Volcanic rocks are considered reliable recorders of past changes in the Earth’s magnetic field. Recent flows, however, sometimes fail to produce the known magnetic field at the time of cooling. Here, we tested the accuracy of paleomagnetic data recorded by Mt. Etna lavas by comparing paleomagnetic data from historical flows to direct measurements of the magnetic field above the current topography. The inclinations and intensities in both data sets are biased towards lower values. They vary as a function of topography; both are higher above ridges and lower in gullies. To suppress this paleomagnetic data bias it is important to take samples several meters apart and from different parts of the flow whenever possible. While this leads to a higher degree of scatter in paleodirections, the results will better represent the Earth’s magnetic field at the time of cooling. This emphasises the importance of reporting paleomagnetic sampling strategies in detail.

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 technique that combines X-ray micro computed tomography and scanning magnetometry data to obtain information about the magnetic potential of individual grains embedded in a sample. Recovering magnetic signals of individual grains in natural and synthetic samples provides a new pathway to study the remanent magnetization that carries information about the ancient geomagnetic field and is the basis of all paleomagnetic studies. MMT infers the magnetic potential of individual grains by numerical inversion of surface magnetic measurements using spherical harmonic expansions. The magnetic potential of individual particles in principle is uniquely determined by MMT, not only by the dipole approximation, but also more complex, higher order, multipole moments. Here we show that such complex magnetic information together with particle shape and mineralogy severely constrains the internal magnetization structure of an individual grain. To this end we apply a three dimensional micromagnetic model to predict the multipole signal from magnetization states of different local energy minima. We show that for certain grains it is even possible to uniquely infer the magnetic configuration from the inverted magnetic multipole moments. This result is crucial to discriminate single-domain particles from grains in more complex configurations such as multi-domain or vortex states. As a consequence, our investigation proves that by MMT it is feasible to select statistical ensembles of magnetic grains based on their magnetization states, which opens new possibilities to identify and characterize stable paleomagnetic recorders in natural samples.

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.

Our understanding of the past behavior of the geomagnetic field arises from magnetic signals stored in geological materials, e.g. (volcanic) rocks. Bulk rock samples, however, often contain magnetic grains that differ in chemistry, size and shape; some of them record the Earth’s magnetic field well, others are unreliable. The presence of a small amount of adverse behaved magnetic grains in a sample may already obscure important information on the past state of the geomagnetic field. Recently it was shown that it is possible to determine magnetizations of individual grains in a sample by combining X-ray computed tomography and magnetic surface scanning measurements. Here we establish this new Micromagnetic Tomography (MMT) technique and make it suitable for use with different magnetic scanning techniques, and for both synthetic and natural samples. We acquired reliable magnetic directions by selecting subsets of grains in a synthetic sample, and we obtained rock-magnetic information of individual grains in a volcanic sample. This illustrates that MMT opens up entirely new venues of paleomagnetic and rock-magnetic research. MMT’s unique ability to determine the magnetization of individual grains in a nondestructive way allows for a systematic analysis of how geological materials record and retain information on the past state of the Earth’s magnetic field. Moreover, by interpreting only the contributions of known magnetically well-behaved grains in a sample MMT has the potential to unlock paleomagnetic information from even the most complex, crucial, or valuable recorders that current methods are unable to recover.

Micromagnetic Tomography (MMT) is a technique that combines X-ray micro tomography and scanning magnetometry data to numerically invert the surface magnetic signal for the magnetic potential of individual magnetic grains via their spherical harmonic expansion [1]. The dipole and higher order multipole moment solutions are uniquely determined, which has been proved in [2]. As a result, this method has allowed to analyze the signal of individual grains in rock samples and synthetic samples, thus providing a new pathway to study the rock magnetic properties of the remanent magnetization carriers [3]. Furthermore, the higher order multipole signals in the magnetic particles are an indication that the grains carry more complex magnetic orderings, such as multi-domain or vortex states. Therefore, these higher order moments can be used to constrain the magnetic configuration of the magnetic particles. In this work we review the multipole expansion method used by MMT. In addition, we show three dimensional micromagnetic modelling results to predict the multipole signal of magnetic particles in different local energy minimum magnetization states. We show that for certain grains it is possible to uniquely infer the magnetic configuration from the inverted magnetic multipole moments. This result is crucial to discriminate single-domain particles from grains in more complex configurations. Our investigation proves the feasibility to statistically select ensembles of magnetic grains with similar properties, such as the magnetic state, which is a step forward to find stable paleomagnetic recorders. [1] L. V. de Groot, K. Fabian, A. Béguin, P. Reith, A. Barnhoorn and H. Hilgenkamp. Determining Individual Particle Magnetizations in Assemblages of Micrograins. Geophysical Research Letters, 45(7):2995–3000, 2018. [2] K. Fabian and L. V. de Groot. A uniqueness theorem for tomography-assisted potential-field inversion. Geophysical Journal International, 216(2):760–766, 2018. [3] D. Cortés‐Ortuño, K. Fabian and L. V. De Groot. Single particle multipole expansions from Micromagnetic Tomography. Geochemistry, Geophysics, Geosystems, 22:e2021GC009663, 2021.