The Earth’s crust is exposed by tectonic processes and is not static over time. Modelling of the Earth’s surface velocities is of utmost importance for research in geodesy, geophysics, structural geology, and other geosciences. It may support positioning, navigation, seismic risk, and volcano notification services, for example. Space geodetic techniques can be used to provide high-quality velocities in a network of geodetic sites. Velocity field modelling should, however, expand the velocities from a discrete set of points to any location in-between. This paper presents four new methods for the Earth’s surface velocity interpolation. Contrary to the widely used approach dividing the velocity field to the horizontal and vertical components, a full 3D interpolation approach is proposed based on the Delaunay triangulation and the n-simplex interpolation. The use of a combination of all three components is advantageous for geophysical interpretation. The proposed interpolation approach is entirely local but enables global modelling, which does not suffer from map projection distortions and singularities at the poles. Various global and regional position/velocity datasets are used to evaluate the performance of the proposed velocity interpolation methods. The latter provide practically the same results when applied to regional velocity field modelling. However, the so-called continuous piecewise quasi-radial 3D velocity field interpolation method is recommended for its favourable properties. It introduces an ellipsoidal Earth model, appropriately considers vertical/up and horizontal velocity components, tends to radial symmetry, and provides continuity for the interpolated velocity components as well as for the estimated uncertainties.

地壳因构造过程而暴露出来，并且不会随着时间的推移而保持静止。地球表面速度的建模对于大地测量学、地球物理学、结构地质学和其他地球科学研究至关重要。例如，它可以支持定位、导航、地震风险和火山通知服务。空间大地测量技术可用于在大地测量站点网络中提供高质量的速度。然而，速度场建模应该将速度从一组离散点扩展到其间的任何位置。本文提出了地球表面速度插值的四种新方法。与广泛使用的将速度场划分为水平和垂直分量的方法相反，提出了一种基于 Delaunay 三角剖分和 n 单纯形插值的全 3D 插值方法。使用所有三个组件的组合有利于地球物理解释。所提出的插值方法完全是局部的，但可以进行全局建模，不会受到地图投影扭曲和极点奇点的影响。各种全球和区域位置/速度数据集用于评估所提出的速度插值方法的性能。当应用于区域速度场建模时，后者实际上提供了相同的结果。然而，所谓的连续分段准径向3D速度场插值方法因其良好的特性而被推荐。它引入了椭球地球模型，适当考虑垂直/向上和水平速度分量，趋于径向对称，并为插值速度分量以及估计的不确定性提供连续性。