In the normal incidence case of Backus averaging, the layer properties of thickness, , compliance, , and mass density, , are replaced by the corresponding properties of the equivalent homogeneous medium, , ,and :
that is, the thickness of is the sum thickness of the layers, , and the equivalent medium mechanical properties are the thickness-weighted averages of those of the layered medium.
However, these layers can also be described in terms of the layer properties of one-way travel-time, , and impedance, , with slowness, acting as the means for changing the independent variable between depth and time. It is well known that:
and from these:
but , so:
and by similar reasoning the slowness equivalent:
and, since = :