Velocity is a key parameter determining the migration imaging resolution of ground penetrating radars (GPR).The method combining minimum image entropy and migration usually estimates the medium velocity by calculating the entropy curves using the overall migration profile as a fixed window.Therefore,such a method is not applicable to non-uniformly distributed media.Moreover,for this method,a too-high or too-low test velocity will make the convergence position of hyperbolic diffracted waves go beyond the fixed window,thus reducing the estimation accuracy.This study proposed a minimum entropy method based on a velocity-controlled moving window,in which the calculation window in the migration profile is accurately controlled by the test velocity.Then,this method was combined with inverse time migration to estimate the optimal migration velocity.By automatically adjusting the position of the calculation window using the trial velocity,this method keeps the convergence position of hyperbolic diffracted waves at the center of the calculation window.In this manner,stable and accurate entropy curves can be obtained.By comparing the calculation results with those of the minimum entropy method based on a fixed window,this study verified the correctness and effectiveness of the minimum entropy method based on a velocity-controlled moving window for a typical hyperbolic diffracted wave.As revealed by numerical experiments and the tests of measured data,compared with the minimum entropy method based on a fixed window,the minimum entropy method based on a velocity-controlled moving window can keep the convergence position of hyperbolic diffracted waves accurately at the center of the calculation window,yielding more stable entropy curves,lower computational complexity,higher estimation accuracy of the migration velocity,and better imaging performance of reverse time migration.
席宇何, 王洪华, 王欲成, 吴祺铭. 基于速度移动窗的最小熵法在GPR逆时偏移中的应用[J]. 物探与化探, 2023, 47(5): 1250-1260.
XI Yu-He, WANG Hong-Hua, WANG Yu-Cheng, WU Qi-Ming. Application of the minimum entropy method based on a velocity-controlled moving window to the reverse time migration of ground-penetrating radars. Geophysical and Geochemical Exploration, 2023, 47(5): 1250-1260.
Zhen Z Z, Wang J G, Shi X X. Ground penetrating radar data imaging via the 2D finite-diffrence migration method[J]. Coal Geology & Exploration, 2007, 35(6):57-60.
Feng D S, Zhang B, Dai Q W, et al. The application of the improved linear transformation of finite difference migration basedon the velocity estimation in the GPR date processing[J]. Chinese Journal of Geophysics, 2011, 54(5):1340-1347.
Cui F, Li S Y, Wang L B. Migration velocity estimation of GPR based on cross-correlation and least square fitting[J]. Progress in Geophysics, 2018, 33(1):353-361.
Deng X Y, Wang T. The measurement of relative dielectic constant of media in GPR exploration[J]. Geophysical and Geochemical Exploration, 2009, 33(1):43-45.
Dai Q W, Ning X B, Zhang B. Common midpoint gather constraint-based impedance inversion of ground penetrating radar[J]. Coal Geology & Exploration, 2020, 48(3):211-218.
Zhang C M, Zhang F K, Li Y. Study of Full Waveform Inversion of Advance Tunnel Geological Prediction by Ground Penetrating Radar.Tunnel Construction[J]. Tunnel Construction, 2019, 39(1):102-109.
[9]
Feng D S, Wang X, Zhang B. Improving reconstruction of tunnel lining defects from ground-penetrating radar profiles by multi-scale inversion and bi-parametric full-waveform inversion[J]. Advanced Engineering Informatics, 2019, 41:100931.
doi: 10.1016/j.aei.2019.100931
Li X J, Wang W H, Guo X B, et al. Comparison of regularization methods for full-wave-form inversion[J]. Oil Geophysical Prospecting, 2022, 57(1):129-139.
