Magnetic signals in igneous rocks arise from assemblages of iron-oxide bearing minerals that differ in e.g. size, shape, and chemistry. Paleomagnetic measurements on bulk samples measure millions of such grains simultaneously, producing a statistical ensemble of the magnetic moments of the individual minerals. Scanning magnetometry techniques such as the Quantum Diamond Microscope (QDM) measure magnetic signals on micrometer scales, allowing the identification of magnetic moments of individual grains in a sample using e.g. Micromagnetic Tomography (MMT). Here we produce a grain-size distribution of iron-oxides in a typical Hawaiian basalt from the superparamagnetic threshold (~40 nm) to grains with a diameter of 10 \(\mu\)m. This grain-size distribution is obtained by combining FIB-SEM and MicroCT data from sister specimens, and normalizing them to the mineral surface area of non-magnetic minerals. Then we use this grain-size distribution to determine the contributions of individual magnetic carriers to bulk magnetic measurements and surface magnetometry. We found that measurements on bulk samples are sensitive to relatively small grain sizes in the realm of single domain or vortex states (<200 nm), while signals in surface magnetometry arise mainly from larger grains with diameters >1 \(\mu\)m. This implies that bulk measurements cannot be compared straightforwardly to signals from surface magnetometry from the same sample. Moreover, our observations explain why MMT results are insensitive to the presence of many small grains in a sample that intuitively should hamper their outcome.

The recently developed Micromagnetic Tomography (MMT) technique combines advances in high resolution scanning magnetometry and micro X-ray computed tomography. This allows precise recovery of magnetic moments of individual magnetic grains in a sample using a least-squares inversion approach. Here we investigate five factors, which are governing the mathematical validity of MMT solutions: grain concentration, thickness of the sample, size of the sample’s surface, noise level in the magnetic scan, and sampling interval of the magnetic scan. To compute the influence of these parameters, we set up series of numerical models in which we assign dipole magnetizations to randomly placed grains. Then we assess how well their magnetizations are resolved as function of these parameters. We expanded the MMT inversion to also produce the covariance and standard deviations of the solutions, and use these to define a statistical uncertainty ratio and signal strength ratio for each solution. We show that the magnetic moments of a majority of grains under the inspected conditions are solved with very small uncertainties. However, increasing the grain density and sample thickness carry major challenges for the MMT inversions, demonstrated by uncertainties larger than 100% for some grains. Fortunately, we can use the signal strength ratio to extract grains with the most accurate solutions, even from these challenging models. Hereby we have developed a quick and objective routine to individually select the most reliable grains from MMT results. This will ultimately enable determining paleodirections and paleointensities from large subsets of grains in a sample using MMT.

Micromagnetic Tomography (MMT) is a new technique that allows to determine magnetic moments of individual grains in volcanic rocks. Current MMT studies either showed that it is possible to obtain magnetic moments of relatively small numbers of grains in ideal sample material, or provided important theoretical advances in MMT inversion theory and/or its statistical framework. Here we present a large-scale application of MMT on a sample from the 1907-flow from Hawaii’s Kilauea volcano producing magnetic moments of 1,646 individual grains. To assess the robustness of the MMT results, we produced 261,305 individual magnetic moments in total: an increase of three orders of magnitude compared to earlier studies and a major step towards the number of grains that is necessary for paleomagnetic applications of MMT. Furthermore, we show that the recently proposed signal strength ratio is a powerful tool to scrutinize and select MMT results. Despite this progress, still only relatively large iron-oxide grains with diameters >1.5-2 µm can be reliably resolved, impeding a reliable paleomagnetic interpretation. To determine the magnetic moments of smaller (< 1 µm) grains that may exhibit PSD behavior and are therefore better paleomagnetic recorders, the resolution of the MicroCT and magnetic scans necessary for MMT must be improved. Therefore, it is necessary to reduce the sample size in future MMT studies. Nevertheless, our study is an important step towards making MMT a useful paleomagnetic and rock-magnetic technique.