Discussion

The proposed formulation of the seislet transform attempts to construct multiscale prediction operators, to enhance the performance of the seislet transform. The prediction operators in the original seislet transform are defined by PWD, so the prediction of distant traces needs recursive computation, which is very time-consuming when it comes to large size dataset. In the proposed RT-seislet transform, an RT volume is used to define a multiscale prediction operator. As shown in the previous sections, the relationship between any two traces can be obtained from the RT volume, which helps avoid the recursive computation for the prediction of distant traces. As a result, the RT-seislet transform is much more efficient than the original seislet transform.

Besides, in the implementation of the proposed method, the choice of reference traces plays an important role in the generation of the RT volume. More reference traces usually mean a better RT volume. The location of reference traces also needs to be considered carefully. In practice, evenly distributed reference traces are recommended. Besides, complex geologic structures need to be treated differently. For example, it is better to put reference traces at each side of faults. Another important issue is about the smoothing radius when estimating local slopes by PWD. For noise-free data, small smoothing radius is enough. The smoothing radius is three for the estimation of Figure 2. And with the increasing of the noise level, larger smoothing radius is needed.

The proposed RT-seislet transform highly depends on the RT volume. In our method, local slopes by PWD, which are easily affected by noise, are utilized to generate the RT volume, so the new formulation is sensitive to the noise. However, this problem certainly can be solved by improving the PWD or using other methods, which are not sensitive to noise, to generate the RT volume.