Solar decimation

The solar data set can act as an excellent modeling exercise for testing our ideas about the passive imaging concept. The impulse response of the sun, while containing no reflective structure, is simple, not laterally variable, and the ambient noise is ubiquitous at all locations and azimuths. These characteristics make it a great laboratory if not a perfect model. The question it won't ever address however is: how long will our records need to be on earth?

 

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Figure 1 The entire data volume processed with the correlation methodology and stacked across offsets. From ()

While the dimensions of the full volume of the solar seismic data set are 256 x 256 x 256, it is easy to window smaller cubes out of the volume or simply take any one line of receivers. Figure , shown for reference, shows the impulse response of the sun as arrived at through the correlation processing of the entire solar data. Events are plunging waves, overturning and returning to the surface, of multiple order bounces within the survey area. Figure is the result of a single line of receivers correlated with each other. While the quality of the image is definitely degraded, the plunging waves are readily interpretable (even the second order events if you really believe).

 

2d Figure 2 By using only one receiver line of the 256 available, the image quality is poor, but interpretable. Is this validation of the 2D experiment?

As an exercise for a well rounded argument, I also began decimating the data by various factors and comparing the result to images that were decimated by the same factor after being constructed with the entire data set. Since Figure is very definitely of worse quality than one of the panels comprising Figure , I expected to see a steady degradation of the image quality from decimating the data space. Interestingly however, it seems that the 256 receiver square array seems to be quite oversampled. The third order body waves apparent in the Figure are just disappearing in Figure which is sub-sampled by 32x in the cross-line axis (only eight receiver lines across the entire cross-line direction!).

 

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Figure 3 Taking only every 32nd receiver line of the available 256, the image manufactured from only 8 lines is not only interpretable, but arguable quite clear.

This result begs the question then: is the degradation in image quality a function of cross-line offset or number of receiver lines available to contribute information? As Figure shows, the image quality is definitely degraded by using eight neighboring receiver lines as compared eight lines spanning the entire data volume. I believe this observation is due to the increase in the aperture of available information to sum into the result.

 

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Figure 4 Utilizing the same number of (this time) contiguous planes of data as used in Figure , we are left with an image of degraded quality.

Now let's go back to considering the end case of only one line. Can adding one more receiver line significantly improve our image quality if chosen correctly? Figure compares images created by processing two consecutive lines (on the left) with one created by line numbers 1 and 256 (on the right). Whereas the left panel is no more clear than Figure , the improvement in the right panel is dramatic.

 

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Figure 5 Surprisingly, two consecutive receiver lines does not produce as good an image as two lines spread across the length of the third axis of acquisition.

As mentioned in the previous article (), only direct ray paths traveling in the same azimuth as the receiver line will record a ghost reflection. When considering the reflection from the free-surface, one can imagine that including larger offset in the perpendicular direction from a single line will allow ever more energy from the lost azimuths to be incorporated into the image. This will only work well in the case of a body with stationary characteristics for the extreme offsets described above. If heterogeneities exits within the offset range, constructive summation will not occur. Therefore, this may be of limited utility on earth, but might be advantageous perpendicular to strike.