GNSS-assisted InSAR tropospheric delay correction model incorporating vertical stratification and turbulent components

doi:10.11947/j.AGCS.2025.20250124

Abstract

Abstract:

GNSS reference station observed tropospheric delays are commonly employed to correct tropospheric delays in InSAR, which involves spatially interpolating the GNSS-observed delays to unmeasured locations. Traditional methods focus solely on the spatial correlation characteristics of turbulent components, achieve interferogram correction through functional or stochastic modeling while neglecting the stratified component. This study proposes a joint correction model that accounts for both stratified and turbulent delay components. Specifically, an elevation-dependent functional model and a stochastic model are adopted to absorb stratified and turbulent delay components, respectively. The deterministic parameters of stratified component and random turbulence at the GNSS-measured points are simultaneously resolved via least squares collocation. Finally, predict them to unmeasured points. Validation using 71 Sentinel-1 datasets over Southern California demonstrates that the proposed method reduces the average standard deviation (STD) of 70 short temporal baseline interferograms from 4.7 rad to 1.4 rad, outperforming both GACOS (average STD reduced to 2.7 rad), linear model (average STD reduced to 4.1 rad), GInSAR (average STD reduced to 2.9 rad) and LSC-GInSAR (average STD reduced to 1.8 rad) corrections. The derived deformation velocity reveals regional long-wavelength deformation pattern that agrees well with GNSS measurements (correlation coefficient is 0.67). These results confirm that the proposed approach can effectively correct medium-to-long-wavelength tropospheric delays in interferogram and is suitable for measuring large-scale deformation signals.

Key words: InSAR, global navigation satellite system, tropospheric delays, least squares collocation, variance component estimation

CLC Number:

P227

Hailu CHEN, Yunzhong SHEN. GNSS-assisted InSAR tropospheric delay correction model incorporating vertical stratification and turbulent components[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(10): 1786-1797.

