Theoretical investigation on magnetic inversion algorithm using second-order Euler deconvolution and thirteen-scalar- magnetometer array

Purpose A magnetic anomaly inversion algorithm based on second-order Euler deconvolution is proposed to reduce geomagnetic background field and time-varying interference. This study aims to investigate the effects of array baseline lengths, noise standard deviations and array geometry imperfections on the accuracy of two types of order gradient measurement and target localization. Design/methodology/approach A 13-scalar-magnetometer array with identical sensor configuration across three coordinate planes simultaneously measures first- and second-order derivatives of total-field magnetic anomalies. The structural index of magnetic sources is determined through nearest neighbor criterion and mean value statistics, while position coordinates are calculated using an iterative search algorithm featuring progressive radius reduction. Validation was conducted through numerical simulations on spherical and infinitely long horizontal cylindrical magnetic sources under the planned flight trajectory. Findings Baseline length significantly impacts gradient measurement errors, which mostly increase with increasing baseline length, while positioning errors exhibit a minimum value at an optimal baseline length, which coincides with the point of minimized second-order gradient errors. Regarding noise effects, characterized by the standard deviation, first-order gradient errors remain stable across different standard deviations; however, second-order gradient errors increase linearly with standard deviations and the amplitude of their fluctuations also increases. The effect of array geometry imperfections are investigated by theoretical analysis and numerical simulation, and results show that the dependence between the errors of two types of order gradients and the percents of magnetometer lateral offset is approximately linear or piecewise linear. Also, the curves of the relative errors of two types of order gradients are consistent with the curves of the relative errors of localization. Crucially, positioning accuracy is primarily governed by the precision of the second-order gradient measurements. Research limitations/implications The scalar magnetometer array proposed in the manuscript was not built, so the experimental verification of the inversion algorithm based on second-order Euler deconvolution was not carried out. Originality/value This novel sensor array features the symmetric tri-planar design, enabling the replacement of components within a single plane. Algorithmically, it innovates by eliminating background fields and time-varying interference through gradient-form Euler equations about total-field magnetic anomaly; integrates structural index determination directly with coordinate solving; and develops radius-reduction iterative filtering for solution refinement. Furthermore, this approach yields new insights by quantifying the dominance of second-order gradients in positioning accuracy under varying noise STD and array baseline lengths, and the quantitative analysis on the effect of array geometry imperfection is given.