A SYNTHETIC EXAMPLE

A synthetic dataset comprising a hundred shot gathers was generated with the modeling scheme described in Cunha (1991). The model includes isotropic and transverse isotropic layers, which are described at each point by five parameters (c₁₁, c₃₃, c₁₃, c₅₅, and $\rho$). Figure  shows the c₁₁ component of the model, while Figure  shows the 2 components of the recorded wavefield for one shot.

 

syntmodel
Figure 2 The c₁₁ stiffness component of the synthetic structural model used to generate the data of Figure . The model includes isotropic and transverse isotropic layers.

 

dataslice
Figure 3 One of the synthetic shot records generated by finite differences elastic modeling. (a) Is the vertical component of the displacement field recorded at the surface. (b) Is the horizontal component of the same field. The relative weakness of the shallow reflection at large offsets is caused by the introduction of a thin absorbing region near the free surface in order to simulate a low Q, unconsolidated sediment. Click the button to see a movie with every tenth shot gather. The first set is the z component and the second set is the x component.

A migrated shot gather and the result of stacking all the migrated shot gathers are shown in Figure . The low resolution around the horizontal position of 2000 meters was caused by the accidental missing of twenty consecutives migrated shot gathers, sufficiently close to the report dead line. The acquisition geometry was off-end, with receivers at the right of the source.

 

migimag
Figure 4 (a) Migrated image of one shot gather. (b) Stacking of the migrated shot gathers.The interfaces of the correct model are overlaid to the stacked session.

The retrieved angle-dependent reflectivity at one of the reflectors is compared in Figure  to the theoretical reflectivity function. Although the retrieved reflectivity function fits the general trend of the theoretical curve, it is clear that the method still needs some refinement to allow its application to real data.

 

refofp
Figure 5 The X represent the retrieved reflectivity as a function of the local Snell parameter and the continuous line, the theoretical reflectivity function