Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2023 / Paper 1 / 6 / n / Solution

Specify the amplitude convention. For incident stress/pressure amplitude one, the normal-incidence seismic reflection coefficient and stress seismic transmission coefficient areAt limestone–sandstone, $R_P=-3/19=-0.1579$ and $T_{\sigma P}=16/19=0.8421$. At sandstone–salt, $R_P=0$ and $T_{\sigma P}=1$. The first return reverses the chosen stress-pulse polarity; the second interface produces no normal-incidence P return.

For a particle-velocity amplitude convention, $R_v=-R$ and $T_v=1-R$, giving $(R_v,T_v)=(0.1579,1.1579)$ and $(0,1)$ respectively. These are amplitude coefficients, not fractions of energy. The lossless reflected and transmitted energy fractions are $\mathcal{R}=R^2$ and $\mathcal{T}=4Z_a{Z}_b/(Z_a+Z_b{)}^2=1-R^2$, which sum to one.