Sensitivity

Figure 3.25: Influence of $V_{s0}$ with a constant Poisson's ratio. $V_{s0}$ varies from 100 to 1900 m/s. $V_{s1}$ is 2000 m/s. Poisson's ratio is 0.25 and the density is 2 t/m$^3$ at all depths.

The case of figure 3.9(b) is taken as an example. Thus, Poisson's ratio is 0.25, and $V_{s0}$ varies from 100 to 1900 m/s. The auto-correlation curves are calculated for all rings described in figure 3.24(b) with equation 3.50. The results are plotted in figure 3.25. All curves are between -0.4 and 1, converging towards 1 for low frequencies, and oscillating around zero for high frequencies. The shapes observed for the dispersion curves are transposed to the auto-correlation, for instance, the strong variation in the slope at 0.9 Hz for the darkest curve. A translation towards higher velocities on the dispersion curve appears as a translation of the first minimum of the auto-correlation curve towards a higher frequency.