We found a physical interpretation of the Cole-Cole relation for the conductivity of fluid-saturated, mineralized rocks. The first step was to rederive a diffusive version of the Cole-Cole relation from a pore-scale description that couples diffusion and electrochemistry in a simplified way. We wanted to give the parameters of the Cole-Cole relation, the chargeability and relaxation time, a microscopic interpretation. In this treatment, the exponent known as the frequency dependence was fixed to either or depending on the ratio of the diffusion length and effective pore length. However, many field observations give . The second step was to calculate the conductivity of a network in which the individual bonds are described by the Cole-Cole conductivity function with . These network simulations, which did not rely on effective medium approximations, turned out to exhibit Cole-Cole behavior as well with taking on a continuous range of values, provided the pore-scale parameters are picked from sufficiently wide distributions. These network results agreed with observations based on field data inversion.