Full-Waveform Inversion For Subsurface Penetrating Radar

Subsurface Penetrating Radar(SPR)utilizes electromagnetic waves to detect the structures and targets in subsurface space.Because of no damage to the medium and the high resolution which can reach millimeter level,SPR has gradually developed into an important subsurface nondestructive detection technology and has been widely used in military security,star detection,municipal engineering and other fields.With the deepening of research and the expansion of application,the demand for detection gradually rises from the information of target spatial position,shape,interface,etc.to the accurate electrical parameter information of subsurface spatial structure or target.General imaging is based on synthetic aperture imaging technology,which mainly utilizes part of wave field information such as phase and amplitude of echo,but it is difficult to make further breakthroughs in imaging result accuracy and result information dimension.Based on the framework of optimization theory,full-waveform inversion(FWI)makes use of the full waveform information.By optimizing the matching between simulated data and observed data,it has great potential to provide refined subsurface structure and accurate quantitative distribution information of electrical parameters,and has become an important research direction in the data analysis and processing of SPR.However,the surface penetrating detection mode is limited to collecting information on one side,the accessible observation angle is far from the required for complete inversion,and the echo information is not complete.Data inversion is faced with problems of solving nonlinearity and ill-posedness,and the inversion results are not stable and the accuracy is lower than expected.To solve above two problems,aiming at more reliable and accurate inversion results,this paper researches the FWI method of SPR in time domain.Firstly,due to the instability and mass computation of SPR FWI,a stable and efficient FWI based on 2D and 3D data is realized by adopting suitable optimization method.Comprehensive consideration of computational efficiency and stability,permittivity inversion is solved by nonlinear conjugate gradient method while,synchronous inversion on permittivity and conductivity is optimized with Limited-Memory Broyden–Fletcher–Goldfarb–Shanno(L-BFGS)and search step determined by line search.Furthermore,according to the results of two-dimensional inversion,the main problems faced by the classical FWI algorithm are analyzed.On account of the data characteristics and inversion performance,the problem is focused on the depth section where the target is located,and the quantitative relative permittivity distribution of the target is obtained with low computational cost and fast convergence for 3D SPR,thus solving the application problem of 3D inversion in limited scenes.Secondly,aiming at the problem that FWI is easy to fall into local optimal solution due to its strong nonlinearity,the frequency multi-scale inversion method is researched.Firstly,the strategy of frequency band selection is proposed,and then the inversion results with different frequency bands are analyzed.Based on the above,the multi-scale inversion of SPR is realized,which obviously improves the stability and accuracy of inversion result and reduces the dependence on the initial model.Finally,the anti-noise performance of frequency multi-scale inversion method is analyzed,and the results show that the multi-scale method has strong adaptability to noisy data.Thirdly,focusing on the ill-posed problem of FWI,the regularization constrained FWI method is studied.Firstly,in view of the distribution characteristics of subsurface spatial media,the FWI method with total variation(TV)regularization constraint is researched,which preserves the target boundary and suppresses the oscillation artifacts in flat background.However,the inversion results constrained by TV regularization have the staircase effect at the smooth area.In order to alleviate this problem and further suppress artifacts,bilateral total variation(BTV)regularization constraint based FWI method is proposed,which improves the reconstruction accuracy of permittivity distribution of subsurface medium.In addition,the standard BTV function adopts a constant weight factor,which can’t give attention to both the smoothing effect at the intra-region and the edge preserving effect.Aiming at this limitation,an adaptive weight matrix is designed,which provides soft-recognition of flat region and edges.Experimental results show that the FWI with adaptive BTV regularization constraint further improves the inversion accuracy.