Examples of the Marmousi data set

In order to see the effects of missing traces in a complex model, I tested the well-known Marmousi data set. Each shot gather of the Marmousi data set has the nearest offset traces at 175 meters from each shot location and leaves 8 near-offset traces missing. Figure  shows a CMP gather at 7500 meters along the surface location. The right half of the CMP gather is appended using the reciprocity principle. The interpolated gather appears in Figure , which shows that the interpolated traces are very close to the known traces. Figures   and   show a common-shot gather at the shot location, 5100 meters, before and after interpolation of the whole CMP gathers, respectively; the interpolated traces follow the pattern of the other known reflection events very closely. Figures   and   show another example at a different shot location, 6250 meters, and demonstrate successful interpolation even for the weak events.

 

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Figure 8 CMP gather at 7500m in the Marmousi data set.

 

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Figure 9 Interpolated CMP gather at 7500m in the Marmousi data set.

 

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Figure 10 Common shot gather at 5100m in the Marmousi data set.

 

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Figure 11 Common shot gather at 5100m in the Marmousi data set after interpolation of the whole CMP gathers.

 

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Figure 12 Common shot gather at 6250m in the Marmousi data set.

 

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Figure 13 Common shot gather at 6250m in the Marmousi data set after interpolation of the whole CMP gathers.

 

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Figure 14 Marmousi image without near offset traces, obtained by synthesizing a plane wave traveling vertically.

 

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Figure 15 Marmousi image with interpolated near offset traces, obtained by synthesizing a plane wave traveling vertically.

 

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Figure 16 Marmousi image without near offset traces, obtained by synthesizing a plane wave traveling 10 degrees to the vertical.

 

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Figure 17 Marmousi image with interpolated near offset traces, obtained by synthesizing a plane wave traveling 10 degrees to the vertical.

In order to see the effects of missing traces in the plane-wave synthesis (PWS) imaging, I performed PWS imaging of the Marmousi data with missing near-offset traces and with interpolated near-offset traces. Figures   and   show the images of a zero-degree plane wave without and with near-offset traces, respectively. The major difference can be found around the flat reflector as annotated in the figure with question marks. Since the plane wave used in these examples travels vertically, most of reflected energy from flat reflectors would be in the near offset. Therefore, the missing near offset traces mostly affect the image of flat reflectors.

Figures   and   show the images of a 10-degree plane wave without and with near-offset traces, respectively. Again, the major difference appears around the reflector, which is close to 10-degrees, as annotated in the figure with question marks. This tells us that the missing near offset traces would affect the image quality of the reflectors whose dip is close to the dip of the synthesized plane wave.