[11]
Gaber A, Gemail K S, Kamel A, et al. Integration of 2D/3D ground penetrating radar and electrical resistivity tomography surveys as enhanced imaging of archaeological ruins:A case study in San El-Hager (Tanis) site,northeastern Nile Delta,Egypt[J]. Archaeological Prospection, 2021, 28(2):251-267.
doi: 10.1002/arp.v28.2
[12]
Liu H, Long Z J, Tian B, et al. Two-Dimensional Reverse-Time Migration Applied to GPR With a 3-D-to-2-D Data Conversion[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2017, 10(10):4313-4320.
doi: 10.1109/JSTARS.4609443
[13]
Liu H, Long Z J, Han F, et al. Frequency-Domain Reverse-Time Migration of Ground Penetrating Radar Based on Layered Medium Green's Functions[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2018, 11(8):2957-2965.
doi: 10.1109/JSTARS.4609443
[14]
Zhu W Q, Huang Q H, Liu L B, et al. Three-Dimensional Reverse Time Migration of Ground-Penetrating Radar Signals[J]. Pure and Applied Geophysics, 2020, 177(2):853-865.
doi: 10.1007/s00024-019-02341-x
[15]
Al-Nuaimy W, Huang Y, Nakhkash M, et al. Automatic detection of buried utilities and solid objects with GPR using neural networks and pattern recognition[J]. Journal of applied Geophysics, 2000, 43(2-4):157-165.
doi: 10.1016/S0926-9851(99)00055-5
[16]
Shihab S, Al-Nuaimy W. Radius estimation for cylindrical objects detected by ground penetrating radar[J]. Subsurface sensing technologies and applications, 2005, 6(2):151-166.
doi: 10.1007/s11220-005-0004-1
[17]
De Vries D, Berkhout A J. Velocity analysis based on minimum entropy[J]. Geophysics, 1984, 49(12):2132-2142.
doi: 10.1190/1.1441629
[18]
Xu X Y, Miller E L, Rappaport C M. Minimum entropy regularization in frequency-wavenumber migration to localize subsurface objects[J]. IEEE Transactions on Geoscience and Remote Sensing, 2003, 41(8):1804-1812.
doi: 10.1109/TGRS.2003.813497
Xiu Z J, Chen J, Fang G Y, et al. Ground penetrating radar imaging based on F-K migration and minimum entropy method[J]. Journal of Electronics and Information Technology, 29(4):827-830.
[20]
Zhou H L, Wan X, Li W, et al. Combining FK filter with minimum entropy Stolt migration algorithm for subsurface object imaging and background permittivity estimation[J]. Procedia Engineering, 2011, 23:636-641.
doi: 10.1016/j.proeng.2011.11.2558
Wu X L, Zheng W J, Hu X S, et al. Water conservancy detection method and application based on migration locationing technology[J]. Journal of Hebei University of Science and Technology, 2019, 40(4):317-324.
[22]
Bradford J H, Privette J, Wilkins D, et al. Reverse-time migration from rugged topography to image ground-penetrating radar data in complex environments[J]. Engineering, 2018, 4(5):661-666.
doi: 10.1016/j.eng.2018.09.004
Wang M L, Liao T Y, Wang H H, et al. 3D reverse time migration of ground penetrating radar based on finite difference time domain method[J]. Progress in Geophysics, 2019, 34(4):1671-1678.
Xue G X, Deng S K, Liu X J. An application of reverse-time migration in the ground-penetrating radar data processing[J]. Coal Geology & Exploration, 2004, 32(1):55-57.
Wang H H, Gong J B, Liang Z H, et al. Three-dimensional reverse time migration of ground pentrating radar data based on electromagnetic wave attenuated compensation[J]. Chinese Journal of Geophysics, 2021, 64(6):2141-2152.
Gong J B, Wang H H, Wang M L, et al. The application of reverse time migration to GPR data processing[J]. Geophysical and Geochemical Exploration, 2019, 43(4):835-842.
Zhu Y F, Wang Q R, Zhang Q, et al. FDTD numeric technique-based analysis of the influence of reverse obstacle on data acquisition of ground penetrating radar[J]. Coal Geology & Exploration, 2016, 44(5):149-154.
[29]
Wu H S, Barba J. Minimum entropy restoration of star field images[J]. IEEE Transactions on Systems,Man,and Cybernetics,Part B (Cybernetics), 1998, 28(2):227-231.
doi: 10.1109/3477.662762
Jiang Q L, Lu J P, Sun T, et al. Defect detection of pole tower grounding body based on GPR offset imaging[J]. High Voltage Engineering, 2021, 47(1):322-330.
Lin Z Q, Wang L, Fan B B. Kirchhoff migration imaging algorithm of ground penetrating radar based on image entropy[J]. Fire Control & Command Control, 2020, 45(12):97-100.