Abstract
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.
Highlights
Horizontal movement velocity fields provide the main basic data for Earth science research
Some scholars have systematically researched their application in horizontal velocity field models in the Chinese mainland (Huang et al, 1993; Nie et al, 2007; Zeng et al, 2013)
The key to applying the collocation model is to establish a reliable covariance function. It tends to adopt an empirical formula in a gravitational field, where the majority of applications are established, by using a measured data covariance model, which affects the optimality of the collocation method and reduces its usable area
Summary
Horizontal movement velocity fields provide the main basic data for Earth science research. How to obtain reliable horizontal velocity fields from measured points has been the focus of a lot of research all over the world (Argus and Gordon, 1991; Huang et al, 1993; Liu et al, 2001, 2002; Chai et al, 2009; Jiang and Liu, 2010; Hu and Wang, 2012; Zeng et al, 2012, 2013). A new combined estimation method using the kernel function of a multi-quadric fitting model to replace the covariance function of collocation was proposed and tested
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