A Comprehensive Study of Gridding Methods for GPS Horizontal Velocity Fields

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 degrees x 1 degrees 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 degrees x 1 degrees grid data and then erased in three 6 degrees x 12 degrees 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.