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An InSAR Tropospheric Delay Correction Method based on a Spatially Adaptive Anchor Network and Local Turbulence Interpolation
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摘要: 对流层延迟是干涉合成孔径雷达(InSAR)的主要误差源之一，尤其在地形复杂或大气异质性强的区域，严重限制了其获取精确地表位移的能力。现有的校正方法或受限于外部数据的粗分辨率，或在对形变与高程关系建模以及处理复杂的湍流效应时能力不足。为此，该文提出了一种基于空间自适应锚点网络的对流层校正方法。该方法利用融合相位稳定性与时序相干性的综合质量指数(CQI)，结合空间迭代筛选策略，构建锚点网络，实现数据质量驱动的空间采样。在每个锚点的邻域内，构建局部联合反演模型，在时空域上稳健地分离形变、地形残差和对流层延迟。此外，引入了局部湍流强度(LTI)因子，抑制插值过程中强湍流区域的误差传播。该团队使用夏威夷和青藏高原的Sentinel-1数据进行的验证表明，所提方法将干涉图相位标准差降低了73%以上，显著优于其他方法。校正后InSAR与GPS测量的时序位移之间的均方根误差(RMSE)从44.4 mm降低至9.3 mm，一致性提高了79%。该文所提方法能够有效且鲁棒地校正对流层延迟，提高InSAR测量精度，增强不同地形条件下形变监测的可靠性。
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关键词:
- 自适应锚点网络 /
- 干涉合成孔径雷达 (InSAR) /
- 联合反演模型 /
- 空间插值 /
- 对流层延迟校正
Abstract: Tropospheric delay is a major error source in interferometric synthetic aperture radar (InSAR) and significantly limits its ability to retrieve accurate surface displacements, particularly in regions with complex topography or strong atmospheric heterogeneity. Existing correction methods are constrained by either the coarse resolution of external data or their inability to model deformation–elevation coupling and complex turbulent effects. To address these challenges, this paper proposes a tropospheric correction method based on a spatially adaptive anchor network. A comprehensive quality index, combining phase stability and temporal coherence, is used along with an iterative spatial selection strategy to construct a quality-driven anchor network. Within each anchor neighborhood, a local joint inversion model is developed to effectively separate deformation, topographic residuals, and tropospheric delay. Additionally, a local turbulence intensity factor is introduced to suppress error propagation from high-turbulence regions during interpolation. Validation using Sentinel-1 data from Hawaii and the Qinghai-Tibet Plateau demonstrates that the proposed method reduces the interferogram phase standard deviation by more than 73%, outperforming conventional methods. The root mean square error between InSAR and GPS time-series displacements decreases from 44.4 to 9.3 mm after correction, representing a 79% improvement in consistency. The proposed method effectively mitigates tropospheric delay, enhances the accuracy of InSAR measurements, and improves the reliability of deformation monitoring across diverse terrain conditions. -
图 1 对流层延迟校正方法流程图
Figure 1. The workflow chart of the tropospheric delay correction method
图 2 自适应锚点选取与 Voronoi 邻域定义示意图
Figure 2. Illustration of the adaptive anchor point selection and Voronoi neighborhood definition
图 3 夏威夷研究区概况及所提方法选择的锚点 (蓝点) 分布图
Figure 3. Overview of the Hawaii study area and the distribution of the anchors (blue dots) selected by the proposed method
图 4 夏威夷单幅干涉图 (
20170615 -20170627 ) 的对流层延迟校正示例Figure 4. Example of tropospheric delay correction for an interferogram (
20170615 -20170627 ) in Hawaii
图 5 夏威夷单幅干涉图 (
20170826 -20170907 ) 不同对流层延迟校正方法结果对比Figure 5. Comparison of tropospheric delay correction results for a single interferogram (
20170826 -20170907 ) in Hawaii
