I don't know anything about impedance spectroscopy, but fractal dimension is a very interesting manner of porosity measure. Look for mass-radius relatioship. The methodology is very simple and can capture the essential nature of materials.
Well, with regards to petrophysics, you can calculate porosity by using Archie's law (easy to google).
Good luck!
Dear Luca, I disaggree with you. In fact, it is quite simple to calculate the porosity.
Regarded to Archie's law, the resistivity of the investigated sample (rho_zero) equals the product of the so called formation resisitivity factor (F) and the resistivity of the saturating fluid (rho_w). So rho_w depends on the porosity (Phi) of your system. Therefrom, the so called 1st Archie equation has been found, which states that
F = 1 / Phi^m, where m is the so called cementation exponent.
A simplification of this formula is the so called Humble-Formula:
F = 0.62 / Phi^2.15
So, you get your rho_zero from your measurement, you know your saturation fluid and can determine its resisitivity with ease and then calculate F. Decompose the formula to Phi and done.
You also might check these publications:
http://www.amazon.de/Physical-Properties-Rocks-Fundamentals-Petrophysics/dp/008044346X/ref=sr_1_1?ie=UTF8&qid=1417684550&sr=8-1&keywords=Sch%C3%B6n+Petrophysics
http://www.amazon.de/Petrophysics-Measuring-Reservoir-Transport-Properties-ebook/dp/B007IIS8KQ/ref=sr_1_fkmr0_1?ie=UTF8&qid=1417684550&sr=8-1-fkmr0&keywords=Sch%C3%B6n+Petrophysics
Dear Luca, aggreed that it is not the same - nevertheless, you get these parameters from your measurement and these relations are very robust. So I would guess, better than nothing ;)
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