Surface acoustic impedance and causality

Several models that are commonly used to calculate the surface acoustic impedance of porous materials are examined in light of the causality requirement in its nonlocal and its approximate local forms. Strict (nonlocal) causality requires that the imaginary part of the surface acoustic impedance be the Hilbert transform of the real part. It is found that the local approximation is not a good test of causality for these models and that, even in its general form, the equation describing the surface acoustic impedance of these porous materials is not strictly causal at high frequencies.