Enhancing Precision in Magnetic Map Interpolation for Regions with Sparse Data

Abstract

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 λ 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.