Articles | Volume 7, issue 3
Research article
24 May 2016
Research article |  | 24 May 2016

Multi-quadric collocation model of horizontal crustal movement

Gang Chen, Anmin Zeng, Feng Ming, and Yifan Jing

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 0.80 mm yr−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.

Short summary
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.