Objective The magnetic flux leakage (MFL) in-line inspection technique is recognized as a crucial method for identifying pipeline defects and preventing leakage accidents in oil and gas pipeline safety assurance. However, current engineering practices typically utilize an axial sampling spacing of over 1 mm. For cracks wider than 1 mm, the collected MFL signals are susceptible to broadening and peak reduction, resulting in a degraded signal-to-noise ratio. Consequently, there is an urgent need to thoroughly investigate the quantitative relationship between axial sampling spacing and the quality of MFL signals from cracks, as well as to establish a scientific theoretical model.

Methods First, an analytical expression was derived for the two-dimensional MFL fields of rectangular surface cracks in the pipe wall, based on the theory of magnetic charge distribution. Next, a Gaussian function was employed to fit the envelope of the MFL signals from these cracks, taking into account their spatial distribution characteristics. By analyzing the aliasing effect of the sampling process, a calculation model was proposed to determine the critical axial sampling spacing required to avoid aliased distortion of signals in relation to crack widths and lift-off heights during inspections. This led to the establishment of a logarithmic relationship between the signal-to-noise ratio and the axial sampling spacing. Finally, the theoretical model was verified through finite element simulations and dual-sensor comparison experiments.

Results The results from the theoretical model were found to be strongly aligned with both the simulation and experimental data, demonstrating for the first time that an increase in sampling spacing results in a precise logarithmic decrement of the signal-to-noise ratio. Experiments showed that the goodness-of-fit coefficient of the reconstructed signals deteriorated rapidly compared to the original signal at \Delta s ＞ \Delta s_c .

Conclusion These study outcomes provide a critical theoretical basis and design criteria for the parameters of MFL in-line inspection equipment for oil and gas pipelines. Specifically, the critical sampling spacing calculation model can be directly utilized to guide the optimization of the sampling system during equipment design. The signal-to-noise ratio model establishes a standard for evaluating and quantifying expected signal quality at a given sampling spacing, which can be used to determine the maximum allowable axial sampling spacing corresponding to the lowest acceptable signal-to-noise ratio. However, the proposed theoretical signal-to-noise ratio attenuation model has limitations due to the simplification of material magnetic permeability and the idealization of boundary conditions. Consequently, quantitative errors may still be present in the calculation results. Future research is expected to incorporate more realistic dynamic magnetic permeability models to further enhance the model’s applicability in practical engineering contexts.