What would be the phase shift and polarity of a seismic wave a) when it hit the free surface b)when the free surface reflection goes down and hit a reflector and returned to the receiver placed on the surface.
In general, the answer is not simple as it depends on the angle of incidence of the wave and the properties of the medium.
The Zoeppritz equations are used to understand the behavior of seismic waves incident on reflectors (or the free surface). The solutions give the reflection and transmission coefficients for P and S waves, which depend on the densities and wave speeds of the lower and upper media as well as the angle upon which the wave is incident. In general, the coefficients are complex valued; the phase shift is encoded in the phase of the complex number.
I have used the Zeoppritz explorer program for this calculation.