Isotropic angle-domain elastic reverse-time migration

Imaging with vector displacements

Consider the images obtained for the model depicted in Figures 3a and 3b. Figure 3a depicts the P-wave velocity (smooth function between $1.6-3.2$ km/s), and Figure 3b shows the density (variable between $1-2$ g/cm$^3$). The S-wave velocity is a scaled version of the P-wave velocity with $V_P/V_S=2$. We use a smooth velocity background for both modeling and migration. We use density discontinuities to generate reflections in modeling, but use a constant density in migration. The smooth velocity background for both modeling and migration is used to avoid back-scattering during wavefield reconstruction. The elastic data, Figures 4a and 4b, are simulated using a space-time staggered-grid finite-difference solution to the isotropic elastic wave equation (Mora, 1988; Virieux, 1986; Mora, 1987; Virieux, 1984). We simulate data for a source located at position $x=6.75$ km and $z=0.5$ km. Since we are using an explosive source and the background velocity is smooth, the simulated wavefield is represented mainly by P-wave incident energy and the receiver wavefield is represented by a combination of P- and S-wave reflected energy. The data contain a mix of P and S modes, as can be seen by comparing the vertical and horizontal displacement components, shown in Figures 4a and 4b, with the separated P and S wave modes, shown in Figures 4c and 4d.

Imaging the data shown in Figures 4a and 4b using the imaging condition from equation , we obtain the images depicted in Figures 5a to 5d. Figures 5a to 5d correspond to the cross-correlation of the $z$ and $x$ components of the source wavefield with the $z$ and $x$ components of the receiver wavefield, respectively. Since the input data do not represent separated wave modes, the images produced with the imaging condition based on vector displacements do not separate PP and PS reflectivity. Thus, the images are hard to interpret, since it is not clear what incident and reflected wave modes the reflections represent. In reality, reflections corresponding to all wave modes are present in all panels.

Isotropic angle-domain elastic reverse-time migration