Full-waveform inversion algorithm for interpreting crosshole radar data: a theoretical approach

Ground-penetrating radar is a useful tool for civil and environmental engineering fields because of its high resolving power and non-destructive measurements. This paper presents a method of full-waveform inversion of borehole radar data for imaging permittivity structures. The inversion algorithm is based on a conjugate gradient search for the minimum of an error functional relating to the difference between measured and predicted data. A small model perturbation in the functional can be efficiently calculated by propagating the data error back into the model in reverse time and correlating the field generated by the back-propagation with the corresponding incident field at each point. A finite difference time domain (FDTD) method is used for solving Maxwell’s equations to obtain incident electromagnetic wavefields. Back-propagated wavefields satisfy adjoint Maxwell’s equations, which are stable in reverse time and can be solved by the same FDTD scheme. The imaging scheme is applied to crosshole radar configuration, thereby demonstrating its capability to reconstruct permittivity structures. Tests on a two-dimensional synthetic model produce good images of target scatterers and show stable convergence.