Inversion of the vertical and horizontal particle velocities

In this section we explore the utility of the vertical and radial particle velocity components measured at the ocean-bottom for the seafloor parameter inversion. The direct wave components are transformed as before into the ($\omega - k$) domain and the AVO coefficient is determined. Inversion of the data yields the following parameters:

v_p2 = 1689 m/s and v_s2 = 426 m/s.

As with the previous technique, the P-wave velocity is very well determined. The S-wave velocity is within a 3% error bound. The AVO coefficient determined from the data and the AVO curve based on the inverted values are shown in Figure 8. The data fit is very good. The theoretical AVO curve is compared with the inverted one in Figure 9. It is obvious that they are in good agreement.

Using different maximum angles of incidence, we evaluated again how robust the method is for different angular coverages:

 

vzvx Figure 8 The AVO coefficient calculated from the Vz-Vx data is represented by +. It is overlain by the AVO curve based on the inverted parameters.

 

vzvxavo Figure 9 Theoretical AVO curve (solid line) versus inverted one (dotted line).

$$^\circ$$ v_p2 (m/s) v_s2 (m/s)

84 1689 - 0.2% 426 - 2.5%

60 1699 + 0.4% 435 - 0.5%

50 1562 - 7.7 % 328 - 25%

40 1665 - 1.7 % 400 - 8.5%

Table 3: Inverted P-wave velocity and S-wave velocity using different maximum angles of incidence. The error with respect to the real values is given in $\pm \%$.

It is obvious that for using a maximum angle of 50$^\circ$, the inversion yields rather badly constrained seafloor parameters. This angle of incidence corresponds exactly to where the AVO coefficient determined from the data reaches approximately 0. Otherwise, seafloor parameters estimated from the two particle velocity components seem to be constrained in a much better way than the one estimated using pressure and vertical particle velocity. This is partly due to the fact that the method inverts only for two parameters, thus making it more stable, and that the AVO coefficient is sensitive to the S-wave velocity over a broader range of angles of incidence. Furthermore, the two data components used in these methods do not need to be calibrated prior to the inversion.