Inversion for dielectric relaxation spectra

A new least squares inversion algorithm is used to invert the real part of dielectric data for a spectrum of relaxation times. This inverse problem is inherently unstable; however, by transforming the linear inverse problem into log-space, the inversion iterates towards the true solution. Inversion of the theoretical distributions of Debye, Cole–Cole, and Davidson–Cole, show that this inversion method is stable, even when up to 5% of Gaussian noise is added to the data. Inversion of dielectric measurements on water, n-pentanol alcohol, and Morrison sandstone, illustrate the ability of this method to invert for relaxation-time distributions of arbitrary shape.