Short note: on the determination of the relaxation time distributions using Bézier curves

SUMMARY For the interpretation of spectral induced polarization spectra, the determination of the relaxation time distributions (RTD) can be useful, for instance to extract the grain size distribution. However, this is an ill-posed problem, and retrieving the RTD often requires regularization during the inversion process. In this note, we use Bézier curves and simulated annealing to determine the RTD. The procedure that does not require any regularization nor smoothing, by reducing the number of parameters thanks to Bézier curves which are intrinsically continuous and infinitely derivable. We successfully applied our methodology to three examples (Cole–Cole model, Davidson–Cole model, and an experimental spectrum), demonstrating its interest and efficiency.