Inverse theory in paleomagnetism
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In the field of paleomagnetism, a technique called micromagnetic tomography is developed to determine the magnetizations of individual particles in magnetic rock (A. Béguin, 2016 and de Groot et. al, 2018). Micromagnetic tomography applies an inversion to a combined data set of information on the locations and shapes of magnetic particles in a sample of magnetic rock and measurements of the magnetic flux density at the surface of that sample. The result of the inversion is the magnetization per particle. A. Béguin (2016) successfully inverted magnetizations of magnetic grains in a synthetic sample. Here, inverse theory is explained and magnetizations of magnetic grains in a natural sample of lava are inverted. About half of the magnetizations of the inversion result are unrealistically high, which seem to be the small particles and particles which are overlapped vertically by other particles. The latter is backed up by creating simple models in Matlab and examining the condition number and covariance matrix. It appears the covariance matrix can be used to detect unreliable particles before inversion.