Source-independent time-domain waveform inversion of cross-hole GPR data

Recently, waveform inversion is one of the most popular methods because it can provide sub-wavelength images. In the inversion of field data, the source wavelet must be estimated. Traditionally, the source wavelet is added in the inversion as a new unknown parameter and updated with iterations. When the results of the inversion are the same as the true models, the estimated source wavelet is same as the true source wavelet. The method is useful in the inversion of synthetic data. But it does not perform well and needs a lot of intervention if the signal-to-noise ratio of field data is not high. In this paper, we realize a source-independent time-domain waveform inversion. The object function of this algorithm consists of the convolution of the modeled data with a reference trace from the field data, and the convolution of the field data with a reference trace from the modeled data. In this way, the effects of the source wavelets are removed. For the inversion of synthetic data, the permittivity and conductivity are simultaneously updated and the results obtained show that the algorithm is effective. Finally, we apply the algorithm to field data.