Random noise attenuation by $f$ -$x$ empirical mode decomposition predictive filtering

f-x empirical mode decomposition predictive filtering

$f-x$ EMDPF utilizes the property that the first few (generally $1\sim3$ ) IMFs for each frequency slice in the $f-x$ domain contain the high-dip-angle components and random noise. Thus the leaked dipping events can be obtained by applying a predictive filter to these IMFs. Adding the predicted signal to the sum of the remaining IMFs will suppress random noise without harming the effective signals.

$F-x$ EMDPF is a new seismic noise attenuation method which combines the advantages of both $f-x$ predictive filtering and $f-x$ EMD. The detailed algorithmic steps of $f-x$ EMDPF are similar to $f-x$ EMD (Bekara and van der Baan, 2009) and 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. apply an AR model to IMF1 and add the result to the sum of the remaining IMFs,
   4. repeat for the imaginary part,
   5. combine to create the filtered complex signal.
3. Transform data back to the $t-x$ domain.
4. Repeat for the next time window.

It should be emphasized that the number of the filtered IMFs is not limited to one, but is selected according to both the noise level and the distribution of the dip components within the specific seismic data set. If the noise level is high, then a larger number of IMFs should be chosen, because the noise remains not only in the first IMF but also in the second or the third, albeit with decreasing energy. If the dip components are mainly distributed in the high-angle range, then the number of IMFs could be relatively smaller, but when the dip components are distributed in the low- or mid-angle range, we should choose more IMFs in order to ensure that noise is removed whilst still preserving these dipping components.

Generally the number of IMFs for filtering is within the range of $1\sim3$ . In conventional EMD, the signal is completely decomposed into all the IMFs, along with the remainder. In our proposed algorithm, EMD decomposes a signal into only $1\sim3$ components, which correspond to the number of IMFs to be filtered. Compared with the conventional EMD, this uncompleted decomposition algorithm can improve the computation efficiency by about 5 times.

Random noise attenuation by $f$ -$x$ empirical mode decomposition predictive filtering