A Discrete Function (DF) Method for Highly Efficient Magnetization Vector Inversion of Magnetic Data

The three-direction magnetization intensities of a source can be obtained by the magnetization vector inversion (MVI) of magnetic data, and therefore, MVI can be well applied to a magnetic anomaly with remanence. However, MVI exhibits poor applicability attributed to its low computational efficiency for a data with large area and undulating terrain. We proposed a discrete function (DF) method to improve the efficiency of MVI, which is suitable for uniform hexahedron mesh and unstructured tetrahedral mesh. In this method, DF was used to fit the magnetization vectors of a given number of cells, and the computation of the physical properties of the cells was replaced by the computation of function coefficients, and the memory and calculation time were reduced, as the number of function coefficients was less than the number of cells. The Gramian constraint item in MVI could be directly computed by function coefficients without increasing the computational process. For uniform hexahedron mesh, the integration of DF with the block-Toeplitz-Toeplitz-block-fast Fourier transform (DF-BTTB-FFT) method can further improve the inversion efficiency. The model tests revealed that the DF method could reduce the storage and computation time by approximately five times without precision loss, and DF-BTTB-FFT method could achieve approximately four times improvement compared with the DF method. Finally, the proposed DF method was used to accomplish the MVI of real magnetic anomaly and its gradient data in Shaanxi Province to delineate the range of the subsurface burned zone, and the distribution was ascertained by combining the nuclear magnetic water measurements.