Full Waveform Inversion of Cross-hole Radar Data Using Envelope Objective Function

The full waveform inversion (FWI) has been used as a high resolution imaging method for cross-hole radar inversion implementation, however, when FWI is used to process field data, it encounters a variety of problems and causes the inversion to fall into a local minimum. One problem is that the GPR data lacks low frequency information. An effective way is to provide an accurate initial model for FWI. The fact is that the underground media is unknown which results in difficult to obtain ideal result in FWI. By means of the derivation of the objective function, the gradient formula of the envelope waveform inversion (EWI) is derived by taking the derivation of the EWI misfit function with respect to the model parameter. By comparing the inversion results of the EWI with that of the traditional FWI without low-frequency information in the observed GPR data, we found that the EWI can effectively restore missing low-frequency information and has better inversion ability for low-frequency missing data.