Fast Magnetization Vector Inversion Method with Undulating Observation Surface in Spherical Coordinate for Revealing Lunar Weak Magnetic Anomaly Feature

Abstract

The three-dimensional magnetic vector structure (magnetization intensity and direction) of the planet can be effectively used to analyze the characteristics of its formation and operation. However, the quick acquisition of a large region of the magnetic vector structure of the planet with bigger observation surfaces undulation is hard and indispensable. We firstly proposed a fast magnetization vector inversion method for the inversion of a magnetic anomaly with the undulating observation surfaces in the spherical coordinate system, which first transforms the data to a plane when the data are distributed on a surface. Then, it uses a block-Toeplitz-Toeplitz-block (BTTB)-FFT to achieve fast inversion with the constraint that the magnetization intensities of the grids between the transformed observation surfaces and the terrain are zero. In addition, Gramian constraint term is used to reduce the ambiguity of the magnetic vector inversion. The theoretical model tests show that the proposed method can effectively improve the computational efficiency by 23 times in the 60 × 60 × 10 grid division compared to the conventional inversion method, and the accuracy of the two computation methods is comparable. The root-mean-square error of the magnetization intensity is only 0.017, and the angle error is within 1°. The magnetization vector structure shows that the largest crater diameter does not exceed 340 km in the Mare Australe region, the amplitude of the magnetic anomaly is much higher than the current meteorite impact simulation results, and the depth of the magnetic source is less than 10 km, which cannot be explained by the impact simulation experiments. In addition, the magnetization directions of adjacent sources differ by 122° (or 238°), and the high-frequency dynamics of the Moon as well as the short-lived dynamics may be responsible for this phenomenon. The magnetization directions of the three adjacent sources in the Mare Crisium region are close to each other and differ in depth with different cooling times, making it difficult to record the transient fields produced by meteorite impacts. In addition to the above characteristics, the magnetization direction of the magnetic sources in both regions is uniformly distributed without reflecting the dispersion of the magnetization direction of the meteorite impact magnetic field. Therefore, it can be inferred that the magnetic anomalies in these two regions are related to the generator hypothesis.