Discussion

This completes the fully elastic least-squares estimation of the $\grave{P}\!\acute{P}$ and $\grave{P}\!\acute{S_1}$ specular reflection coefficients from displacement vector wavefield seismic data. By analogy, any of the other 7 components of the elastic scattering matrix ${\bf {\cal R}}_{ij}$ in (2) can be derived in a similar manner. Perhaps in the next theory paper I will append all 9 integral solutions, but I am most interested in the $\grave{P}\!\acute{P}$ and $\grave{P}\!\acute{S_1}$ expressions at this point in time.

In a future paper, I will re-express the integral solutions derived here in the common-offset domain, and derive companion integral solutions for the least-squares estimation of the specular reflection angles $\Theta_{PP}$ and $\Theta_{PSv}$ directly as a weighted migration of the vector wavefield seismic data. At that point, I will discuss pertinent implementational issues.