An Improved Algorithm for Unmixing First‐Order Reversal Curve Diagrams Using Principal Component Analysis

First‐order reversal curve (FORC) diagrams of synthetic binary mixtures with single‐domain, vortex state, and multidomain end‐members (EMs) were analyzed using principal component analysis (FORC‐PCA). Mixing proportions derived from FORC‐PCA are shown to deviate systematically from the known weight...

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Bibliographic Details
Published in:Geochemistry, geophysics, geosystems : G3 geophysics, geosystems : G3, 2018-05, Vol.19 (5), p.1595-1610
Main Authors: Harrison, Richard J., Muraszko, Joy, Heslop, David, Lascu, Ioan, Muxworthy, Adrian R., Roberts, Andrew P.
Format: Article
Language:English
Subjects:
first‐order reversal curves
FORCs
greigite
Magnetism
Mathematical models
Methods
Palaeomagnetism
Paleomagnetism
PCA
principal component analysis
Principal components analysis
unmixing
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Summary:First‐order reversal curve (FORC) diagrams of synthetic binary mixtures with single‐domain, vortex state, and multidomain end‐members (EMs) were analyzed using principal component analysis (FORC‐PCA). Mixing proportions derived from FORC‐PCA are shown to deviate systematically from the known weight percent of EMs, which is caused by the lack of reversible magnetization contributions to the FORC distribution. The error in the mixing proportions can be corrected by applying PCA to the raw FORCs, rather than to the processed FORC diagram, thereby capturing both reversible and irreversible contributions to the signal. Here we develop a new practical implementation of the FORC‐PCA method that enables quantitative unmixing to be performed routinely on suites of FORC diagrams with up to four distinct EMs. The method provides access not only to the processed FORC diagram of each EM, but also to reconstructed FORCs, which enables objective criteria to be defined that aid identification of physically realistic EMs. We illustrate FORC‐PCA with examples of quantitative unmixing of magnetic components that will have widespread applicability in paleomagnetism and environmental magnetism. Key Points The FORC‐PCA unmixing method is tested on synthetic mixtures of magnetic domain states A new FORC‐PCA algorithm is developed that solves the linear mixing problem for end‐members with different domain states (including superparamagnetism) Feasibility metrics are developed that help to guide identification of physically realistic end‐members
ISSN:1525-2027
1525-2027
DOI:10.1029/2018GC007511