Recovering material properties of the subsurface using ground-penetrating radar (GPR) data of finite bandwidth with missing low frequencies and in the presence of strong attenuation is a challenging problem. We have adopted three nonlinear inverse methods for recovering electrical conductivity and permittivity of the subsurface by joining GPR multioffset and electrical resistivity (ER) data acquired at the surface. All of the methods use ER data to constrain the low spatial frequency of the conductivity solution. The first method uses the envelope of the GPR data to exploit low-frequency content in full-waveform inversion and does not assume structural similarities of the material properties. The second method uses cross gradients to manage weak amplitudes in the GPR data by assuming structural similarities between permittivity and conductivity. The third method uses the envelope of the GPR data and the cross gradient of the model parameters. By joining ER and GPR data, exploiting low-frequency content in the GPR data, and assuming structural similarities between the electrical permittivity and conductivity, we are able to recover subsurface parameters in regions where the GPR data have a signal-to-noise ratio close to one.

中文翻译：

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全波形探地雷达和电阻率数据的联合反演—第2部分：通过包络变换和交叉梯度增强低频

使用具有有限带宽的地探雷达（GPR）数据来丢失地下低频的材料数据，并且缺少低频并且存在强衰减，这是一个具有挑战性的问题。我们通过结合GPR多偏移量和在地面获得的电阻率（ER）数据，采用了三种非线性逆方法来恢复地下的电导率和介电常数。所有方法都使用ER数据来约束电导率解决方案的低空间频率。第一种方法使用GPR数据的包络来利用全波形反演中的低频内容，并且不假定材料特性的结构相似性。第二种方法通过假设介电常数和电导率之间的结构相似性，使用交叉梯度来管理GPR数据中的弱振幅。第三种方法使用GPR数据的包络和模型参数的交叉梯度。通过合并ER和GPR数据，利用GPR数据中的低频成分，并假设介电常数和电导率在结构上相似，我们能够恢复GPR数据信噪比接近的区域的地下参数到一个。