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Solid Earth An interactive open-access journal of the European Geosciences Union
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Volume 7, issue 3
Solid Earth, 7, 817-825, 2016
https://doi.org/10.5194/se-7-817-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Solid Earth, 7, 817-825, 2016
https://doi.org/10.5194/se-7-817-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 24 May 2016

Research article | 24 May 2016

Multi-quadric collocation model of horizontal crustal movement

Gang Chen1,2, Anmin Zeng3,4, Feng Ming3,4, and Yifan Jing3,4 Gang Chen et al.
  • 1Faculty of Information Engineering, China University of Geosciences, Wuhan 430074, China
  • 2National Engineering Research Center for Geographic Information System, Wuhan 430074, China
  • 3Faculty of Geospatial Information, Information Engineering University, Zhengzhou 410052, China
  • 4State Key Laboratory of Geographic Information Engineering, Xi'an 710054, China

Abstract. To establish the horizontal crustal movement velocity field of the Chinese mainland, a Hardy multi-quadric fitting model and collocation are usually used. However, the kernel function, nodes, and smoothing factor are difficult to determine in the Hardy function interpolation. Furthermore, the covariance function of the stochastic signal must be carefully constructed in the collocation model, which is not trivial. In this paper, a new combined estimation method for establishing the velocity field, based on collocation and multi-quadric equation interpolation, is presented. The crustal movement estimation simultaneously takes into consideration an Euler vector as the crustal movement trend and the local distortions as the stochastic signals, and a kernel function of the multi-quadric fitting model substitutes for the covariance function of collocation. The velocities of a set of 1070 reference stations were obtained from the Crustal Movement Observation Network of China, and the corresponding velocity field was established using the new combined estimation method. A total of 85 reference stations were used as checkpoints, and the precision in the north and east component was 1.25 and 0.80mmyr−1, respectively. The result obtained by the new method corresponds with the collocation method and multi-quadric interpolation without requiring the covariance equation for the signals.

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In this paper, we presented a new method on the basis of a collocation and multi-quadric equation interpolation. We introduce a multi-quadric kernel function to determine the covariance of local deformation and use the method to be a simple approximation of the covariance function. We established a horizontal velocity field model for the Chinese mainland by using a set of observed velocity data of GPS stations. The result is simple and reasonable and has a significant reference value.
In this paper, we presented a new method on the basis of a collocation and multi-quadric...
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