Subgrade subsurface anomalous body full-waveform inversion based on ground-penetrating radar
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摘要:
路面塌陷及地下空洞隐患往往较为隐蔽且事发突然，造成了人们生命和财产的巨大损失，对于道路塌陷及地下空洞隐患的检测分析显得至关重要。探地雷达(Groud Penetrating Radar, GPR)因其具有精度高、效率快、连续无损、实时成像等优点，是目前城市道路塌陷隐患探测的主要方法。针对GPR传统目标函数全波形反演(Full Waveform Inversion, FWI)中激励源子波估计不准确而导致反演准确性和可靠性降低的问题，提出了一种褶积型目标函数FWI算法。对于路面塌陷及地下空洞2种情况，通过建立合成数据模型，与传统目标函数FWI的反演结果进行对比，说明了褶积型目标函数FWI算法在激励源子波估计不准确的情况下依然可以得到良好的反演结果，验证了该算法的有效性；最后将该算法用于2组不同灾害类型的GPR实测数据中，分析反演得到的地下介质相对介电常数分布情况，验证了褶积型目标函数FWI算法对于实测数据的实用性，从而为路基地下异常体探测提供理论依据。
Abstract:The hidden dangers of road collapse and underground voids are usually difficult to notice and easy to occur in sudden. They have caused huge losses in people's lives and properties. Therefore, the detection and analysis of road collapse and underground voids are crucial. The ground-penetrating radar (GPR) is the main method for detecting the hidden dangers of urban road collapse currently by virtue of its high accuracy, high efficiency, continuous non-destructiveness and real-time imaging. A convolution type objective function FWI algorithm was proposed to solve the problem of the lower inversion accuracy and practicability caused by the inaccurate estimation of GPR conventional objective function full-waveform inversion (FWI). For the two situations, i.e., road collapse and underground voids, synthetic data models were established, and compared with the inversion results obtained using the conventional objective function FWI, which indicated that the convolution objective function FWI algorithm can still provide favorable inversion results under the condition of inaccurate excitation source estimation. Accordingly, the effectiveness of the algorithm was verified. Finally, the algorithm was used in the GPR measured data of the two groups of different defect types, and the relative dielectric constant distribution of the underground medium was obtained through analysis and inversion, which verified the practicability of the convolution type objective function FWI algorithm for measured data. In this way, the theoretical basis related to the underground anomalous body detection for the subgrade was provided, and guidance was offered for practical production.
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图 1 路面塌陷异常相对介电常数分布
Fig. 1 Relative dielectric constant distribution in case of road collapse exceptions
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图 3 路面塌陷异常传统目标函数和褶积型目标函数FWI结果对比
Fig. 3 Comparison between results from conventional objective function and convolution type objective function
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图 4 路面塌陷异常FWI重构误差曲线
Fig. 4 Error curve of ground surface collapse model reconstruction
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图 5 地下空洞异常相对介电常数分布
Fig. 5 Relative dielectric constant distribution in case of underground void exceptions
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图 8 地下复杂介质模型重构误差曲线
Fig. 8 Error curve of reconstruction for underground complex medium models
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图 11 实测数据全波形反演介电常数分布
Fig. 11 Dielectric constant distribution in full-waveform inversion for measured data
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图 13 实测数据全波形反演介电常数分布
Fig. 13 Dielectric constant distribution in full-waveform inversion for measured data
表 1 合成数据全波形反演效率对比
Table 1 Comparison of full-waveform inversion efficiency for synthetic data
算法 网格大小 使用道数 记录时长/ns 迭代次数 单次迭代耗时/s 总耗时/s 传统算法 120×300 300 30 20 45.234 3 1 885.363 8 本文算法 120×300 300 30 20 47.234 6 1 269.668 5 
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表 2 合成数据全波形反演效率
Table 2 Full-waveform inversion efficiency for synthetic data
网格大小 使用道数 记录时长/ns 迭代次数 单次迭代耗时/s 总耗时/s 200×400 200 40 20 156.834 0 4 186.338 7
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表 3 实测数据全波形反演效率
Table 3 Full-waveform inversion efficiency for measured data
网格大小 使用道数 记录时长/ns 迭代次数 单次迭代耗时/s 总耗时/s 实测1 200×200 200 40 40 35.590 2 1 502.007 3 实测2 200×400 400 60 40 247.106 4 11 723.320 0
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