The high-precision magnetic anomaly reference map is a prerequisite for magnetic navigation and magnetic target detection. However, it is difficult to reflect the detailed characteristics of magnetic anomaly changes by using conventional data interpolation and reconstruction in the areas where magnetic anomaly gradients vary drastically and the distribution of magnetic survey lines is sparse. To solve the problem, an improved variogram of the Kriging interpolation method is proposed to improve the spatial resolution of magnetic anomaly feature. This method selects the spherical variogram model and uses the third power of the lag distance to fit the trend of magnetic anomalies. Meanwhile, the second power of the lag distance is introduced to solve the problem of under-fitting between the lag distance and the value of the variation function near the origin of the sparse variogram graph of measured data. Hyperparameter $\lambda$ is introduced to compensate for the unbalance caused by the introduction of quadratic lag in the spherical variogram model. The results of several sets of simulated and measured data show that the interpolation accuracy of the proposed method is improved by 30–50% compared with the traditional Gaussian, spherical, and exponential models in the region where the magnetic anomaly gradient changes drastically, and the proposed model provides an effective way to build a high-precision magnetic anomaly reference map of the complex magnetic background under the condition of sparse survey lines.

In aeromagnetic detection and geomagnetic navigation, the reference geomagnetic maps usually need to be continued to different altitudes. Traditionally, the geomagnetic field upward continuation is stable. Nevertheless, the downward continuation is instable near the magnetic source and sensitive to the high-frequency noise. To address the problem, this article proposes a recursive truncated Taylor expansion (RTTE) downward continuation method for geomagnetic field. This method models the geomagnetic field in the vertical direction. The coefficients of the model are calculated based on the harmonicity of the geomagnetic field to ensure stability; a recursive process is implemented to extend its effect under a large continuation distance. To demonstrate the effectiveness of the proposed method, this paper compares the effects of the traditional Landweber iteration method and the proposed method using simulation data and real measured data. Under real measurement conditions, the MAE and RMSE of the proposed RTTE method are 0.1878 nT and 0.3184 nT, respectively, representing a reduction of 90.33% and 95.75% compared to the Landweber iteration method. The results show that the proposed RTTE method significantly improves the continuation accuracy compared with traditional methods, providing support for geomagnetic navigation and aeromagnetic exploration.