Angle-corrected GPR hyperbolic fitting models for improved parameter estimation

Abstract

Ground-penetrating radar (GPR) is commonly employed as a non-destructive technique for detecting subsurface cylindrical objects such as pipes, cables, rebars, and tree roots. Hyperbolic features generated in GPR radargrams are often used to estimate key parameters like burial depth, object radius, and electromagnetic wave velocity. However, traditional approaches frequently rely on the assumption that GPR traverses are perpendicular to the alignment of target—an assumption or a negligence that is not always valid in real-world scenarios. To address this limitation, a novel method is introduced for simultaneously estimating the orientation and burial depth of pipes, as well as wave velocity, from the hyperbolic patterns observed in GPR data. The method innovates by incorporating an angle correction index into the classical hyperbolic fitting model. This modified model is then formulated as an optimization problem, which is solved using a hybrid approach combining the Multi-Verse Optimizer (MVO) and Gradient Descent (GD) algorithms. A unique index, termed the “C-value,” is introduced to quantitatively analyse the influence of oblique angles on the hyperbolic fitting models. Two distinct fitting models are validated through both simulation and field experiments. The study also scrutinizes the impact of varying pipe radius and burial depth on the accuracy of parameter estimation at different pipe orientation. The methodology presented herein enables the simultaneous estimation of burial depth, wave velocity, and pipe orientation directly from hyperbolic fitting—a significant advancement, as orientation is typically assumed as a known input yet is often challenging to ascertain obtain in practical field situations.