The resistivity of rocks will change with the change of measurement frequency, and it is necessary to discuss the applicability of Archie's formula in the frequency domain because the measurement frequency used by various resistivity logging tools is different from each other. Based on the complex resistivity spectrum of four artificial pure sandstone samples in the range of 1 kHz ~110 MHz, 15 discrete frequencies were selected to analyze the relationship between the real part, imaginary part and amplitude of complex resistivity and porosity and water saturation. The results show that the real part and amplitude of complex resistivity at the frequency of 1 kHz are consistent with those of conventional rock electrical experiments. With the increase of the measurement frequency, the complex resistivity of the sample decreases gradually and sharply within a certain frequency range. The smaller the sample's porosity or the lower the water saturation is, the lower the frequency corresponding to the sudden drop of the real part of the complex resistivity will be. Therefore, the samples with smaller porosity or lower water saturation may have a smaller real part of complex resistivity and show "inverse Archie law" under some special frequencies. The dispersion of resistivity leads to a gradual decrease in the applicability of Archie's formula at high-frequency. Therefore, resistivity dispersion correction is required before high-frequency resistivity logging data is applied to Archie's formula. The above conclusions should be paid attention to by logging interpretation and evaluation staff.