地下开采引起的地表变形具有时间依赖性和高度非线性，在地下开采过程中会对地表结构造成渐进破坏。传统的监测方法存在一定的缺陷，差分合成孔径雷达测量技术（InSAR）的主要特点是在较宽的覆盖范围内具有较高的空间分辨率和较高的精度。由于其独特的优点，该技术被广泛应用于地表变形监测。然而在煤矿区，地表在短时间内会发生大规模塌陷，导致InSAR结果不准确，限制了其在采矿沉降监测中的应用。基于此本文提出了一种探测矿区大规模形变的新方法，将SBAS-InSAR技术与用于预测采矿沉降的概率积分方法相结合，克服了这些缺点，并结合改进knothe时间函数建立了矿区沉降动态预计模型，得到了该矿区的地表沉降动态变化过程。主要进行了以下研究：

（1）首先利用SBAS-InSAR技术对覆盖陕北某煤矿的41景sentienl-1A数据处理，包括影像的配准、滤波、解缠、以及提取高相干点进行回归分析，分离形变相位和误差相位，并通过SVD分解和最小二乘法提取了矿区LOS向矿区的时间序列累积沉降量，得到了矿区沉陷盆地边缘稳定的边界点的沉降信息，并选择与走向和倾向GPS观测站重合的两个边界点的精度进行了验证。发现走向边界点B12的最大残差为3mm，倾向边界点B14的最大残差为6mm，均在限差范围内，说明其沉降盆地边界点结果值得信赖。

（2）由于静态概率积分法无法预计矿区随时间变化的动态开采沉陷，所以本文提出了将改进的knothe时间函数模型与静态概率积分法相结合的动态时间概率积分法预测模型。静态概率积分法的模型参数获取往往存在一定的困难，本文通过静态概率积分模型与InSAR侧视方向得到的边界点形变信息结合建立适应度函数，然后利用差分进化灰狼优化算法对该矿区的概率积分法预计参数进行求取。根据InSAR得到的边界点时间序列LOS向形变，建立多余观测方程，通过最小二乘法求取出改进knothe时间函数的模型参数。从而建立起InSAR-ITPIM动态概率积分预计模型对开采过程中的地表沉降进行预计，并将预计结果与实测GPS结果进行对比验证。

（3）结合矿区的地质构造岩层信息，通过FLAC3D软件建立摩尔－库伦模型求解不平衡力，根据回采距离选择开挖距离。从而对该工作面的开采沉陷过程进行动态模拟，得到了该工作面的地表动态沉降信息。

研究成果表明，InSAR-ITPIM动态沉降预计结果与实测GPS的沉降拟合度较好，其中最大平均误差达到了0.111m，最大均方根误差达到了0.135m。误差在限差范围内，有一定的实际应用价值。FLAC3D数值模拟的沉降规律与InSAR-ITPIM的沉降规律较符，说明了FLAC3D数值模拟在开采沉陷动态沉降模拟有一定的参考价值，可以为矿区采后治理和地表沉陷模拟提供理论依据。

The surface deformation caused by underground mining is time-dependent and highly nonlinear, and it will cause gradual damage to the surface structure during the underground mining process. Traditional monitoring methods have certain shortcomings. The main feature of differential synthetic aperture radar measurement technology (InSAR) is that it has high spatial resolution and high accuracy in a wide coverage area. Due to its unique advantages, this technology is widely used in ground deformation monitoring. However, in coal mining areas, large-scale subsidence of the surface will occur in a short period of time, resulting in inaccurate InSAR results and limiting its use in monitoring mining subsidence. Based on this, this paper proposes a data processing method that combines the SBAS-InSAR technology with the probability integration method used to predict mining subsidence to overcome these shortcomings. Combined with the improved knothe time function, a dynamic prediction model for the settlement of the mining area was established, and the dynamic change process of the surface settlement of the mining area was obtained. Mainly conducted the following research:

(1) First, use SBAS-InSAR technology to process 41 scenes sentienl-1A data covering a coal mine in northern Shaanxi, including image registration, filtering, unwrapping, and extraction of high-coherence points for regression analysis to separate deformation phase and error Phase, and through SVD decomposition and least square method to extract the time series cumulative settlement from the LOS to the mining area, obtain the settlement information of the stable boundary point on the edge of the subsidence basin in the mining area, and select the two GPS observation stations that coincide with the direction and inclination The accuracy of the boundary points was verified. It is found that the maximum residual error of the strike boundary point B12 is 3mm, and the maximum residual error of the tendency boundary point B14 is 6mm, both of which are within the tolerance range, indicating that the results of the boundary point of the subsidence basin are trustworthy.

