Construction codes demand ever increasing earthquake-resisting features for strategic buildings such as dams and nuclear plants and the incorporation of uncertainty in the design models for these structures, particularly in soil domains, becomes a major issue. Parametric methods and a recent non-parametric method are considered for the construction of a probabilistic model of the soil impedance matrix, the latter supplying interesting features provided that the matrices of a certain mean model can be identified. This difficulty is tackled using a hidden state variables model, ensuring causality of the impedance and necessary positive definiteness conditions on the generated matrices. The identification of the uncertain parameters in the soil and the difficult task of quantifying their variability are not required and computational costs are significantly reduced.