Comparison of full-waveform inversion approaches for crosshole GPR: A synthetic study

Crosshole ground-penetrating radar (GPR) is an effective tool for characterizing shallow subsurface electromagnetic properties. Ray-based methods utilize only partial information from GPR data, such as the first arrival times, and their resolution is limited to the first Fresnel zone. In contrast, full-waveform inversion (FWI) exploits the entire waveform information and can achieve subwavelength resolution. FWI is typically solved through iterative optimization, in which the search direction and step-length are two key factors for model updating. Although numerous methods have been developed to calculate these two factors for different GPR applications, few studies have examined their differences in performance and accuracy. Two commonly used search directions are conjugate gradient (CG) and limited-memory BFGS (L-BFGS). For each direction, the permittivity and conductivity step-lengths can be calculated using either two separate step-lengths or one step-length combined with a scaling factor. Here, we investigate and compare these four approaches using crosshole GPR data generated from a challenging synthetic model. Since FWI strongly depends on the initial model, two types of initial models are considered: a smoothed representation of the true model using a Gaussian filter, and a model obtained from ray-based inversion. Synthetic experiments are performed using these two initial models to evaluate the permittivity and conductivity reconstruction performance of the four approaches in the time domain. Whereas L-BFGS with combined step-length achieves the lowest final root-mean-square value and the highest computational efficiency, the CG with separate step-lengths provides the most accurate model reconstruction. Additional experiments using synthetic data with added noise at signal-to-noise ratios of 30 and 10 dB show that both CG with separate step-lengths and L-BFGS with combined step-length remain stable under the considered noise levels. The former retains a slight advantage in reconstruction accuracy, whereas the latter maintains its advantage in computational efficiency.