(2) Because the static probability integration method cannot predict the dynamic mining subsidence of the mining area over time, this paper proposes a dynamic time probability integration prediction model that combines the improved power exponent knothe time function model with the static probability integration method. It is often difficult to obtain the model parameters of the static probability integration method. In this paper, the static probability integration model is combined with the boundary point deformation information obtained from the InSAR side view direction to establish the fitness function, and then the

differential evolution gray wolf optimization algorithm is used to optimize the probability of the mining area. The integral method predicts the parameters to be calculated. According to the LOS deformation of the boundary point time series obtained by InSAR, the redundant 

observation equation is established, and the model parameters of the improved knothe time function are obtained by the least square method. Thus, the InSAR-ITPIM dynamic probability integral prediction model is established to predict the surface subsidence during the mining process, and the predicted results are compared with the actual GPS results for verification.

(3) Combining the geological structure and rock layer information of the mining area, establish a Moore-Coulomb model to solve the unbalanced force through FLAC3D software, and select the excavation distance according to the stoping distance. Thus, the mining subsidence process of the working face is dynamically simulated, and the dynamic surface subsidence information of the working face is obtained.

The research results show that the predicted result of InSAR-ITPIM dynamic settlement is better than the actual GPS settlement. The maximum average error reaches 0.111m, and the maximum root mean square error reaches 0.135m. The error is within the tolerance range, which has certain practical application value. The settlement law of FLAC3D numerical simulation is consistent with that of InSAR-ITPIM, which shows that FLAC3D numerical simulation has certain reference value in dynamic settlement simulation of mining subsidence, and can provide theoretical basis for post-mining treatment and surface subsidence simulation of mining area.

[1]国家发展和改革委员会.煤炭工业发展“十一五”规划[J]. 2008中国煤炭企业信息化管理高峰论坛，2013, 1(1): 1-21.

[2]赵秋雁.科技创新与煤炭高效清洁利用[J].国际经济合作，2012, (6): 33-39.

[3]黎炜，陈龙乾，赵建林.我国煤炭开采对生态环境的破坏及对策[J].煤矿开采，2011, 20(5):35-37.

[4]杨秀敏，胡桂娟，李宁，等.煤研石山的污染治理与复垦技术[f].中国矿业，2008, 17(6):34-35.

[5]H. Y. Dai, J. Z. Wang, M. F. Cai, L. X. Wu, and Z. Z. Guo, “Seam dip angle based mining subsidence model and its application,” Int. J. Rock Mech. Mining Sci. vol. 39, no. 1, pp. 115–123, Jan. 2002.

[6]H. Kratzsch, Mining Subsidence Engineering. New York, NY, USA:Springer-Verlag, 1983, pp. 183–231.

[7] G. Ren, D. J. Reddish, and B. N. Whittaker, “Mining subsidence and displacement prediction using influence function methods,” Mining Sci.Technol. vol. 5, no. 1, pp. 89–104, May 1987.

[8] Q. Sun et al. “Slope deformation prior to Zhouqu, China landslide fromInSAR time series analysis,” Remote Sens. Environ. vol. 156, pp. 45–57,Jan. 2015.

[9]Q. Sun et al. “Characterizing sudden geo-hazards in mountainous areas by D-InSAR with an enhancement of topographic error correction,” Nat.Hazards, vol. 75, no. 3, pp. 2343–2356, Feb. 2015.

[10]C. C. Miguel, J. Andrew, and R. H. Hooper, “Surface deformation induced by water influx in the abandoned coal mines in Limburg, The Netherlands observed by satellite radar interferometry,” J. Appl. Geophys. vol. 88,pp. 1–11, Jan. 2013.

[11] J. Hu et al. “3D coseismic displacement of 2010 Darfield, New Zealand earthquake estimated from multi-aperture InSAR and D-InSAR measurements,” J. Geod. vol. 86, no. 11, pp. 1029–1041, Nov. 2012.

[12] J. Hu et al. “Resolving three-dimensional surface displacements from InSAR measurements: A review,” Earth-Sci. Rev. vol. 133, pp. 1–17,Jun. 2014.

[13] Dong S. Samsonov S. Yin H. et al. Time-series analysis of subsidence associated with rapid urbanization in Shanghai, China measured with SBAS InSAR method [J]. Environmental Earth Sciences, 2014, 72(3): 677-691.

[14] Osmanog1u B. Dixon T. H. Wdowinski S. et al. Mexico City subsidence observed with persistent scatterer InSAR [J]. International Journal of Applied Earth Observations&Geoinformation, 2011, 13(1): 1一12.

