods and their reliability. Geophysical Journal International, 185, 703–717. doi:10.1111/j.1365-246X.2011.04976.x.

    Article  Google Scholar 

  • Wu, Y. Q., Jiang, Z. S., Zhao, J., Liu, X. X., Wei, W. X., Liu, Q., et al. (2015). Crustal deformation before the 2008 Wenchuan MS8.0 earthquake studied using GPS data. Journal of Geodynamics, 85, 11–23. doi:10.1016/j.jog.2014.12.002.

    Article  Google Scholar 

  • Yu, S. B., Hsu, Y. J., Kuo, L. C., Chen, H. Y., & Liu, C. C. (2003). GPS measurement of postseismic deformation following the 1999 Chi-Chi, Taiwan, earthquake. Journal of Geophysical Research, 108(108), 183. doi:10.1029/2003JB002396.

    Google Scholar 

  • Zhang, P. Z., Deng, Q. D., & Zhang, G. M. (2003). Active tectonic blocks and strong earthquakes in the continent of China. Science China Earth Sciences, z2, 13–24.

    Google Scholar 

Download references

Acknowledgements

The GPS data were from the Engineering Research Center of the China Crust Movement Observation Network. The vector image of simulated data and surveying GPS velocity are drawn using the GMT package (Wessel and Smith 2006). Special thanks to Dr. Bofeng Guo and Jingyang Zhao for their helpful advice. This work was financially supported by the National Science Foundation of China (41474002, 41274008), and Special Program for Key Basic Work of the Ministry of Science and Technology of China (2015FY210403).

Author information

Authors and Affiliations

  1. First Crust Deformation Monitoring and Application Center, CEA, Tianjin, China

    Yanqiang Wu & Shuang Zhu

  2. CEA Key Laboratory of Earthquake Prediction, Institute of Earthquake Science, China Earthquake Administration, Beijing, China

    Yanqiang Wu, Zaisen Jiang, Xiaoxia Liu, Wenxin Wei, Long Zhang, Zhenyu Zou, Xiaohui Xiong, Qixin Wang & Jiliang Du

Authors
  1. Yanqiang Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zaisen Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaoxia Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wenxin Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shuang Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Long Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Zhenyu Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Xiaohui Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Qixin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Jiliang Du
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zaisen Jiang.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (TXT 72 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, Y., Jiang, Z., Liu, X. et al. A Comprehensive Study of Gridding Methods for GPS Horizontal Velocity Fields. Pure Appl. Geophys. 174, 1201–1217 (2017). https://doi.org/10.1007/s00024-016-1456-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00024-016-1456-z

Keywords

Search

Navigation