Reflection and refraction of the near-surface $P$-waves on a line of elastic parameters discontinuity

The reflected and refracted problems on elastic surface waves of horizontal polarization (P-waves) from a line of elastic parameters jump are under consideration. The relevant coefficients of reflection, refraction, and transformation are obtained by means of the parabolic equation method. The comparison of the Rayleigh waves, $SV$-waves, and $P$-waves is carried out. Numerical values of the transformation matrix are obtained for the case of the passage of a wave of the whispering gallery to the sum of waves of the whispering gallery and a homogeneous wave to the first five modes of waves of the whispering gallery.