Synthetic Data Example

To demonstrate the effectiveness of the proposed method, super-virtual diffraction arrivals are extracted from synthetic shot gathers computed with a 2-4 FD forward modeling code for part of the BP2004 model. Three diffractors are placed under the salt body as shown in Figure 4.3. The goal is to extract the diffraction arrivals associated with these diffractors. Four hundred shot gathers are generated with a 20-Hz Ricker wavelet and a 20 m interval. All the shots are recorded by the same 800 receivers with a 10 m interval. The sources and receivers are placed at the depth of 10 m, and the free surface condition is not implemented. A common shot gather is shown in Figure 4.4(a). The diffractions associated with the point diffractor on the right of the salt body are indicated with dashed red lines. These diffractions are identified by comparison against the predicted diffraction traveltimes for that diffractor, and Figure 4.4(b) shows these time-windowed diffractions. In order to eliminate other coherent events in the time window, a median filter is applied to these data in Figure 4.4(b) along the diffraction moveout curve (Moser et al., 1999) and the result is shown in Figure 4.4(c), where the diffractions are enhanced. However, Figure 4.4(c) contains strong artifacts from other coherent signals, because within the time window in Figure 4.4(b) the amplitudes of the direct waves are an order of magnitude greater than the amplitudes of the diffraction events. Figure 4.4(d) shows the super-virtual diffraction with improved SNR compared to the result after median filtering in Figure 4.4(c).

Another synthetic example is shown to illustrate that the super-virtual diffraction can be used to estimate the source and receiver statics. Synthetic data are generated with the same acquisition geometry as in the previous example for the Figure 4.5 velocity model. Random noise and random statics are added in the common shot gather in Figure 4.6(a), where the red lines outline the diffraction arrivals for the left most diffractor. In Figure 4.6(b), the diffraction energy is almost invisible because of the random noise, so that median filtering fails when it is applied along the predicted hyperbolic moveout (Figure 4.6(c)). Since the diffraction arrivals are temporally isolated from other events, the super-virtual diffraction is obtained without median filtering and shown in Figure 4.6(d). The actual moveout curve of the diffraction is preserved and plotted as the blue line in Figure 4.7. In this figure, the red line indicates the predicted arrival time of the diffraction without considering the source and receiver statics. The source and receivers statics can now be estimated from the difference between the blue and red lines or by a phase closure principle (Sheng et al., 2005). In addition, the moveout curve can be used to represent the Green's function for a point source at , which can be used as the natural migration operator (Schuster, 2002).