Full waveform inversion based on inequality constraint for cross-hole radar

Abstract

Cross-hole radar is an effective method for geophysical exploration of underground geological conditions. Besides cross-hole radar, some geological information can be obtained by other methods, such as preliminary geological survey, geologic drilling and long-distance geophysical prospecting. This information can work as priori information to help interpret cross-hole radar detection data. Full waveform inversion (FWI) is an advanced inversion method for cross-hole radar, having higher resolution than the ray tomography method. However, traditional FWI for cross-hole radar takes less advantage of the prior information. Therefore, the introduction of the priori information into FWI is worthy of in-depth study to improve inversion quality. Here we use a special penalty function to impose inequality constraint on the objective function, and then calculate a new update step length value different from the traditional FWI. We use this method to introduce the priori information and improve the accuracy and stability of FWI. The reasonable value range of weight coefficients is discussed, which can control the strength of inequality constraint. Several inversion examples are designed to validate the effect of this improved FWI method. The inversion examples for synthetic and field data show that FWI based on inequality constraint for cross-hole radar has better inversion effect than the traditional FWI. To a certain extent, the introduction of inequality constraint can constrain inversion process, improve the inversion stability and provide higher precision inversion results.