[15]孙亚飞.藏东南和祁连山冰川物质平衡的双站InSAR探测研究[J].测绘学报，2019,48(09):1203.

[16]Jin B. Kim S. W. Park H. J. et al. Analysis of ground subsidence in coal mining area using SAR interferometry [J]. Geosciences Journal, 2008, 12(3): 277-284.

[17] Berardino P, Fornaro G, Lanari R, et al. A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms[J]. Geoscience and Remote Sensing,IEEE Transactions on, 2002, 40(11): 2375-2383.

[18]Ferretti A, Colesanti C, Prati C, et al. Radar permanent scatters identification in urban area: target characterization and sub-pixel analysis[C].Proceedings of IEEE/ISPRS Joint Workshop 2001:Remote Sensing and Data Fusion over Urban Areas, November8-9, 2001,Rome, Italy.Rome:IEEE:52.

[19] 陈俊杰，王礼，郭延涛.基于概率积分法的矿山地表移动观测[J].测绘科学，2014,39(03):146-148+152.

[20]吕伟才，黄晖，池深深，韩必武.概率积分预计参数的神经网络优化算法[J].测绘科学，2019,44(09):35-41.

[21] 赵忠明，施天威，董伟，刘永良.灰色关联分析与BP神经网络的概率积分法参数预测[J].测绘科学，2017,42(07):36-40+51.

[22] 李培现，谭志祥，闫丽丽，邓喀中.基于支持向量机的概率积分法参数计算方法[J].煤炭学报，2010,35(08):1247-1251.

[23]查剑锋，冯文凯，朱晓峻.基于遗传算法的概率积分法预计参数反演[J].采矿与安全工程学报，2011,28(04):655-659.

[24]徐孟强，查剑锋，李怀展.基于PSO算法的概率积分法预计参数反演[J].煤炭工程，2015,47(07):117-119+123.

[25]G.M. Komaki,Vahid Kayvanfar. Grey Wolf Optimizer algorithm for the two-stage assembly flow shop scheduling problem with release time[J]. Journal of Computational Science,2015,8.

[26]Rogers,A.E. and Ingalls, R.P. Venus:Mapping the surface reflectivity by radar interferometry[J],Science,1969,(165):797-799

[27]Zisk, S.H. A new earth-based radar technique for the measurement of lunar topography[J],Moon,1972,(4):296-306

[28]Gabruel A K,Goldstein R M,Zebker H A.Mapping small elevation changes over large areas-Differential radar interfermetry[J].Journal of Geophysical Research Solid Earth,1989,94(B7):9183-9191.0

[29]Massonnet D，Rossi M，Carmona C,et,al.The displacement field of the Landers earthquakemapped by radar interfereometry[J].Nature,1993,(364):138-142.

[30]Massonnet D ， Briol P,Amaud A. Deflation of Mount Etna Monitored by spaceborne radar interferometry[J].Nature,1995,375:567-570.

[31] Carnec C,Delacourt C.There years of mining subsudence monitored by SAR interferometry,near Gardanne,Fance[J].Journal of Applied Geo-physics,2000,43(1):43-54.

[32] Ferretti A, Prati C, Rocca F. Permanent scatters in SAR interferometry[J]IEEE Transcations on Geoscience and Remote Sensing,2001,39(1)：8-20.

[33]Ferretti A,Colesanti C;Perssin D,et al.Evaluating the effect of the observation time on the distribution of SAR permanent scatterers[C]Proc of FRINGE 03,ESA-ESRIN,2003.

[34]穆家雷. 基于SBAS-InSAR 的深部硬石膏开采引起地表形变规律研究[D].中国地质大学（北京）,2018.

[35]Beradino P,Fornaro G,Lanari R,et al.A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms[J] .Geoscience & Remote Sensing IEEE Transactions on,2002,40(11):2375-2383.

[36]Mora O,Mallorqui J J,Broquetas A.Linear and nonlinear terrain deformation maps from a reduced set of interferometric SAR images[J].IEEE Transactions on Geoscience & Remote Sensing,2003,41(10):2243-2253.

[37] Balik Sanli F,Abdikan S,et al.Analysis of deformation patterns through advanced DINSAR techniques in Istanbul megacity[J].International Archives of the Photogrammetry Remote Sensing & S,2014,XL-7(7):19-21.

[38] Nadudvari A. Using radar interferometry and SBAS technique to detect surface subsidence relating to coal mining in Upper Silesia from 1993-2000 and 2003-2010[J].Environmental & Socio-economic Studies,2016,4(1):24-34.

