Accounting for Geometric Anisotropy in Sparse Magnetic Data Using a Modified Interpolation Algorithm

Abstract

The construction of a high-precision geomagnetic map is a prerequisite for geomagnetic navigation and magnetic target-detection technology. The Kriging interpolation algorithm makes use of the variogram to perform linear unbiased and optimal estimation of unknown sample points. It has strong spatial autocorrelation and is one of the important methods for geomagnetic map construction. However, in a region with a complex geomagnetic field, the sparse geomagnetic survey lines make the ratio of line-spacing resolution to in-line resolution larger, and the survey line direction differs from the geomagnetic trend, which leads to a serious effect of geometric anisotropy and thus, reduces the interpolation accuracy of the geomagnetic maps. Therefore, this paper focuses on the problem of geometric anisotropy in the process of constructing a geomagnetic map with sparse data, analyzes the influence of sparse data on geometric anisotropy, deduces the formula of geometric anisotropy correction, and proposes a modified interpolation algorithm accounting for geometric anisotropy correction of variogram for sparse geomagnetic data. The results of several sets of simulations and measured data show that the proposed method has higher interpolation accuracy than the conventional spherical variogram model in a region where the geomagnetic anomaly gradient changes sharply, which provides an effective way to build a high-precision magnetic map of the complex geomagnetic field under the condition of sparse survey lines.