Three-Dimensional Magnetic Inversion Based on an Adaptive Quadtree Data Compression

Abstract

Three-dimensional magnetic inversion allows the distribution of magnetic parameters to be obtained, and it is an important tool for geological exploration and interpretation. However, because of the redundancy of the data obtained from large-scale investigations or high-density sampling, it is very computationally intensive to use these data for iterative inversion calculations. In this paper, we propose a method for compressing magnetic data by using an adaptive quadtree decomposition method, which divides the two-dimensional data region into four quadrants and progressively subdivides them by recursion until the data in each quadrant meets the regional consistency criterion. The method allows for dense sampling at the abnormal boundaries with large amplitude changes and sparse sampling at regions with small amplitude changes, and achieves the best approximation to the original data with the least amount of data, thus retaining more anomalous information while achieving the purpose of data compression. In addition, assigning values to the data in the quadrants using the averaging method is essentially equivalent to average filtering, which reduces the noise of the magnetic data. Testing the synthetic model and applying the method to mineral exploration a prove that it can effectively compress the magnetic data and greatly improve the computational efficiency.

Fast and flexible spatial sampling methods based on the Quadtree algorithm for ocean monitoring

“…This process is repeated iteratively until each stratum meets some criterion of homogeneity. QT algorithm is widely used in the structuring of spatial data, image and data compression, spatial sampling design, grid division, and even path planning (Csillag and Kabos, 1996;Poveda and Gould, 2005;Minasny et al, 2007;Huo et al, 2019;Jiang et al, 2020;Jewsbury et al, 2021;Lee et al, 2021).…”

Gravity modelling by using vertical prismatic polyhedra and application to a sedimentary basin in Eastern Anatolia

“…Jiang et al. (2020) used squares as the basis to create an adaptive quadtree mesh structure: The mesh increases its resolution by subdividing itself into smaller squares where the data have higher amplitude variation. Kalmar et al.…”

“…Richardson and MacInnes (1989) and Leliévre et al (2012) are two of the example studies that adopted this approach to build constrained basin models that incorporate faults. Jiang et al (2020) used squares as the basis to create an adaptive quadtree FIGURE 2 Random data points that are slightly biased towards the centre and data reliability of using a regular mesh grid: (a) Defined data points; (b) sample frequency contour map of a mesh grid. Colours of the contour map represent data reliability, meanings and parities of which are given on the table on the right.…”

“…There are also some forward modelling suggestions for nonregular shaped bodies available in the literature (Plouff, 1976;Richardson & MacInnes, 1989;Ren et al, 2018). Jiang et al (2020) handled model unit placement in a different way via defining variously sized square prisms around magnetic anomalies, with sizes decreasing in proportion to amplitude variety. Smith (2000) employed polyhedra as modelling units to calculate terrain corrections from digital elevation model data.…”

“…Jiang et al. (2020) handled model unit placement in a different way via defining variously sized square prisms around magnetic anomalies, with sizes decreasing in proportion to amplitude variety. Smith (2000) employed polyhedra as modelling units to calculate terrain corrections from digital elevation model data.…”