We develop an algorithm to integrate GPS and InSAR data for a 3‐dimensional crustal deformation field at the Earth's surface. In the algorithm discrete GPS data points are interpolated to obtain a 3‐dimensional continuous velocity field, which is then combined with the InSAR line‐of‐sight (LOS) velocity data pixel by pixel using the least‐squares method. Advantages of our method over previous ones are that: 1) The GPS data points are optimally interpolated by balancing a trade‐off between spatial resolution and solution stability. 2) A new algorithm is developed to estimate realistic uncertainties for the interpolated GPS velocities, to be used as weights for GPS data in GPS‐InSAR combination. 3) Realistic uncertainties for the InSAR LOS rate data are estimated and used as weights for InSAR data in GPS‐InSAR combination. 4) The ramps and/or offsets of the InSAR data are globally estimated for all the images to minimize data misfit, particularly at regions where the data overlaps. Application of this method to real data from southern California shows its capability of successfully restoring 3‐dimensional continuous deformation field from spatially limited GPS and dimensionally limited InSAR data. The deformation field reveals water withdrawal induced subsidence and drought caused uplift at various regions in southern California.

中文翻译：

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集成GPS和InSAR数据以解决3维地壳变形

我们开发了一种算法，可将GPS和InSAR数据整合为地球表面3维地壳变形场。在该算法中，对离散的GPS数据点进行插值以获得3维连续速度场，然后使用最小二乘法将其与InSAR视线（LOS）速度数据逐像素组合。与以前的方法相比，我们的方法的优势在于：1）通过平衡空间分辨率和解决方案稳定性之间的折衷，可以对GPS数据点进行最佳插值。2）开发了一种新算法来估计内插GPS速度的实际不确定性，以用作GPS-InSAR组合中GPS数据的权重。3）估算InSAR LOS速率数据的实际不确定性，并将其用作GPS-InSAR组合中InSAR数据的权重。4）针对所有图像全局估计InSAR数据的斜率和/或偏移量，以最大程度地减少数据失配，尤其是在数据重叠的区域。该方法在来自加利福尼亚南部的真实数据中的应用表明，它具有从空间受限的GPS和维度受限的InSAR数据中成功恢复3维连续变形场的能力。变形场揭示了加利福尼亚南部各地区的水提取引起的沉降和干旱引起的隆升。该方法在来自加利福尼亚南部的真实数据中的应用表明，它具有从空间受限的GPS和维度受限的InSAR数据中成功恢复3维连续变形场的能力。变形场揭示了加利福尼亚南部各地区的水提取引起的沉降和干旱引起的隆升。该方法在来自加利福尼亚南部的真实数据中的应用表明，它具有从空间受限的GPS和维度受限的InSAR数据中成功恢复3维连续变形场的能力。变形场揭示了加利福尼亚南部各地区的水提取引起的沉降和干旱引起的隆升。