[39]汪文杰， 贾东宁， 许佳立， 褚宏奎， 董晓睿. 全球海洋遥感卫星发展综述[J]. 测绘通报，2020(05):1-6.

[40]王超，刘智，张红，单新建.张北－尚义地震同震形变场雷达差分干涉测量[J].科学通报，2000,45(23):2550-2553.

[41]刘国祥，刘文熙 ，黄丁发 .InSAR技术及其应用中的若干问题[J].测绘通报，2001(08):10-12.

[42]李德仁， 廖明生，王艳.永久散射体雷达干涉测量技术[J].武汉大学学报（ 信息科版）,2004(08):664-668.

[43]尹宏杰. 基于 InSAR 的矿区地表形变监测研究[D].中南大学，2009.

[44]胡乐银，张景发，商晓青.SBAS-InSAR 技术原理及其在地壳形变监测中的应用[J].地壳构造与地壳应力文集，2010(00):82-89.

[45]刘欣，商安荣，贾勇帅，魏超.PS-InSAR 和 SBAS-InSAR 在城市地表沉降监测中的应用对比[J].全球定位系统，2016,41(02):101-105.

[46]赵盟. 基于SBAS-InSAR技术的矿区地表形变提取方法研究[D].河南理工大学，2017.

[47]陈秋计，张越，田柳新.基于剩余变形的采煤沉陷损毁土地动态复垦研究阴.煤炭技术，2019 38 (1) :4-6.

[48]Litwiniszyn J .Application of the equation of stochastic processes to mechanics of loose bodies[J].Archives of Mechanics, 1956, 8(4):393-411.

[49] Litwiniszyn J .Statistical methods in the mechanics of granular bodies[J].Rheologica Acta,1958, 1(3):146-150.

[50] Whittaker B N，Smith S F .Stability and Operational Aspects of Room and Pillar Mining in U.K. Sedimentary Iron-Ore Deposits[J].Advances in Mining Science&Technology, 1987,6(1):393-402.

[51]杨居荣，田润浓，赵玉霞，等.采煤塌陷地的生态复垦—以唐山开滦煤矿为例阴.中国环境科学，1999 ,9(1):85-90.

[52]刘宝琛，戴华阳.概率积分法的由来与研究进展田.煤矿开采，2016,21(2):1-3.

[53]张玉卓，仲惟林，姚建国.断层影响下地表移动规律的统计和数值模拟研究闭.煤炭学报，1989(1):23-31.

[54]郭增长，王金庄，戴华阳.极不充分开采地表移动与变形预计方法阴.矿山测量，2000. (3):35-36.

[55]闫大鹏. 基于D-InSAR技术监测云驾岭煤矿区开采沉陷的应用研究[D].中国地质大学（北京）,2011.

[56] Hongdong F，Xiaoxiong G，Junkai Y，et al. Monitoring Mining Subsidence Using A Combination of Phase-Stacking and Offset-Tracking Methods[J].Remote Sensing, 2015,7(7):9166-9183.

[57]刘一霖. 矿区开采沉陷大量级形变监测与反演分析[D].长安大学，2013.

[58]朱建军，邢学敏，胡俊，等.利用InSAR技术监测矿区地表形变明.中国有色金属学报，2011，21(10):2564-2576.

[59]甘洁，胡俊，李志伟，等.基于InSAR和地应变特征获取2015MW7.2级Murghab地震同震三维地表形变声明.中国科学：地球科学，2018 48 (10):1335-1351.

[60]王磊，张鲜妮，池深深，等.融合InSAR和GA的开采沉陷预计参数反演模型研究[J].武汉大学学报（信息科学版），2018 43(11):1635-1641.

[61]Wegmuller U, Strozzi T, Werner C, et al. Monitoring of mining-induced surface deformation in the Ruhrgebiet (Germany) with SAR interferometry: Geoscience and Remote Sensing Symposium, 2000. Proceedings. IGARSS 2000. IEEE 2000 International, 2000[C].

[62]Jin Baek, Sang-Wan Kim, Hyuck-Jin Park,Hyung Jung, et al. Analysis of ground subsidence in coal mining area using SAR interferometry[J]. Geosciences Journal, 2008,12(3), 277-284.

[63]Ng A H, Ge L, Zhang Ket. Deformation mapping in three dimensions for underground mining using In SAR – Southern highland coalfield in New South Wales, Australia[J]. International Journal of Remote Sensing, 2011,32(22):7227-7256.

[64]Bateson L, Cigna F, Boon D. The application of the Intermittent SBAS (ISBAS) InSAR method to the South Wales Coalfield, UK[J]. International Journal of Applied Earth Observation and Geoinformation, 2015, 34: 249-257.

