Wave propagation in earth’s crust has been under study long before seismic prospecting using refracted and reflected waves in a layered medium. The initial interest was the study of the earthquake waves around the globe; see, for example, Ergin (Bull Seismol Soc Am 42:349–372, 1952), Ewing et al. (Elastic waves in layered media. McGraw-Hill, 1957), Kennett (The seismic wavefield. Volume-1: Introduction and theoretical development. Cambridge University Press, 2001) and references therein. The early seismic exploration focus was on the reflection and transmission of the plane seismic waves across a plane boundary between two homogeneous isotropic elastic media. The plane wave assumption is valid in seismic applications since the source-reflector-receiver distances are much higher than the seismic wavelengths. The seismic wave propagation equations are simplified with the plane wave assumption. However, the theory is very much involved, and derivations are still complicated such that prompted the quote of Sir Harold Jeffreys. Here only some of the results of seismic reflection and sometimes transmission is reported.