Figures/Tables 12

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Tab. 1

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Tab. 2

References 41

[1]	李振洪, 宋闯, 余琛, 等. 卫星雷达遥感在滑坡灾害探测和监测中的应用：挑战与对策[J]. 武汉大学学报(信息科学版), 2019, 44(7): 967-979.
	LI Zhenhong, SONG Chuang, YU Chen, et al. Application of satellite radar remote sensing to landslide detection and monitoring: challenges and solutions[J]. Geomatics and Information Science of Wuhan University, 2019, 44(7): 967-979.
[2]	LI Zhenhong, YU Chen, XIAO Ruya, et al. Entering a new era of InSAR: advanced techniques and emerging applications[J]. Journal of Geodesy and Geoinformation Science, 2022, 5(1): 168-172.
[3]	刘计洪, 胡俊, 李志伟, 等. InSAR三维同震地表形变监测：窗口优化的SM-VCE算法[J]. 测绘学报, 2021, 50(9): 1222-1239. DOI: . doi: 10.11947/j.AGCS.2021.20200610
	LIU Jihong, HU Jun, LI Zhiwei, et al. Estimation of 3D coseismic deformation with InSAR: an improved SM-VCE method by window optimization[J]. Acta Geodaetica et Cartographica Sinica, 2021, 50(9): 1222-1239. DOI: . doi: 10.11947/j.AGCS.2021.20200610
[4]	朱建军, 杨泽发, 李志伟. InSAR矿区地表三维形变监测与预计研究进展[J]. 测绘学报, 2019, 48(2): 135-144. DOI: . doi: 10.11947/j.AGCS.2019.20180188
	ZHU Jianjun, YANG Zefa, LI Zhiwei. Recent progress in retrieving and predicting mining-induced 3D displace-ments using InSAR[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(2): 135-144. DOI: . doi: 10.11947/j.AGCS.2019.20180188
[5]	ZHANG Lei, LU Zhong, DING Xiaoli, et al. Mapping ground surface deformation using temporarily coherent point SAR interferometry: application to Los Angeles basin[J]. Remote Sensing of Environment, 2012, 117: 429-439.
[6]	ZHAO Chaoying, LU Zhong, ZHANG Qin, et al. Large-area landslide detection and monitoring with ALOS/PALSAR imagery data over Northern California and Southern Oregon, USA[J]. Remote Sensing of Environment, 2012, 124: 348-359.
[7]	LI Zhiwei, CAO Yunmeng, WEI Jianchao, et al. Time-series InSAR ground deformation monitoring: atmospheric delay modeling and estimating[J]. Earth-Science Reviews, 2019, 192: 258-284.
[8]	DOIN M P, LASSERRE C, PELTZER G, et al. Corrections of stratified tropospheric delays in SAR interferometry: validation with global atmospheric models[J]. Journal of Applied Geophysics, 2009, 69(1): 35-50.
[9]	JOLIVET R, AGRAM P S, LIN N Y, et al. Improving InSAR geodesy using global atmospheric models[J]. Journal of Geophysical Research: Solid Earth, 2014, 119(3): 2324-2341.
[10]	YU Chen, LI Zhenhong, PENNA N T, et al. Generic atmospheric correction model for interferometric synthetic aperture radar observations[J]. Journal of Geophysical Research: Solid Earth, 2018, 123(10): 9202-9222.
[11]	HANSSEN R F. Radar Interferometry: data interpretation and error analysis[M]. London: Springer Science & Business Media, 2001.
[12]	CHEN Hailu, SHEN Yunzhong. LSC-GInSAR: a GNSS-enhanced InSAR approach by using least squares collocation open access[J]. Geophysical Journal International, 2023, 236(1): 49-61.
[13]	ZHANG Xuesong, LI Zhenhong, LIU Zhenjiang. Reduction of atmospheric effects on InSAR observations through incorporation of GACOS and PCA into small baseline subset InSAR[J]. IEEE Transactions on Geoscience and Remote Sensing, 2023, 61: 5209115.
[14]	LOHMAN R B, SIMONS M. Some thoughts on the use of InSAR data to constrain models of surface deformation: noise structure and data downsampling[J]. Geochemistry, Geophysics, Geosystems, 2005, 6: Q01007.
[15]	BEKAERT D P S, HOOPER A, WRIGHT T J. A spatially variable power law tropospheric correction technique for InSAR data[J]. Journal of Geophysical Research: Solid Earth, 2015, 120(2): 1345-1356.
[16]	LIANG Hongyu, ZHANG Lei, DING Xiaoli, et al. Toward mitigating stratified tropospheric delays in multitemporal InSAR: a quadtree aided joint model[J]. IEEE Transactions on Geoscience and Remote Sensing, 2019, 57(1): 291-303.
[17]	HOOPER A. A multi-temporal InSAR method incorporating both persistent scatterer and small baseline approaches[J]. Geophysical Research Letters, 2008, 35: L16302.
[18]	LIANG Hongyu, ZHANG Lei, LU Zhong, et al. Correction of spatially varying stratified atmospheric delays in multitemporal InSAR[J]. Remote Sensing of Environment, 2023, 285: 113382.
[19]	WANG Shuai, LU Zhong, WANG Bin, et al. A phase-based InSAR tropospheric correction method for interseismic deformation based on short-period interferograms[J]. IEEE Transactions on Geoscience and Remote Sensing, 2023, 61: 5212318.
