Synthetic data

My synthetic CMP gather is generated from a velocity model that consists of six layers. Figure 3a displays the stacking velocity function of the model on the background of the velocity spectrum of the data. Figure 3b shows the synthetic CMP gather. Several strong water-bottom multiples can be identified. The result of forward transformation is shown in Figure 3c. Clearly the water-bottom reflection and its multiples are migrated entirely to the negative offsets and are well separated from other events. Now we set the traces at negative offsets to zero and then do backward transformation. The result is shown in Figure 3d. The water-bottom reflection and its multiples are eliminated. At far offsets, some events with linear moveout are truncation artifacts. For simplicity, constant weighting functions are used in the transformations. Therefore, operator ${\bf Q}(v)$ is the transpose, not the inverse, of operator ${\bf P}(v)$. We see that the amplitudes of the events are not preserved after backward transformation.

 

synexa
Figure 3 A synthetic example: (a) stacking velocity function of the layered model; (b) a synthetic CMP gather generated from the velocity model; (c) the result of forward transformation; (d) the output of backward transformation after the traces at negative offsets have been set to zero; the events at far offsets with linear moveout are truncation artifacts.