A rapid inversion and resolution analysis of magnetic microscope data by the subtractive optimally localized averages method

Modern scanning magnetic microscopes have the potential for fine-scale magnetic investigations of rocks. Observations at high spatial resolution produce large volumes of data, and the interpretation of these data is a nontrivial task. We have developed software using an efficient magnetic inversion technique that explicitly constructs the spatially localized Backus–Gilbert averaging kernel. Our approach, using the subtractive optimally localized averages (SOLA) method (Pijpers, R.P., Thompson, M.J., 1992. Faster formulations of the optimally localized averages method for helioseismic inversions. Astronomy and Astrophysics 262, L33–L36), yield a unidirectional magnetization. The averaging kernel expresses the spatial resolution of the inversion and is valuable for paleomagnetic application of the scanning magnetic microscope. Inversion examples for numerical magnetization patterns are provided to exhibit the performance of the method. Examples of actual magnetic field data collected from thin sections of natural rocks measured with a magnetoimpedance (MI) magnetic microscope are also provided. Numerical tests suggest that the data-independent averaging kernel is desirable for a point-to-point comparison among multiple data. Contamination by vector magnetization components can be estimated by the averaging kernel. We conclude that the SOLA method is a useful technique for paleomagnetic and rock magnetic investigations using scanning magnetic microscopy.