The previously proposed Strain Model and Variance Component Estimation (SM-VCE) method estimates three-dimensional (3-D) deformations based on heterogeneous synthetic aperture radar (SAR) observations from three or more distinct observing geometries. This method establishes an observation function by exploiting the spatial correlation of adjacent point deformations based on a geo-kinematic model (i.e., SM), and it determines an accurate weight of heterogeneous observations using the VCE algorithm; this method has been demonstrated to be superior to the traditional pixel-by-pixel-based weighted least square (WLS) method. However, since the SM-VCE method employs the adjacent points' observations to estimate 3-D deformations at a target point, it is inevitable that it results in a bias in the solution near the deformation jump area (e.g., the fault zone in an earthquake). In this paper, a Strain Model-based Adaptive Neighborhood Determining (SMAD) method is proposed to identify homogeneous deformation observations in such a way that the accuracy of the 3-D deformations estimated by the SM-VCE method can be increased, especially near the surface rupture area. This method is used for mapping 3-D coseismic deformations associated with the 2016 Mw7.8 Kaiköura earthquake in New Zealand. Furthermore, with increasing SAR data available for a single event, the effect of the number/type of independent observations on the accuracy of the 3-D deformations remains poorly understood and requires further discussion. To accomplish this goal, we define a term, the deformation dilution of precision (DDOP), to represent the quality of the 3-D deformation vector; this term is similar to the position dilution of precision (PDOP) in global navigation satellite system (GNSS), and we investigate different combinations with different numbers/types of independent observations to explore the 3-D deformations of this earthquake. The results demonstrate that the type of incorporated observations can significantly dominate the accuracy of the 3-D deformations compared to the number of observations, which can provide an important reference for relevant studies that estimate 3-D deformations. Furthermore, the proposed methods and conclusions are beneficial for estimating 3-D surface deformations associated with other geophysical processes, such as volcanic eruptions.

先前提出的应变模型和方差分量估计（SM-VCE）方法基于异类合成孔径雷达（SAR）的观测值，从三个或更多不同的观测几何形状估算三维（3-D）变形。该方法利用地质运动学模型（SM），利用相邻点变形的空间相关性建立观测函数，并使用VCE算法确定异质观测的准确权重。该方法已证明优于传统的逐像素加权最小二乘（WLS）方法。但是，由于SM-VCE方法利用相邻点的观测值来估计目标点处的3-D变形，因此不可避免地会导致变形跳跃区域附近的解出现偏差（例如，地震中的断层带）。本文提出了一种基于应变模型的自适应邻域确定（SMAD）方法来识别均匀变形观测值，从而可以提高SM-VCE方法估计的3-D变形的精度，尤其是在表面破裂面积。该方法用于绘制与2016年新西兰Mk7.8凯库拉地震有关的3-D同震变形图。此外，随着可用于单个事件的SAR数据的增加，独立观测的数量/类型对3-D变形精度的影响仍然知之甚少，需要进一步讨论。为了实现这一目标，我们定义了一个术语，即精度变形稀释度（DDOP），以表示3-D变形矢量的质量；该术语类似于全球导航卫星系统（GNSS）中的精度位置稀释（PDOP），并且我们研究了具有不同数量/类型的独立观测值的不同组合，以探索该地震的3-D变形。结果表明，与观测值数量相比，合并观测值的类型可以显着支配3-D变形的准确性，这可以为估计3-D变形的相关研究提供重要参考。此外，提出的方法和结论对于估算与其他地球物理过程（如火山喷发）相关的3-D表面变形是有益的。我们研究了具有不同数量/类型的独立观测值的不同组合，以探索这次地震的3-D变形。结果表明，与观测数量相比，合并观测的类型可以显着支配3-D变形的准确性，这可以为估计3-D变形的相关研究提供重要参考。此外，提出的方法和结论对于估算与其他地球物理过程（如火山喷发）相关的3-D表面变形是有益的。我们研究了具有不同数量/类型的独立观测值的不同组合，以探索这次地震的3-D变形。结果表明，与观测值数量相比，合并观测值的类型可以显着支配3-D变形的准确性，这可以为估计3-D变形的相关研究提供重要参考。此外，提出的方法和结论对于估算与其他地球物理过程（如火山喷发）相关的3-D表面变形是有益的。这可以为估计3-D变形的相关研究提供重要参考。此外，提出的方法和结论对于估算与其他地球物理过程（如火山喷发）相关的3-D表面变形是有益的。这可以为估计3-D变形的相关研究提供重要参考。此外，提出的方法和结论对于估算与其他地球物理过程（如火山喷发）相关的3-D表面变形是有益的。