does only cover the inner inductance of a wire.
If I use scattering parameters (switching to Zpar) to extract
the inductance, I will get the sum of inner and outer inductance. RIGHT ???
Yes. You're impedance analyzer (or whatever) is just computing inductance. It has no idea what makes up the inductance. Mutual, partial, inner, outer... it does not know. It just inductance.
You would agree, the formula derived from the skin depth model
does only cover the inner inductance, while impedance analyzers
measure the total inductance, which is the sum of all..