Source wavelet independent time-domain full waveform inversion(FWI) of cross-hole radar data

In recent years, waveform inversion is one of the hot methods because it can provide sub-wavelength images. In the inversion of field data, waveform inversion requires a good estimation of the source wavelet to reach the global convergence. Traditional method is that the source wavelet is added into the inversion as a new unknown parameter and updated with iterations. When the results of inversion are same to the true models, the estimated source wavelet is same to the true source wavelet. The method is effective in the inversion of synthetic data, but it doesn't perform well and need lots of intervention in the field data inversion. In this paper, we realize a source-independent time-domain waveform inversion. A new objective function is based on the convolved wavefields. The observed wavefields are convolved with a reference trace from the modeled wavefields, and then the modeled wavefields are convolved with a reference trace from observed wavefields. In that case, the source wavelets of the field and modeled wavefields are equally convolved with both terms in the objective function, and thus, the effects of the source wavelet are removed. We test the algorithm on layered media with two embedded cylindrical inclusions. Permittivity and conductivity are simultaneously updated. Though the results of permittivity perform much better than the results of conductivity, the overall results are not good enough. This is because we have to do convolution and cross-correlation to compute the gradients. These convolution and cross-correlation operations increase the nonlinearity of the inversion. Therefore, the source-independent waveform inversion requires more accurate initial models.