Uncertainty propagation using some common mixing rules for the modelling and interpretation of electromagnetic data

This study deals with the calculation of the uncertainty that occurs when one wants to estimate the porosity of a mixture from its electric and electromagnetic response. The uncertainty when estimating the electric and/or electromagnetic response (conductivity, permittivity or magnetic permeability) of a saturated granular medium, from the responses of its components has also been calculated. Some of the most common mixing rules used in geophysics have been analysed. Particular attention has been paid to the uncertainties that can be encountered in field surveys in order to make the user aware of the range of variability of the results. A comparative analysis shows that in the porosity range (10% < ϕ <25%), some commonly used mixing rules can lead to results that differ by even 100%. In the same porosity range, when uncertainty bars are considered, some mixing rules show such overlapped uncertainty bands that the choice among different mixing rules seems to depend more on the achievable uncertainty than the physical hypotheses on which they are built. In fully saturated materials, such as in river bed sediments or in the saturated zone of aquifers, the estimation of the water content can easily be affected by an uncertainty of 10%. Particular attention should therefore be paid when dealing with multi-phase materials: the Archie mixing rule, for example, when applied to low saturated, loose material, may give rise to high uncertainties.