Parameter sensitivity of the reflection coefficient

In this first section, we demonstrate the sensitivity of the reflection coefficient to changes in P-wave velocity, S-wave velocity and density. In each case, one of the parameters was varied while the other two were kept constant. Similar studies have been done by Chapman and Rohr Chapman and Rohr (1991) and Amundsen and Reitan Amundsen and Reitan (1995).

Figure 1 shows the sensitivity of the reflection coefficient to derivations of the original P-wave velocity (1693 m/s) by $\pm$ 100 m/s. The coefficient is very sensitive to P-wave velocity changes near the critical angle (R=1). An increase in v_p shifts the critical angle to smaller angles of incidence. Furthermore, the higher v_p, the higher the reflection coefficient for vertical incident waves.

 

refp Figure 1 Reflection coefficient for P velocity variations of $\pm$ 100 m/s.

 

refs Figure 2 Reflection coefficient for S velocity variations of $\pm$ 100 m/s

 

refrho Figure 3 Reflection coefficient for density variations of $\pm$ 100 kg/m3.

The sensitivity to variations in S-wave velocity is shown in Figure 2. The velocity varies from the original sediment velocity of 437 m/s by $\pm$100 m/s. In contrast to the P-wave velocity sensitivity, the reflection coefficient is only slightly sensitive to changes in v_s for angles less than the critical angle. A considerable dependence on the S-wave velocity exists for post-critical angles, however.

Figure 3 displays the sensitivity to density variations of $\pm$ 100 kg/m³. The reflection coefficient is only sensitive to the density variations until close to the critical angle. The higher the density, the larger the pre-critical reflection coefficient.

When the data include post-critical reflections, the critical reflection angle will determine the P-wave velocity, the post-critical reflections the S-wave velocity, and the small angles of incidence the density.