基于改进全变差正则化的GPR多尺度全波形双参数同步反演

针对探地雷达（GPR）双参数全波形反演中电导率反演精度差、双参数存在串扰现象、反演计算量大、易陷入局部极值等问题.作者将具有多参数调节功能的L-BFGS算法引入到GPR时间域全波形反演中，它避免了对Hessian矩阵的直接存储与精确求解，减小了存储量和计算量.结合参数调节因子的选取，有效减小了同步反演时介电常数与电导率的串扰影响，在不降低介电常数反演精度的前提下，提高电导率参数的反演精度.通过在反演目标函数中加载改进全变差正则化方法，提高了反演的稳定性，使目标体边缘轮廓更加清晰.首先以简单模型为例，对比了单尺度反演与多尺度串行反演策略的优劣，说明多尺度串行反演有利于逐步搜索全局最优解；而开展参数调节因子的选取实验，说明合适的参数调节因子可以有效改善介质电导率的反演精度；测试了不同正则化的反演效果，表明改进全变差正则化能提高反演稳定性，显著降低模型重构误差.最后，分别对含噪合成数据和实测数据进行了反演测试，说明本文提出的多尺度、双参数反演具有较强的鲁棒性，能提供更丰富的信息约束，重构图像界面清晰、反演效果好.

GPR multiple-scale full waveform dual-parameter simultaneous inversion based on modified total variation regularization

The dual-parameter Full Waveform Inversion (FWI) of Ground Penetrating Radar (GPR) needs a vast amount of calculation and can easily fall into a local minimum. In addition, the crosstalk noise caused by coupling the permittivity and conductivity can affect the accuracy of the inversion for conductivity. To solve these problems, this study introduces the Limited-memory Broyden-Fletcher-Goldfarb-Shanno(L-BFGS)algorithm with multiple-parameter adjustment function into the time-domain full waveform inversion of GPR, which avoids the direct storage and accurate solution of the Hessian matrix, and reduces the storage and calculation. Combined with the selection of parameter adjustment factors, the effects of the crosstalk with the permittivity and the conductivity during synchronous inversion are reduced, and the inversion accuracy of the conductivity parameter is improved without reducing the accuracy of the reconstruction permittivity. By loading the Modified Total Variation regularization (MTV) method in the inversion, the stability of the inversion is enhanced, and the edge contour of the target body becomes clearer. First of all, taking a simple model as an example, we compare the advantages and disadvantages of single-scale inversion and multi-scale serial inversion strategies, and the results show that multiple-scale serial inversion is beneficial to step-by-step search for global optimal solution. Then, the experiment of parameter adjustment factor is carried out to demonstrate that the appropriate adjustment factor can effectively improve the inversion accuracy of dielectric conductivity, and the test of the inversion effect with different regularization shows that the improved total variation regularization can effectively improve the stability of inversion and significantly reduce the reconstruction error of the model. Finally, the full waveform inversion of the synthetic noisy data and field data shows that the multiple-scale dual-parameter inversion proposed in this paper has strong robustness, can provide more information constraints, and works effectively in reconstructing the permittivity and conductivity distribution.