Geomagnetic field observation constitutes a vital part of geophysical data acquisition. In recent years, the employment of smaller and more compact bins for geomagnetic observations has emerged as a novel trend. A geomagnetic observation bin typically takes the form of a cylindrical structure with a bottom. By utilizing the equivalent magnetic charge （EMC） method, a system of equations is initially solved at the boundaries between the object and the surrounding air. This facilitates the determination of the surface magnetic charge density on N discrete elements, which is subsequently employed to compute the magnetic field at any point in space. When applying this method to a cylindrical bottomed bin with non-axial magnetization, we obtain the distribution of surface magnetic charge density and the magnetic field within the bin, followed by the calculation of the magnetic field gradient inside.

In the calculations, the magnetic susceptibility of typical concrete was referred to, and the background magnetic field characteristics were acquired using the International Geomagnetic Reference Field （IGRF）. The results reveal that, due to the small geomagnetic declination angle D, the magnetic field intensity inside the observation bin exhibits approximate axial symmetry in the east-west direction, and near-central symmetry in the north-south direction. Near the bottom of the bin, the magnetic field intensity mainly increases, with a maximum increment of approximately 1.2 nT compared to the background field. Near the top of the bin, the magnetic field intensity predominantly decreases, with a maximum decrease of around 1.5 nT. The largest magnetic field gradients are concentrated at the edges of the top and bottom of the bin.

Finite element simulations along three measuring lines were compared with actual measurement data. These measuring lines include: ① a vertical line inside the bin, ② a north-south line one meter above the bin’s bottom, and ③ an east-west line one meter below the bin’s top, with a measurement interval of 0.1 meters. The results demonstrate that the magnetic field calculated using the EMC method deviates from the measured results by less than 0.1 nT, with a relative error of less than 0.000 1%. In the region near the bottom of the bin along the vertical line, the magnetic field intensity increases by approximately 0.7 nT, while near the top of the bin, it decreases by about 0.2 nT.

The effects of the bin’s bottom thickness, the ratio of its height to diameter, and the magnetic susceptibility of the material on the internal magnetic field gradient were also explored. The results indicate that as the bottom thickness of the bin decreases, the effective horizontal space inside the bin enlarges. When the bin is bottomless, it offers the maximum horizontal effective space. However, a bottomless structure does not augment the vertical effective space inside the bin. When the external and internal heights of the bin are kept constant, an increase in the inner diameter leads to more effective vertical space inside the bin, without significant alteration in the horizontal direction. When the inner and outer diameters of the bin are fixed, increasing the internal height results in more effective horizontal space inside the bin, with no pronounced impact on the vertical direction. The highest magnetic field gradients inside the bin are concentrated near the edges of the top and bottom. As the bin’s dimensions expand, the proportion of effective space inside the bin also rises. Moreover, when the bin size remains unchanged, the influence of varying magnetic susceptibilities on the magnetic field gradient inside the bin was analyzed. The results suggest that for magnetic susceptibilities ≤800×10⁻⁶, increasing the susceptibility does not trigger significant changes in the effective space inside the bin.