Unraveling composite magnetic fabrics through tensor decomposition

Magnetic anisotropy plays a central role in many petrofabric and paleomagnetic studies. Anisotropy is typically represented by a second-order symmetric tensor that reflects the combined contributions from mineral populations with differing grain sizes, orientation distributions and particle scale anisotropies. Thus, the quality of geologically significant information obtained from magnetic anisotropy data depends on our ability to disentangle the complexity of these coexisting fabrics. In this study, we present a least-squares technique that can be employed in combination with additional geological or other supporting evidence to separate measured anisotropy tensors into independent contributions with distinct physical meaning. The analysis is readily adaptable and widely applicable to interpreting composite hybrid magnetic anisotropies, like those which arise from tectonic forces. Here, we revisit published deposition experiments and anisotropy of anhysteretic remanence (AARM) measurements to demonstrate the usefulness of the tensor decomposition approach. Remanence anisotropy measurements are decomposed into idealized tensorial sub-components originating from the preferred alignment of particles parallel to the magnetic field (field-aligned fabric) and within the bedding plane (sedimentary fabric). The least-squares decomposition isolates the field-aligned fabric by subtracting the sedimentary-compaction fabric. After subtraction of the sedimentary fabric, quantitative paleofield strength and direction can be directly inferred from the field-aligned subfabric. • We introduce a novel least-squares method for decomposing composite magnetic fabrics into meaningful components. • The method's effectiveness is demonstrated by isolating a field-aligned lineation to estimate relative paleointensity. • Unknown paleofield vectors can be extracted by the decomposition method.