Isotropic angle-domain elastic reverse-time migration

Imaging with scalar wavefields

As mentioned earlier, assuming single scattering in the Earth (Born approximation), a conventional imaging procedure consists of two components: wavefield extrapolation and imaging. Wavefield extrapolation is used to reconstruct in the imaging volume the seismic wavefield using the recorded data on the acquisition surface as a boundary condition, and imaging is used to extract reflectivity information from the extrapolated source and receiver wavefields.

Assuming scalar recorded data, wavefield extrapolation using a scalar wave equation reconstructs scalar source and receiver wavefields, ${W_s}{}\left ({\bf x}, t \right)$ and ${W_r}{}\left ({\bf x}, t \right)$, at every location $\mathbf{x}$ in the subsurface. Using the extrapolated scalar wavefields, a conventional imaging condition (Claerbout, 1985) can be implemented as cross-correlation at zero-lag time:

$${I}_{}\left ({\bf x}\right)= \int {W_s}{}\left ({\bf x}, t \right){W_r}{}\left ({\bf x}, t \right)dt \;.$$ (2)

Here, ${I}_{}\left ({\bf x}\right)$ denotes a scalar image obtained from scalar wavefields ${W_s}{}\left ({\bf x}, t \right)$ and ${W_r}{}\left ({\bf x}, t \right)$, ${\bf x}=\{x,y,z\}$ represent Cartesian space coordinates, and $t$ represents time.

Isotropic angle-domain elastic reverse-time migration