Editing Reflection seismology (section)

===Reflection and transmission at normal incidence===
[[File:Normal reflection at an interface.png|thumb|P-wave reflects off an interface at normal incidence]]
When a seismic P-wave encounters a boundary between two materials with different acoustic impedances, some of the energy in the wave will be reflected at the boundary, while some of the energy will be transmitted through the boundary.  The [[amplitude]] of the reflected wave is predicted by multiplying the amplitude of the incident wave by the seismic ''[[reflection coefficient]]'' <math>R</math>, determined by the [[Acoustic impedance|impedance]] contrast between the two materials.<ref name=rs>{{cite book |last1=Sheriff |first1=R. E. |last2=Geldart |first2=L. P. |title=Exploration seismology, Volume 1, History, theory, and data acquisition |date=1982 |publisher=Cambridge University Press |location=Cambridge |isbn=0521243734 |pages=67}}</ref>

For a wave that hits a boundary at [[surface normal|normal]] incidence (head-on), the expression for the reflection coefficient is simply

:<math>R=\frac{Z_2 - Z_1}{Z_2 + Z_1}</math>,

where <math>Z_1</math> and <math>Z_2</math> are the impedance of the first and second medium, respectively.<ref name=rs/>

Similarly, the amplitude of the incident wave is multiplied by the ''[[transmission coefficient]]'' <math>T</math> to predict the amplitude of the wave transmitted through the boundary.  The formula for the normal-incidence transmission coefficient is

:<math>T=1+R=\frac{2 Z_2}{(Z_2 + Z_1)}</math>.<ref name=rs/>

As the sum of the energies of the reflected and transmitted wave has to be equal to the energy of the incident wave, it is easy to show that

:<math>\frac{R^2}{Z_1}+\frac{T^2}{Z_2}=\frac{Z_2(Z_2 - Z_1)^2+4Z_1Z_2^2}{Z_1Z_2(Z_1+Z_2)^2}=\frac{1}{Z_1}</math>.

By observing changes in the strength of reflections, seismologists can infer changes in the seismic impedances. In turn, they use this information to infer changes in the properties of the rocks at the interface, such as [[density]] and [[Phase velocity|wave velocity]],<ref name=rs/> by means of [[seismic inversion]].