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

Selective hybrid denoising approach

Considering that in most seismic profiles, dipping events or steeply dipping events takes up a small percent of the total signals, thus the dipping-events retrieving process shown in equation 5 in the above proposed hybrid approach doesn't need to be applied in each processing window for the whole seismic profile. Instead, we can select specific processing window for hybrid processing, this type of incomplete hybrid approach is termed as selective hybrid approach. The detailed algorithmic steps of the selective hybrid approach for random noise attenuation using $f-x$ EMD are shown below:

1. Select a time window and transform the data to the $f-x$ domain.
2. For every frequency,
   1. separate real and imaginary parts in the spatial sequence,
   2. compute IMF1, for the real signal and subtract it to obtain the filtered real signal,
   3. repeat for the imaginary part,
   4. combine to create the filtered complex signal.
3. Transform data back to the $t-x$ domain.
4. If selective hybrid denoising,
   1. forward transform the noise section to a transform domain,
   2. apply a dipping-events retriever,
   3. inverse transform to $t-x$ domain,
   4. combine the horizontal-events section and the dipping-events section to form the denoised section.

5. Repeat for the next time window.

The approach can be best applied to post-stack sections or pre-stack common offset sections, where most of the seismic signal are horizontal. The lost dipping events after $f-x$ EMD can be retrieved by a small processing window using $f-x$ SSA for specific regions instead of processing for the whole profile. For those hyperbolic common midpoint gathers, the new approach should be used carefully by first removing sufficient noise and far-offset dipping events, and then using far-offset processing window for retrieving the useful signal. The selective hybrid approach aims at maximizing the effectiveness of $f-x$ EMD and the whole processing efficiency. When a $f-x$ domain dipping-event retriever is used, e.g., $f-x$ predictive filtering and $f-x$ SSA, the computational efficiency can be improved more because a pair of transforms can be saved. For comparison, we list the detailed algorithmic steps of the selective hybrid approach when $f-x$ SSA is selected as the dipping-events retriever:

1. Select a time window and transform the data to the $f-x$ domain.
2. For every frequency,
   1. separate real and imaginary parts in the spatial sequence,
   2. compute IMF1, for the real signal and subtract it to obtain the filtered real signal,
   3. repeat for the imaginary part,
   4. combine to create the filtered complex signal.
   5. If selective hybrid denoising,
      Apply SSA filtering on the complex IMF1 and add the result to the sum of the initially filtered complex signal,
3. Transform data back to the $t-x$ domain.
4. Repeat for the next time window.

The selective hybrid processing windows can only be manually selected for the current stage. The manual selection will not bring too much trouble considering those profiles that only have dipping signals in few number of local time-space windows. For more complicated seismic profile, we need to automatically decide the selective hybrid processing windows in order to preserve the effectiveness of the selective hybrid processing strategy. The automatic checking technique is still being investigated. For those profiles that do not need processing in local time-space windows, e.g. not too large seismic data, we can first process the whole profile using $f-x$ EMD, and manually select the regions that have dipping signals for hybrid processing. In this case, the size and tapering width for the selective hybrid window can be chosen with more adaptivity and the selective hybrid windows do not need to have the same sizes. This procedure can also be implemented with a GUI manner and this topic is still being investigated.

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