Spectral analysis of the balance equation of ground water hydrology

The spectral analysis of the balance equation of ground water flow, associated to an asymptotic expansion of the conductivity (K) and head (h) fields, permits to show that the high wave number components of the source terms, F, and of the conductivity, K, are attenuated when h is computed as solution to the balance equation. This has important consequences on the inverse mapping (h, F) → K: in fact it is not possible to recover in a reliable way the high wave number components of K, because small errors on the corresponding components of h are amplified so that they can hidden the true signal.