Frenk Out: Exploring the mathematical limits of Micromagnetic Tomography
Channel: Institute for Rock Magnetism
Date: 2021-06-02

12th Institute for Rock Magnetism Conference 

Lightning Talk

Title: Exploring the mathematical limits of Micromagnetic Tomography

Authors: Frenk Out (1), David Cortés Ortũno (1), Karl Fabian (2), Tristan van Leeuwen (3) & Lennart de Groot (1)

(1) Paleomagnetic laboratory Fort Hoofddijk, Department of Earth Sciences, Utrecht University
(2) Norwegian University of Science and Technology (NTNU)
(3) Mathematical Institute, Utrecht University

Abstract:
Micromagnetic Tomography (MMT) makes it possible to obtain the characteristic remanent magnetization of individual magnetic grains in volcanic samples. This is achieved by combining the results of a Quantum Diamond Magnetometer and a MicroCT. These machines can image the magnetic field on a surface of a sample, and the position of individual magnetic grains, both on a very small scale. These two types of information are then used in a least-squares inversion approach to obtain the magnetizations of individual grains in a sample. The mathematical validity and accuracy of this inversion given the experimental set-up, however, has not been assessed yet. To obtain an indication of the validity of the solution, we determined a 95% confidence interval for the magnetization solution for each individual grain. The relative size of the confidence interval indicates the accuracy of the retrieved magnetization. This accuracy is primarily governed by four initial parameters, namely, (1) the grain concentration in the sample, (2) the noise level in the magnetic surface scan, (3) the sampling interval of the magnetic surface scan, and (4) the size/volume of the sample. In this study, we aim to describe the relationship between these four parameters and the accuracy of MMT results. To assess the influence of these parameters, we set up a series of numerical models, and varied these parameters. For all models the ‘synthetic’ grains were assigned a random dipolar magnetization and were randomly placed in the sample volumes. Then, the magnetic field at the surface of the sample was calculated. These ‘surface scans’ are then disturbed by Gaussian noise using one of four different noise levels. These surface scans were used as input for a MMT inversion to obtain the magnetization for each grain. By translating the magnetization results into a spherical coordinate system, the 95% confidence interval for the magnetization vector can be obtained by bootstrapping. We show that all grains in the models with a grain density lower than or equal to 25.000 grains per mm3 have very low confidence intervals (less than 1%) for all initial parameters – i.e. are very well resolved. Overall, the thickness of the sample has the largest influence on the quality of the solutions. To select the grains with the most credible magnetization solution we define a ‘signal strength parameter’. With the signal strength we can estimate the potential of a grain to create a magnetic expression at the surface of the sample. After obtaining this parameter, we identified the relation between this signal strength and the four initial parameters, and the chosen maximum size of the confidence intervals. In this way we have developed a quick way to select the most reliable grains, which can then be used in subsequent interpretations of MMT results. This can ultimately enable us to determine paleodirections and paleointensities from subsets of grains in a sample.