Crosscorrelation

Crosscorrelation can be used to enhance a signal embedded in noise. For instance, if we had a source waveform for the surface source that we see in Figure 2, we could crosscorrelate our recorded traces with this wavelet. Energy from this surface source would be enhanced after crosscorrelation at the expense of other signals.

While we suspect the surface source in Figure 2 to be a nearby river, we do not have a source waveform to use in crosscorrelation. However, we might suppose that traces near the source are strongly influenced by it and use one of these traces as the source waveform in crosscorrelation. Figure 3 shows the result of crosscorrelating the raw data from Figure 1 with a single channel from the array. Moveout of a signal (the surface source) is readily apparent in the crosscorrelated result.

 

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Figure 3 The raw data from Figure 1 have been crosscorrelated with a single channel to enhance the strong surface noise source. Crosscorrelation preserves the moveout present in the raw data.

An interesting point to note is that crosscorrelation preserves the moveout in the original data. Thus we can beam steer the crosscorrelated output just as we would the raw data. And since crosscorrelation compresses the data, moveouts are located in a small zone centered on the zero lag, and beam steering can be less expensive than when long time records must be stacked. The improvement in quality of Figure 3 over the raw data in Figure 1 suggests that beam steering will be able to define the source much more accurately after crosscorrelation.

The result of beam steering the crosscorrelated data is shown in Figure 4. Because it dominated the near trace that we used in crosscorrelation, the nearby surface source is the dominant feature in the beam steered result. In a later section of this paper, we will use the improved image of the surface source provided by crosscorrelation to suppress this source and enhance sources at depth.

 

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Figure 4 Data from the array have been crosscorrelated with a single trace and the nearby surface source has been enhanced.

A single trace selected from the array may not be the best estimate we could make of the source waveform. From Figure 4, we know very well the parameters that characterize the moveout trajectory of energy from the nearby surface source. We can compute this trajectory, stack the data along it, and use this stacked trace as the source signal in crosscorrelation. After doing so, we have beam steered the crosscorrelated data. The result is shown in Figure 5. Using the stacked trace has improved the correlation and made the surface source even more dominant in the beam steered result. This improved picture of the source will aid us when we try to suppress it.

 

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Figure 5 Data from the array have been crosscorrelated with a trace formed by stacking the array data along the moveout trajectory for energy arriving from the nearby surface source. This improved source estimate has improved the correlation and reduced the influence of other sources on the beam steered result.