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.

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