Induced polarization is a geophysical method looking to image and interpret low-frequency polarization mechanisms occurring in porous media. Below 10 kHz, the quadrature conductivity of metal-free sandy and clayey materials exhibits a distribution of relaxation times, which can be related to the pore size distribution of these porous materials. When the polarization spectra are fitted with a Cole-Cole model, we first observe that the main relaxation time is controlled by the main pore size of the material and that the Cole-Cole exponent c is never much above 0.5, a value corresponding to a Warburg function. The complex conductivity is then obtained through a convolution product between the pore size distribution and such Warburg function. We also provide a way to recover the pore size distribution by performing a deconvolution of measured spectra using the Warburg function. A new dataset of mercury porosimetry and induced polarization data of six siliciclastic materials supports the hypothesis that the Cole-Cole relaxation time is strongly controlled by the pore size, and especially the characteristic pore size corresponding to the peak of the pore size distribution from mercury porosimetry. The distribution of the pore throat sizes of these materials seems fairly well recovered using the Warburg decomposition of the spectral induced polarization spectra but additional data will be needed to confirm this finding.