Vector unmixing of multicomponent palaeomagnetic data

Palaeomagnetic investigations often encounter multiple magnetization components, where secondary processes have obscured, partially overprinted or completely replaced the original (primary) remanent magnetization. Identification and separation of primary and secondary magnetizations are generally carried out with principal component analysis of stepwise demagnetization data. However, rocks may contain multiple generations of magnetic minerals with overlapping unblocking ranges that complicate the discrimination of components when applying best-fitting line procedures. Developing a method to differentiate and quantify contributions of overlapping magnetic components using directional data is therefore highly desirable. This paper presents a method to unmix stepwise demagnetization data using an inverse modelling approach. We show that the method is capable of accurately resolving two or three magnetic components with overlapping or superimposed unblocking spectra as well as quantifying absolute component contributions. The method depends on accurate identification and selection of end-member components prior to analysis; in doing so, the method can help palaeomagnetists understand how magnetization components combine to explain their data. We show that the dilution of one component by more than ca. 25 per cent from another component can result in linear demagnetization curves that decay to the origin on orthogonal plots, but whose best-fitting direction can significantly deviate from both end-members. The efficacy of the method is demonstrated through examples of demagnetization data from hematite and/or magnetite-bearing sandstones from China. This method can be broadly applied to all multicomponent magnetization problems in palaeomagnetism.