(37) |

(38) |

(39) |

We tested the theory with the set of anisotropic Thomsen parameters of the Taylor Sand () described in Tsvankin (2001).

Figures 8 to 10 show examples of the application of the RMO function expressed in equation (30) when perturbing the velocity uniformly (). In the different examples, we didn't approximate the values of but computed them from the values of .

Figure 8 shows that for flat reflectors, the RMO function we derived accurately tracks the actual RMO function when the perturbations are sufficiently small to be within the range of accuracy of the linearization. This is consistent with the results presented in Biondi (2005b). The relative lack of accuracy at large aperture angle is due to the limited offset range we used for the modeling and the migration.

The top panel of Figure 9 shows that for a dipping reflector the RMO function we derived accurately tracks the actual RMO function (the relative lack of accuracy at large aperture angle is due to the limited offset range we used). However the bottom panel shows that the use of the RMO function given in Biondi (2005b) (i.e. assuming that the reflector is flat) gives comparable results.

The top panel of Figure 9 shows that for a dipping reflector, the RMO function we derived perfectly matches the actual RMO (we used a larger offset range). The bottom panel shows that the RMO function given in Biondi (2005b) (i.e. assuming that the reflector is flat) gives poor results. It justifies a posteriori the need for generalizing to dipping reflectors the concepts of quantitatively relating perturbations in anisotropic parameters to the corresponding reflector movements in anisotropic ADCIGs.

Figure 8

Figure 9

Figure 10

4/6/2006