I am working with a numerical modelling program allowing to simulate wave propagation in a drill string.
The reflected waves are modelled using the reflection coefficient between the drill bit and the underlying rock, defined as the difference between the impedances of both media, $Z_1$ and $Z_2$, divided by the sum of these impedances: $$\frac{Z_1-Z_2}{Z_1+Z_2}.$$
So far so good. However, the primary waves rely on another "reflection coefficient" defined as $$\frac{Z_1Z_2}{Z_1+Z_2}.$$
What bugs me here is that this coefficient is not dimensionless: it is actually homogeneous with an impedance!
Assuming that this is not a typo from the author of the code, what would be the physical meaning of a non-dimensionless reflection coefficient?