Synthetic examples

A simple 2-D example serves to demonstrate the different methods and their noise suppression capabilities. Figure  shows a synthetic dataset containing two dipping events. Random noise with a signal to noise amplitude ratio of 1:1 has been added.

In Figure , the straightforward 3-D interpolation scheme of SEP-73 is applied. For each output location, we select the N (here N=15) nearest neighbors. Each pair of traces is cross-correlated, and the results are combined to give an estimate of event coherency as a function of dip. The dip which gives the maximum coherency is chosen, and the traces are summed along this trajectory to give a new trace at the desired output location. Although the stack is over fifteen traces, the noise has not been attenuated significantly.

In Figure , the stack is weighted by the coherency, computed as a function of time, measured along the best dip direction. (Actually semblance is being used here instead of the generalized coherency of SEP-73.) This weighting supplements the noise suppression power of the stack and makes a cleaner result. In Figure , the median is used instead of the mean, and in Figure , both the median and semblance weight are used. This combination gives the best overall noise suppression.

An example of velocity filtering is shown in Figure . Here we have limited the algorithm to scan over only a certain range of dips; the more steeply dipping event is filtered out. Note that this method does not attempt to deal with the problem of aliased energy.

 

noise
Figure 1 Synthetic example containing two dipping events. Random noise has been added with a signal to noise ratio of 1:1.

 

interp
Figure 2 Synthetic interpolated to same geometry to test noise suppression properties. No semblance weighting has been applied, and the mean is used for stacking, so there is little noise suppression.

 

semb
Figure 3 Semblance weighting has been applied.

 

med
Figure 4 Median filter has been applied along the best dip trajectory, rather than the mean of conventional stacking.

 

medsemb
Figure 5 Both median and semblance weighting used.

 

filt
Figure 6 A velocity filtering example. Limiting the range of dips searched by the algorithm can attenuate other dips.