Random noise attenuation by a selective hybrid approach using f-x empirical mode decomposition

Discussions

In this section, we would like to give some comments on the practical aspects of the applications of the proposed approach.

1. Currently, $f-x$ EMD can not be widely used in real seismic data processing because of two main reasons: (1) not efficient and (2) causing damage to dipping energy. For the efficiency issue, as modern computational power is increasing very fast and fortunately the $f-x$ EMD is implemented in frequency-space domain frequency by frequency, we can developing parallel version of $f-x$ EMD codes in order to make it run fast. We also want to clarify that with the incomplete EMD as proposed in Chen and Ma (2014), the computational cost of $f-x$ EMD is actually not too heavy, especially when compared with EEMD and CEEMD, which are prohibitively unaffordable and are difficult for parallelizing. For the dipping-removal issue, we can solve it easily by using a hybrid $f-x$ EMD approaches, which is being discussed in the paper and also investigated a lot in the literature.

2. The proposed selective hybrid approach is designed specifically following the special property of seismic data. As we all know, the post-stack or post-migration seismic images mainly contain horizontal events. How to fully use the advantage of $f-x$ EMD in handling horizontal events and also deal with complex structure becomes the focus of the presented work. Instead of using a full hybrid $f-x$ EMD approach, which make sure no coherent dipping events are lost, we propose to use a selective hybrid strategy. The hybrid approach is only applied to those regions where complex structure exist, leaving other simple horizontal events processed only using $f-x$ EMD. The selective hybrid $f-x$ EMD can be applied in local processing windows, in which case an automatic approach for detecting complex structure should be developed, and can also be applied to the global window, where complex structures are manually picked out for processing with a variable hybrid processing window, such as the second example in this paper (even though it is a pre-stack test). The local selective hybrid approach is applicable to relatively bigger dataset and with relatively more complicated structures. The global selective hybrid approach is applicable to relatively smaller dataset and with relatively simpler structures.

3. A graphical user interface (GUI) can be developed to best utilize the proposed selective hybrid $f-x$ EMD. In the GUI software, the seismic data can be processed section by section. The $f-x$ EMD is applied to the whole dataset initially, then we can pick out different area in the graphical interface for hybrid denoising conveniently. The GUI approach can deal with any dataset with different complexities and do not need the automatic complex-structure detection algorithm.

4. The horizontal-preservation property mentioned in this paper does not mean strictly horizontal preservation. Unlike 1D mean and median filters, $f-x$ EMD can also preserve useful reflections with small dip angle. Compared with KL or SVD transforms, the $f-x$ EMD can be much more adaptive, because the horizontal events mainly lay in the first 1$-$ 3 IMFs after EMD in the $f-x$ domain, however, the number of singular values corresponding to the useful horizontal reflections for KL or SVD transforms have a large range and thus is not convenient to chose. According to our experience, the performance for preserving horizontal events of $f-x$ EMD is also much better that that of KL or SVD transforms.

Random noise attenuation by a selective hybrid approach using f-x empirical mode decomposition