Abstract
Modern magnetic microscopy (MM) provides high-resolution, ultra-high-sensitivity moment magnetometry, with the ability to measure at spatial resolutions better than 10^{-4} m and to detect magnetic moments weaker than 10^{-15} Am^2. These characteristics make modern MM devices capable of particularly high-resolution analysis of the magnetic properties of materials, but generate extremely large data sets. Many studies utilizing MM attempt to solve an inverse problem to determine the magnitude of the magnetic moments that produce the measured component of the magnetic field. Fast Fourier techniques in the frequency domain and non-negative least-squares (NNLS) methods in the spatial domain are the two most frequently used methods to solve this inverse problem. Although extremely fast, Fourier techniques can produce solutions that violate the non-negativity of moments constraint. Inversions in the spatial domain do not violate non-negativity constraints, but the execution times of standard NNLS solvers (the Lawson and Hanson method and Matlab’s lsqlin) prohibit spatial domain inversions from operating at the full spatial resolution of an MM. In this paper, we present the applicability of the TNT-NN algorithm, a newly developed NNLS active set method, as a means to directly address the NNLS routine hindering existing spatial domain inversion methods. The TNT-NN algorithm enhances the performance of spatial domain inversions by accelerating the core NNLS routine. Using a conventional computing system, we show that the TNT-NN algorithm produces solutions with residuals comparable to conventional methods while reducing execution time of spatial domain inversions from months to hours or less. Using isothermal remanent magnetization measurements of multiple synthetic and natural samples, we show that the capabilities of the TNT-NN algorithm allow scans with sizes that made them previously inaccesible to NNLS techniques to be inverted. Ultimately, the TNT-NN algorithm enables spatial domain inversions of MM data on an accelerated timescale that renders spatial domain analyses for modern MM studies practical. In particular, this new technique enables MM experiments that would have required an impractical amount of inversion time such as high-resolution stepwise magnetization and demagnetization and 3-dimensional inversions.
Highlights
Modern magnetic microscopes (MMs) have been developed to analyze the microscale natural remanent magnetization and rock magnetic properties of rocks and minerals (Harrison and Feinberg 2009) and are capable of high-resolution, high-sensitivity measurements on geologic samples (Weiss et al 2007b)
We find an acceptable match between the numerically obtained magnetic moment of the basalt saturation isothermal remanent magnetization (SIRM) using TNT-NN, lsqlin, the Fourier method, and the measured moment using a 2G
The numerical methods obtain magnetic sources with similar remanence magnetization. These results are on the same order of magnitude, but slightly less than the measured remanence magnetization for this sample obtained by experimental hysteresis (7.52 ×10−8 Am2, found by Noguchi et al (2017b, Table S1)). lsqlin produces the highest residual root mean square (RMS) value of all scenarios due to early termination
Summary
Modern magnetic microscopes (MMs) have been developed to analyze the microscale natural remanent magnetization and rock magnetic properties of rocks and minerals (Harrison and Feinberg 2009) and are capable of high-resolution, high-sensitivity measurements on geologic samples (Weiss et al 2007b). MMs are capable of measuring samples with magnetic moments weaker than 10−15 Am2 (Fong et al 2005; Weiss et al 2007a; Oda et al 2016; Lima and Weiss 2016) at spatial resolutions on the order of micrometers (Liu et al 2002; Liu and Xiao 2003; Liu et al 2006; Hankard et al 2009; Lima et al 2014; Glenn et al 2017). The high-resolution capability of MMs can yield extremely large data sets Analyzing these data sets is dominated by solving an inversion problem, which obtains the distribution of magnetic sources from the measured magnetic field. As with mapping of magnetic fields of magnetization, retrieving magnetization from magnetic fields is non-unique without the use of other constraints and can be computationally expensive (Weiss et al 2007b; Lima and Weiss 2016)
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