图 6 夏威夷另外三幅干涉图的对流层延迟校正结果对比
Figure 6. Comparison of tropospheric delay correction results for three additional interferograms in Hawaii
图 7 夏威夷所有干涉图在使用不同校正方法后的标准差对比图
Figure 7. Comparison of standard deviation for all interferograms in the Hawaii using different correction methods
图 8 基拉韦厄火山附近两点 (P1 和 P2) 校正前后的视线方向 (LOS) 形变时间序列对比
Figure 8. Comparison of LOS deformation time-series before and after correction at two points (P1 and P2) near the Kilauea volcano
图 9 青藏高原北麓河冻土研究区概况及所提方法选择的锚点 (蓝点) 分布图
Figure 9. Overview of the Beiluhe permafrost study area in the QTP and the distribution of the anchors (blue dots) selected by the proposed method
图 10 北麓河地区两幅干涉图的对流层延迟校正结果对比
Figure 10. Comparison of tropospheric delay correction results for two interferograms in the Beiluhe region
图 11 北麓河研究区所有 59 幅连续干涉图的相位标准差对比
Figure 11. Comparison of phase standard deviation for all 59 sequential interferograms in the Beiluhe study area
图 12 北麓河研究区校正前 (左) 与校正后 (右) 的视线方向 (LOS) 年平均形变速率图
Figure 12. Mean annual LOS deformation velocity maps for the Beiluhe study area before (left) and after (right) correction
图 13 两个典型冻土点校正前 (蓝色阴影线) 与校正后 (红色实线) 的视线方向 (LOS) 形变时间序列对比。阴影区域表示该点周围 400 米半径范围内的标准差范围
Figure 13. Comparison of LOS deformation time-series before (blue shaded line) and after (red solid line) correction for two typical permafrost points. The shaded area indicates the standard deviation range within a 400-meter radius around the point
图 14 夏威夷 InSAR 结果与 GPS 数据的验证 (GPS 站点位置用三角形表示)
Figure 14. Validation of InSAR results with GPS data in Hawaii (locations of GPS stations are represented by triangles)
图 15 选定9个 GPS 站点的 InSAR 与 GPS 时间序列位移对比
Figure 15. Comparison of InSAR and GPS time-series displacements at 9 selected GPS stations
1 锚点迭代空间筛选算法
1. Anchor point iterative space selection algorithm
输入：按 CQI 降序排列的候选像素集$ {S}_{C} $，预定义的最小间距
$ {d}_{\min } $。输出：最终确定的锚点集合$ {S}_{A} $。 1: 初始化锚点集合$ {S}_{A} $。 2: 初始化与图像尺寸一致的布尔型掩膜$ {\text{Mask}}_{\text{locked}}({r}_{i},{c}_{i}) $，所有
像素设为 False (未锁定)。3: 对于 候选像素集$ {S}_{C} $中的每个像素$ {p}_{i} $执行： 4: 获取像素$ {p}_{i} $的空间坐标$ ({r}_{i},{c}_{i}) $。 5: 如果$ {\text{Mask}}_{\text{locked}}({r}_{i},{c}_{i}) $的值为False，则： 6: 将像素$ {p}_{i} $加入最终锚点集合$ {S}_{A} $。 7: 以坐标$ ({r}_{i},{c}_{i}) $为圆心，$ {d}_{\min } $为半径，定义一个圆形排他
区域$ {\Omega }_{i} $。8: 将$ {\text{Mask}}_{\text{locked}}({r}_{i},{c}_{i}) $中位于圆形区域$ {\Omega }_{i} $内的所有像素值更
新为True (锁定)。9: 结束如果 10: 结束循环 11: 返回 最终锚点集合$ {S}_{A} $。 
下载: 导出CSV
表 1 夏威夷不同校正方法的相位标准差统计对比
Table 1. Statistical Comparison of Phase Standard Deviation for Different Correction Methods in Hawaii
方法 相位标准差均值 (rad) 相位标准差中值 (rad) 相位标准差最小值 (rad) 相位标准差最大值 (rad) 相位标准差降低比例 未校正 5.47 4.93 2.44 13.13 N/A 线性 4.54 4.14 2.14 8.22 17.0% RALM 2.48 2.29 1.53 3.85 54.8% GACOS 4.43 4.23 2.19 7.23 18.8% 所提方法 1.46 1.37 0.96 2.41 73.2%
下载: 导出CSV
表 3 北麓河不同校正方法的相位标准差统计对比
Table 3. Statistical Comparison of Phase Standard Deviation for Different Correction Methods in Beiluhe.
方法 相位标准差均值 (rad) 相位标准差中值 (rad) 相位标准差最小值 (rad) 相位标准差最大值 (rad) 相位标准差降低比例 未校正 1.82 1.66 0.47 6.43 N/A 线性 1.56 1.45 0.42 4.90 14.4% RALM 0.57 0.59 0.27 0.97 68.7% GACOS 1.90 1.60 0.44 5.82 -4.4% 所提方法 0.48 0.47 0.24 0.74 73.8%
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