I employed numerical modeling to examine the formation of the apparent resistivity phase spectrum first of a polarizable prism situated in a polarizable half-space, and second of two polarizable prisms joined in an unpolarizable half-space. The calculations were done using the integral equation technique. The frequency dependence of the resistivity of the polarizable medium is depicted by means of the Cole-Cole dispersion model.The effect of a weakly polarizable half-space may be handled by simply adding the phase angle of the half-space to the apparent phase due to the body. The apparent spectral parameters can be inverted by fitting the sum of two Cole-Cole dispersion model phase spectra to the apparent phase spectrum. Of the parameters describing the prism, the apparent chargeability is smaller than the chargeability of the original petrophysical spectrum because of geometric attenuation. The apparent frequency dependence, on the other hand, is very close to the value of the original frequency dependence. The apparent time constant is commonly also near the true time constant of the petrophysical spectrum. The values of the apparent spectral parameters of the polarizable half-space are all close to their petrophysical or true values.The apparent spectrum of two polarizable prisms builds up in a complex fashion. Nevertheless, by measuring the spectra at a number of points along a profile crossing over two formations differing in time constant, the various components can be discriminated from the apparent spectrum even if the difference in time constant is small. As the conductivity contrast decreases, the share of the spectrum of the formation in the apparent spectrum increases. Similarly, the formation with the smaller time constant is in a more advantageous position than the body with the greater time constant.