SPATIALLY ALIASED DATA

The datasets we have processed were spatially aliased (at least in part). The traditional conclusion is that for the aliased high frequencies we cannot obtain useful information about source locations, and we should filter the traces accordingly before any multichannel processing. Contrary to this traditional view, we obtained some interesting and promising results using high-frequency data that were supposedly aliased. The question is, how reliable are these results?

All pictures below show the semblance patterns for horizontal slices taken at depths where the source was actually located. These pictures were obtained for different parameters (spectrum, depth) of the source, so we can get an idea how the picture changes for different situations.

For the Iceland array, the distance between channels was 200 meters and the near-surface velocity about 2000 m/s. This means that for steep dips the data are aliased for frequencies greater than 5 Hz (in other words, nearly all frequencies). Figures , , and show semblance patterns for frequencies 10, 20, and 50 Hz (here I used monochromatic sources); the depth was 100 meters. For all these frequencies (well above aliasing) the location of the source is unambiguously determined.

The same patterns for sources at a depth of 1000 meters are shown in Figures , , and . These patterns are clearly contaminated with ``sidelobes'', and locating of sources for frequencies higher than roughly 10-15 Hz becomes much less reliable.

For an intermediate depth of 500 meters (Figure ) the picture is not much worse than for 100 meters even for as high a frequency as 50 Hz.

Figures  and were obtained using a broad band (60-100 Hz) signal for depths of 100 and 1000 meters, respectively. The results have improved considerably. Apparently, this improvement is due to destructive interference of the sidelobes of different frequencies.

The drill-bit array is much more dense than the Iceland array. Assuming a velocity of about 10000 feet/s the data is aliased for frequencies higher than roughly 50 Hz.

Semblance patterns for this array were obtained for two source depths - 900 and 450 meters - and frequencies 100 and 200 Hz (Figure , , and ). The results show that for very high frequencies and shallow depths sidelobes can be present, but their amplitudes are significantly smaller than that of the main peak. Figure  shows the result for a broadband signal for the depth of 450 meters. The picture again is much better than the monochromatic case.

 

al10s.100
Figure 6 al10s.100

Semblance for depth 100 meters, frequency 10 Hz. Iceland array.

 

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Figure 7 al20s.100

Semblance for depth 100 meters, frequency 20 Hz. Iceland array.

 

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Figure 8 al50s.100

Semblance for depth 100 meters, frequency 50 Hz. Iceland array.

 

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Figure 9 al10s

Semblance for depth 1000 meters, frequency 10 Hz. Iceland array.

 

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Figure 10 al20s

Semblance for depth 1000 meters, frequency 20 Hz. Iceland array.

 

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Figure 11 al50s

Semblance for depth 1000 meters, frequency 50 Hz. Iceland array.

 

al50s.500
Figure 12 al50s.500

Semblance for depth 500 meters, frequency 50 Hz. Iceland array.

 

b60100.100
Figure 13 b60100.100

Semblance for depth 100 meters, broadband signal 60-100 Hz. Iceland array.

 

b60100.1000
Figure 14 b60100.1000

Semblance for depth 1000 meters, broadband signal 60-100 Hz. Iceland array.

 

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Figure 15 tun100s

Semblance for depth 900 meters, frequency 100 Hz. Drill-bit array.

 

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Figure 16 tun200

Semblance for depth 900 meters, frequency 200 Hz. Drill-bit array.

 

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Figure 17 tun200.1500

Semblance for depth 450 meters, frequency 200 Hz. Drill-bit array.

 

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Figure 18 tun150200

Semblance for depth 450 meters, broadband signal 150-200 Hz. Drill-bit array.