Elastic wave-vector decomposition in heterogeneous anisotropic media

Homogeneous triclinic model

To further test the proposed method in a low-symmetry anisotropic model, we use next a triclinic model with parameters specified in equation 20. Similar to before, a point displacement source with equal magnitude in all components is used. The full elastic wavefield is generated in the same manner and shown in Figure 11 at time $0.13~s$ . We observe a complicated behavior of the two S-wave modes in comparison with the orthorhombic case in Figure 7. We show only the y-component of the separated S1 and S2 wavefields in Figures 12 and 13 for conciseness. We observe reduced planar artifacts after the implementation of the proposed smoothing method and further correct the amplitudes. The y-component of the resultant separated wavefields with and without corrected amplitudes are shown in comparison in Figure 12. We observe again clean separated wavefields with no apparent artifacts and correct amplitudes similar to the previous case of homogeneous orthorhombic model.

hTRIw-lr-x,hTRIw-lr-y,hTRIw-lr-z
Figure 11. Original elastic wavefield in ${[x,z]}$ , ${[y,z]}$ , and ${[x,y]}$ planes generated from the stiffness tensor coefficients of the triclinic model (equation 20) a) x-component b) y-component c) z-component. One can observe more complicated S-wave behaviors that those in the orthorhombic model (Figure 7).

nohTRIw-dlr-S1-y,hTRIw-dlr-S1-y,comhTRIw-dlr-S1-y
Figure 12. Separated y-component of S1 elastic wavefield in the triclinic model (equation 20) with $\tau$ equal to a) 0 (no smoothing) b) 0.2. The final seprated wavefield with amplitude compensation (equation 28) is shown in c). Notice planar artifacts disappearing when the proposed smoothing filter is applied as shown in b) and with the restored amplitude as shown in c). The clipping has been adjusted to enhance visualization and stay constant in all three plots.

nohTRIw-dlr-S2-y,hTRIw-dlr-S2-y,comhTRIw-dlr-S2-y
Figure 13. Separated y-component of S2 elastic wavefield in the triclinic model (equation 20) with $\tau$ equal to a) 0 (no smoothing) b) 0.2. The final seprated wavefield with amplitude compensation (equation 28) is shown in c). Notice planar artifacts disappearing when the proposed smoothing filter is applied as shown in b) and with the restored amplitude as shown in c). The clipping has been adjusted to enhance visualization and stay constant in all three plots.

Elastic wave-vector decomposition in heterogeneous anisotropic media