Improving reconstruction of tunnel lining defects from ground-penetrating radar profiles by multi-scale inversion and bi-parametric full-waveform inversion

Abstract

Complex irregular defects of tunnel linings under complicated geological conditions cannot be accurately reconstructed with the traditional full-waveform inversion (FWI) method due to their irregular geometrical characteristics and complex dielectric properties. Because of extensive inversion calculations and high memory requirements, the traditional FWI method is very sensitive to the initial model and plunge into a local minimum or cycle skipping. To solve this problem, a novel ground-penetrating radar (GPR) FWI method involving two parameters (i.e. permittivity and conductivity) is proposed for improving reconstruction accuracy of lining defects using the total variation (TV) regularization. First, the Delaunay unstructured triangular mesh in finite element time-domain (FETD) method is employed to perform GPR forward modeling, and then the total-variation model constraint and multi-scale inversion strategy are implemented during execution of the conjugate gradient (CG) algorithm, which facilitates the quick search for the global optimal minimum value, thus guaranteeing the avoidance of the ill-posed problem during the inversion process. Accordingly, the detailed features of lining defects can be characterized and reconstructed even for those complicated geological conditions, more specifically, the results show that, with fewer iterations (up to 59 times less), the proposed method present a lower reconstruction error both on permittivity (up to 12.05% lower) and conductivity (up to 7.35% lower). From a comparison of the inversion results and the model, it can be concluded that the proposed FWI algorithm can effectively eliminate the non-physical oscillation and artifacts in the image reconstruction, which may significantly improving the accuracy of defects interpretation and assessing the severity of complex defects.