Least-squares collocation (LSC) is a widely used method applied in physical geodesy to separate observations into a signal and noise part but has received only little attention when interpolating velocity fields. The advantage of the LSC is the possibility to filter and interpolate as well as extrapolate the observations. Here, we will present several extensions to the traditional LSC technique, which allows the combined interpolation of both horizontal velocity components (horizontal velocity (HV)-LSC), the separation of velocity observations on different tectonic plates, and the removal of stationarity by moving variance (the latter as HV-LSC-ex(tended)\(^2\)). Furthermore, the covariance analysis, which is required to find necessary input parameters for the LSC, is extended by finding a suitable variance and correlation length using both horizontal velocity components at the same time. The traditional LSC and all extensions are tested on a synthetic dataset to find the signal at known as well as newly defined points, with stations separated on four different plates with distinct plate velocities. The methodologies are evaluated by calculation of a misfit to the input data, and implementation of a leave-one-out cross-validation and a Jackknife resampling. The largest improvement in terms of reduced misfit and stability of the interpolation can be obtained when plate boundaries are considered. In addition, any small-scale changes can be filtered out using the moving-variance approach and a smoother velocity field is obtained. In comparison with interpolation using the Kriging method, the fit is better using the new HV-LSC-ex\(^2\) technique.

最小二乘搭配 (LSC) 是一种广泛应用于物理大地测量学的方法，用于将观测结果分为信号和噪声部分，但在插值速度场时很少受到关注。LSC 的优点是可以过滤和内插以及外推观察结果。在这里，我们将介绍传统 LSC 技术的几个扩展，它允许对两个水平速度分量（水平速度 (HV)-LSC）进行组合插值，分离不同构造板块上的速度观测值，以及通过移动来消除平稳性方差（后者为 HV-LSC-ex(tended) \(^2\)）。此外，通过同时使用两个水平速度分量找到合适的方差和相关长度，扩展了为 LSC 找到必要输入参数所需的协方差分析。传统的 LSC 和所有扩展都在合成数据集上进行测试，以在已知点和新定义的点上找到信号，站点分隔在具有不同板速度的四个不同板上。通过计算与输入数据的不匹配以及实施留一法交叉验证和折刀重采样来评估这些方法。当考虑板块边界时，可以在减少失配和插值稳定性方面获得最大的改进。此外，使用移动方差方法可以滤除任何小尺度变化，并获得更平滑的速度场。与使用 Kriging 方法的插值相比，使用新的 HV-LSC-ex 的拟合效果更好\(^2\)技术。