Multi-Layer Statistical Dependence of Weak Magnetic Signals in Non-Contact Pipeline Inspection: Controlled Experiments and Finite Element Analysis

Buried pipelines require reliable non-destructive inspection, whereas weak magnetic signals measured at the ground surface are strongly affected by lift-off values, material interfaces, and environmental noise. This study investigates the lift-off-dependent statistical dependence of magnetic field profiles generated by a controlled equivalent magnetic dipole source in an X80 steel pipeline. A current-carrying coil was used as a reproducible source surrogate, and axial magnetic-field profiles were measured at lift-off values of 0–150 mm using fluxgate magnetometers. Pearson correlation coefficient (PCC), wavelet squared coherence, mutual information (MI), and empirical attenuation modeling were combined to characterize the relationships between signals measured at different spatial layers. Three-dimensional finite element simulations were further performed to provide a field-distribution reference. Adjacent air-layer signals showed substantial similarity, with reported global PCC values of 0.61–0.83 and peak wavelet squared coherence values of 0.99–1.00 over the investigated conditions. Wall–air signal pairs exhibited lower linear correlation but retained measurable statistical dependence. Their estimated MI exceeded the value predicted by a bivariate Gaussian dependence model with the same PCC, indicating that the signal pairs cannot be fully characterized by a simple Gaussian-linear model. This observation may reflect a combination of interface-related field redistribution, non-Gaussian spatial waveform structure, preprocessing effects, and finite sample estimation characteristics; it should not be interpreted as direct proof of a nonlinear magnetostatic transfer law. An empirical exponential model provided a descriptive fit to the observed PCC variation over the investigated lift-off range. The results establish a controlled source baseline for understanding multi-layer signal similarity and lift-off effects in non-contact magnetic pipeline inspection. The observed inter-layer dependence may support future development of correlation-weighted signal enhancement and combined amplitude-correlation localization methods, which require validation using stress-induced magnetic memory sources and field measurements.