Grain-size Distributions from Deconvolved Broadband Magnetic Susceptibility

A magnetic susceptibility meter with several-decade frequency band has recently made it possible to obtain superparamagnetic grain-size distributions only by room-temperature measurement. A rigorous deconvolution scheme of frequency dependence of susceptibility is already available. I have made some corrections on the deconvolution scheme and present its applications to broadband susceptibility data on loess and volcanic rocks. Deconvolution of frequency dependence of susceptibility was originally developed by Shchervakov and Fabian [2005]. Suppose an ensemble of grains distributed for two independent variables of volume (grain-size) and energy barrier. Applying alternating magnetic field with varying frequency results in differentiating grains by energy barrier - not directly by volume. Since the response function for frequency is known, deconvolution of frequency dependence of susceptibility provide a rigorous solution for the second moment of volume on the volume-energy barrier distribution. Based on a common assumption of a linear relation between volume and energy barrier, we can obtain analytical volume or grain-size distributions of superparamagnetic grains. A ZH broadband susceptibility meter comprises of two separated devices for lower (SM-100, 65 - 16kHz) and higher (SM-105, 16k - 512kHz) frequency ranges. At every frequency susceptibility calibration was conducted using three kinds of paramagnetic rare earth oxides [Fukuma and Torii, 2011]. Almost all samples exhibited seemingly linear dependences of in-phase susceptibility on logarithmic frequency. This indicates that the measured data do not suffer serious noise, and that the second moment of volume is relatively constant against energy barrier. Nonetheless, third-order polynomial fittings revealed slight deflections from the quasi-linear susceptibility - logarithmic frequency relations. Deconvolving the polynomials showed that such slight defections come from peaks or troughs in varying second moment of volume against energy barrier. Assuming a linear relation between volume and energy barrier, peaks or troughs around 1 x 10^{-24} m^{3} were found for the derived volume distributions. Long-tailed volume distributions from Chinese loess samples suggest the broad grain-size distribution.