Complex conductivity measurements of carbonate rocks are scarce despite the occurrence of these rocks at the surface of the Earth. The complex conductivity spectra of 57 carbonate samples were measured in a broad frequency range and at four salinities (NaCl). A simple model of induced polarization is developed to be applied to induced polarization measurements in the field. The in-phase conductivity (related to conduction) is reported as a function of the pore water conductivity to determine the (intrinsic) formation factor and the surface conductivity. The surface conductivity and the normalized chargeability are linearly correlated to the specific surface area divided by the tortuosity of the pore space. This observation is consistent with a dynamic Stern layer polarization model, the Stern layer being the inner layer of the electrical double layer coating the grains. The quadrature conductivity is observed to be proportional to the measured normalized chargeability in agreement with the prediction of the constant phase model. The effect of the texture is discussed and we observe a power-law relationship between the permeability and the formation factor. Then, we illustrate how this model can be applied to field data performed over a carbonate syncline in the French Alps. A 1.9 km long profile is used to separate the glacial till infilling the depression from the underlying limestones in terms of induced polarization properties. The induced polarization survey allows imaging the water content and the specific surface area of the formations down to a depth of 220 m.