Unmixing of magnetic hysteresis loops through a modified Gamma-Cauchy
exponential model
Abstract
Quantifying the contributions of distinct mineral populations in bulk
magnetic experiments greatly enhances the analysis of environmental and
rock magnetism studies. Here we develop a new method of parametric
unmixing of susceptibility components in hysteresis loops. Our approach
is based on a modified Gamma-Cauchy exponential model, that accounts for
variable skewness and kurtosis. The robustness of the model is tested
with synthetic curves that examine the effects of noise, sampling, and
proximity of susceptibility components. We provide a Python-based
script, the Hist-unmix package, which allows the user to adjust a direct
model of up to three ferromagnetic components as well as a
dia/paramagnetic contribution. Optimization of all the parameters is
achieved through least squares fit (Levenberg-Marquardt method), with
uncertainties of each inverted parameter calculated through a Monte
Carlo error propagation approach. For each ferromagnetic component, it
is possible to estimate the magnetization saturation (Ms), magnetization
saturation of remanence (Mrs) and the mean coercivity (Bc). Finally,
Hist-unmix was applied to a set of weakly magnetic carbonate rocks from
Brazil, which typically show distorted hysteresis cycles (wasp-waisted
and potbellied loops). For these samples, we resolved two components
with distinct coercivities. These results are corroborated by previous
experimental data, showing that the lower branch of magnetic hysteresis
can be modeled by the presented approach and might offer important
mineralogical information for rock magnetic and paleomagnetic studies.