Seismic data processing consists of a continual series of trade-offs. This is especially true when you are trying to deal with noise and multiple attenuation. If you are besieged by coherent noise all you can hope is that you have some type of leverage between such noise and your signal of interest. Historically the leverage has been in terms of dip and/or frequency content. If your noise has a specific dip that is different from your signal over the zone of interest you may filter it out in FK. If your noise has a dominant frequency and is not too broad band you could filter it our with a temporal filter. Both of these techniques must be applied to the entire trace.
With the advent of the stft [short time Fourier transform] routine we have the ability to filter noise from the data in a very localized fashion both in terms of time and frequency. In addition we avoid non-stationarity problems prevailing when using FFT over the whole time interval.
The stft routine uses a short time Fourier transform to build up an output time-frequency spectrum for each input trace. This is accomplished using the following algorithm:
1. Center a sampling window of user defined length at the desired output sample.
2. Apply Gaussian weighting to the samples within the window
3. Perform an FFT on the windowed data
4. Express the transformed data in terms of amplitude and phase
5. Place the amplitude in the upper and the phase in the lower portion of the output trace.
6. Move the window down a sample and repeat the above process.
There are two output modes available with which to view the transformed data. The default is to build in memory N sub-band records for every input record where N is the sampling window size in samples divided by 2. The second is to output a time-frequency spectrum record of N traces for each input trace.
If flagged with a -R the stft routine will perform an inverse transform of the input data. This is done using the following algorithm:
1. Load the amplitude and phase information from a given sample into memory.
2. Convert to complex data type.
3. Perform an inverse FFT on the data.
4. Extract the central sample of the resulting time series to output at this sample position.
5. Move down one sample and repeat the procedure.
This results in a single output trace for every N input traces where N is the number of samples in the sampling window divided by 2.
As it turns out this is a very robust inverse. Full circle transforms have shown amplitude differences between zero and a tenth of a percent.
The data in this example (fig. 1) is from a 3D vibroseis survey acquired in the Cement area of western Oklahoma. The problem is the high amplitude linear noise that interferes with the zone of interest between 1200 and 2400 milliseconds. The processing crew desired to use the primary data from within this interval as input to an automatic statics picking routine. The presence of the linear noise caused severe cycle skipping and a poor static solution. Application of standard dip filtering was ineffective due to the aliased nature of the linear noise.
An stft test was run on this line and it was found that the noise in question was locally separated from the primary signal over the zone in terms of frequency. When examining the sub-band display of the input record (fig.'s 2) it can be seen that the undesired noise is
present on sub - bands 2 thru 7 while the dominant primary energy associated with the event upon which statics are to determined covers sub - bands 7 and up. By applying a local polygonal mute to sub-bands 2 thru 7 followed by an inverse transform of the data the noise was effectively eradicated from the data but only over the zone of interest (fig. 3). The remainder of the data received no filtering. A statics solution was then derived from the processed data yielding significantly better results.
In this example the presence of a large acoustic impedance at the water bottom over the October Oil Field in Egypt's Gulf of Suez has resulted in a significant amount of seismic energy being trapped in the water column. This energy reverberates throughout the entire recording cycle and hence is present on the data from time zero through maxtime (fig. 4).
When examining the stft forward transform of the test records it was observed that on sub-bands 9 and 10 a signal with a period associated with the water bottom lag was found to exist (fig. 5). This energy did not decay with time as would be expected of a signal travelling through the subsurface at this frequency. It was assumed that these reflections were caused by wave energy reverberating within the water column. The two sub - bands were muted and an inverse transform applied (fig. 6).
The resulting dataset had a much cleaner primary [and multiple] signature at depth. A difference dataset (fig. 7) revealed the extent of the water-born noise that had previously been destructively interfering with the dataset.
In this example, from the Arapahoe 3D survey from the MCBU, there is extremely high amplitude air blase and ground roll (fig. 8). Both of these events are slow, aliased and broad band in nature. They are however localized in terms of their destructive interference on the dataset. In this case the time - frequency transform was muted using a pair of surgical mutes, one using the velocity of the air blast and the other using the velocity associated with the ground roll. This was applied to the first 5 sub-bands (fig. 9) with excellent results (fig. 10). It is noted that there was a loss of low frequency character at depth however a significant improvement of both the statics solution and stacking velocities was to be had. Once derived, these solutions were applied to the data prior to filtering producing a much improved stacked section.
Unlike a regular whole trace FFT this type of transform provides not only localized amplitude but also localized phase values
The actual value of the phase at a given sample in each sub-band appears to be physically realizable. Examination of the decomposition off a wedge model determined that the phase value corresponded very closely to theory as the wedge narrowed and the sampling wavelets began mixing. This implies that measurement of localized phase variations with offset along an event is possible.
So much interesting work and so little time left in life.....
To actually accomplish the filtering in the above examples an XIKP net was constructed where the output from stft was passed to a splitr with as many outputs as sub-bands.
In this fashion each sub-band could be treated individually and either muted of passed accordingly. A merge of the sub-bands was added and the output was passed to an inverse stft to provide the filtered output. At the moment this approach is the only way to make use of this procedure. If you wish more information on this topic or need consulting on application in USP please do not hesitate to give anyone in the USP shop a call.
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