[20]	LIU Jihong, HU Jun, BÜRGMANN R, et al. Mitigating atmospheric delays in InSAR time series: the DetrendInSAR method and its validation[J]. Journal of Geophysical Research: Solid Earth, 2024, 129(5): e2024JB028920.
[21]	CHEN Hailu, SHEN Yunzhong, ZHANG Lei, et al. Mitigation of tropospheric turbulent delays in InSAR time series by incorporating a stochastic process[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 2025, 222: 186-203.
[22]	LI Z W, XU W B, FENG G C, et al. Correcting atmospheric effects on InSAR with MERIS water vapour data and elevation-dependent interpolation model[J]. Geophysical Journal International, 2012, 189(2): 898-910.
[23]	LI Zhenhong, MULLER J P, CROSS P, et al. Interferometric synthetic aperture radar (InSAR) atmospheric correction: GPS, moderate resolution imaging spectroradiometer (MODIS), and InSAR integration[J]. Journal of Geophysical Research: Solid Earth, 2005, 110(B3): B03410.
[24]	CAO Yunmeng, JÓNSSON S, LI Zhiwei. Advanced InSAR tropospheric corrections from global atmospheric models that incorporate spatial stochastic properties of the troposphere[J]. Journal of Geophysical Research: Solid Earth, 2021, 126(5): e2020JB020952.
[25]	YU Chen, PENNA N T, LI Zhenhong. Generation of real-time mode high-resolution water vapor fields from GPS observations[J]. Journal of Geophysical Research: Atmospheres, 2017, 122(3): 2008-2025.
[26]	NEELY W R, BORSA A A, SILVERII F. GInSAR: a cGPS correction for enhanced InSAR time series[J]. IEEE Transactions on Geoscience and Remote Sensing, 2020, 58(1): 136-146.
[27]	LIU Yuhao, WANG Guoquan, YU Xiao, et al. Sentinel-1 InSAR and GPS-integrated long-term and seasonal subsidence monitoring in Houston, Texas, USA[J]. Remote Sensing, 2022, 14(23): 6184.
[28]	GUNS K, XU Xiaohua, BOCK Y, et al. GNSS-corrected InSAR displacement time-series spanning the 2019 Ridgecrest, CA earthquakes[J]. Geophysical Journal International, 2022, 230(2): 1358-1373.
[29]	LIU Ning, DAI Wujiao, SANTERRE R, et al. High spatio-temporal resolution deformation time series with the fusion of InSAR and GNSS data using spatio-temporal random effect model[J]. IEEE Transactions on Geoscience and Remote Sensing, 2019, 57(1): 364-380.
[30]	GE L, HAN S, RIZOS C. The double interpolation and double prediction (DIDP) approach for InSAR and GPS integration[J]. International Archives of Photogrammetry and Remote Sensing, 2000, 33(B2): 205-212.
[31]	占文俊, 李志伟, 韦建超, 等. 一种InSAR大气相位建模与估计方法[J]. 地球物理学报, 2015, 58(7): 2320-2329.
	ZHAN Wenjun, LI Zhiwei, WEI Jianchao, et al. A strategy for modeling and estimating atmospheric phase of SAR interferogram[J]. Chinese Journal of Geophysics, 2015, 58(7): 2320-2329.
[32]	KRAUP T A. Contribution to the mathematical foundation of physical geodesy[M]//mathematical foundation of geodesy. Berlin: Springer, 2006: 29-90.
[33]	YANG Y, ZENG A, ZHANG J. Adaptive collocation with application in height system transformation[J]. Journal of Geodesy, 2009, 83(5): 403-410.
[34]	ROSEN P A, GURROLA E M, SACCO G F, et al. The InSAR scientific computing environment[C]//Proceedings of 2012 European Conference on Synthetic Aperture Radar. Hangzhou: IEEE, 2012.
[35]	GOLDSTEIN R M, WERNER C L. Radar interferogram filtering for geophysical applications[J]. Geophysical Research Letters, 1998, 25(21): 4035-4038.
[36]	CHEN C W, ZEBKER H A. Two-dimensional phase unwrapping with use of statistical models for cost functions in nonlinear optimization[J]. Journal of the Optical Society of America, 2001, 18(2): 338.
[37]	FATTAHI H, AMELUNG F. DEM error correction in InSAR time series[J]. IEEE Transactions on Geoscience and Remote Sensing, 2013, 51(7): 4249-4259.
[38]	宋鑫友, 张磊, 李涛, 等. 陆探一号干涉SAR在轨测试阶段基线精化与DEM精度分析[J]. 测绘学报， 2024, 53(10): 1920-1929. DOI: . doi: 10.11947/j.AGCS.2024.20230540
	SONG Xinyou, ZHANG Lei, LI Tao, et al. Baseline refinement and DEM accuracy analysis during the in-orbit test phase of LT-1SAR[J]. Acta Geodaetica et Cartographica Sinica, 2024, 53(10): 1920-1929. DOI: . doi: 10.11947/j.AGCS.2024.20230540
[39]	ZHANG Yunjun, FATTAHI H, AMELUNG F. Small baseline InSAR time series analysis: unwrapping error correction and noise reduction[J]. Computers & Geosciences, 2019, 133: 104331.
[40]	MILBERT D. Solid: solid earth tide[EB/OL]. [2024-10-15]. http://geodesyworld.github.io/SOFTS/solid.html.
[41]	DABBERDT W F, SHELLHORN R A. On the optimal spatial sampling of atmospheric data[J]. Journal of Applied Meteorology, 1973, 12(1), 34-44.

高度/m	类型
[0，200）	低海拔
[200，800）	中海拔
[800，∞）	高海拔

GNSS站点间距/km	GInSAR/cm	LSC-GInSAR/cm	本文方法/cm
65.1	3.4	2.5	1.7
44.5	2.3	1.9	1.3
32.8	2.5	1.8	1.1
21.7	2.3	1.3	0.7