[65]Pawluszek-Filipiak, K.; Borkowski, A. Integration of DInSAR and SBAS Techniques to Determine Mining-Related Deformations Using Sentinel-1 Data: The Case Study of Rydułtowy Mine in Poland. Remote Sens. 2020, 12, 242.

[66]马飞. InSAR技术及其在矿区大梯度沉陷监测中的应用研究[D].西安科技大学，2013.

[67]Chaoying Zhao, Zhong Lu, Qin Zhang. Time-series deformation monitoring over mining regions with SAR intensity-based offset measurements[J]. Remote Sensing Letters, 2012, 7(7):9166-9183.

[68]范洪冬， 顾伟， 秦勇， 等. 基于 D-In SAR 和概率积分法的矿区大变形地表沉降提取方法[J]. 中国有色金属学报， 2014,24(04):1242-1247.

[69]Fan H, Gao X, Yang J, et al. Monitoring Mining Subsidence Using A Combination of Phase-Stacking and Offset-Tracking Methods[J]. Remote Sensing, 2015,.61(11):1617-20.

[70]牛玉芬. SAR/InSAR技术用于矿区探测与形变监测研究[D].长安大学，2015.

[71]Huang J, Deng K, Fan H, et al. An improved pixel-tracking method for monitoring mining subsidence[J]. Remote Sensing Letters, 2016,7(8):731-740.

[72]Fan H, Lu L, Yao Y. Method Combining Probability Integration Model and a Small Baseline Subset for Time Series Monitoring of Mining Subsidence. Remote Sensing. 2018; 10(9):1444.

[73]Yang Z, Li Z, Zhu J, et al. Retrieving 3-D Large Displacements of Mining Areas from a Single Amplitude Pair of SAR Using Offset Tracking[J]. Remote Sensing,2017, 9: 3384.

[74] A. K. Gabriel, R. M. Goldstein, and H. A. Zebker, “Mapping small elevation changes overlarge areas: differential radar interferometry,” Geophys. Res. Lett. 94, 9183–9191 (1989).

[75]李晖，肖鹏峰，冯学智，林金堂，汪左，满旺.基于重轨 InSAR 的积雪深度反演方法[J].冰川冻土，2014,36(03):517-526.

[76] C. W. Chen and H. A. Zebker, “Phase unwrapping for large SAR interferograms: statistical segmentation and generalized network models,” IEEE Trans. Geosci. Remote Sens. 40(8),1709–1719 (2002).

[77]金星，邵珠超，王盛慧.一种基于差分进化和灰狼算法的混合优化算法[J].科学技术与工程，2017,17(16):266-269.

[78] 高延法， 贾君莹， 李冰， 等. 地表下沉衰减函数与塌陷区稳定性分析[J]. 煤炭学报， 2009, 34(7): 892－896.

[79] HU Q F, CUI X M, WANG G, et al. Key Technology of predicting dynamic surface subsidence based on Knothe time function[J]. Journal of Software, 2011, 6(7): 1273－1280.

[80] 陈庆发， 牛文静， 刘严中， 等. Knothe 模型改进及充填开采岩层移动动态过程分析[J]. 中国矿业大学学报， 2017, 46(2): 250－256.

[81] 王军保， 刘新荣， 刘小军. 开采沉陷动态预测模型[J]. 煤炭学报， 2015, 40(3): 516－521.

[82] 常占强， 王金庄. 关于地表点下沉时间函数的研究－改进的克诺特时间函数[J]. 岩石力学与工程学报， 2003,22(9): 1496－1499.

[83]何国清 ，杨 伦 ，凌赓娣 ，等 .矿山开采沉陷学 [M ].徐 州： 中国矿业大学出版社 , 1994.

[84]Jiang, L.S.; Wang, P.; Zhang, P.P.; Zheng, P.P.; Xu, B. Numerical analysis of the effects induced by normal faults and dip angles on rock bursts. C. R. Mecanique 2017, 345, 690–705.

[85]J. Hu, Z.W. Li, X.L. Ding, J.J. Zhu, L. Zhang, Q. Sun,Resolving three-dimensional surface displacements from InSAR measurements: A review,Earth-Science Reviews,Volume 133,2014,Pages 1-17.

[86]Z. Yang et al. "An InSAR-Based Temporal Probability Integral Method and its Application for Predicting Mining-Induced Dynamic Deformations and Assessing Progressive Damage to Surface Buildings," in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 11, no. 2, pp. 472-484, Feb. 2018,