Sources of inaccuracy

Figure 2 shows a synthetic example of conversion from the angle domain to offset domain and back to the angle domain. The original ADCIG is described by polarity reversal at zero incidence angle. After conversion to offset and back to angle, the image gather displays the same polarity reversal. The angle-gathers are also flat, which indicates that the transformation is kinematically correct.

The obvious question that remains to be addressed is how reliable in general are the amplitude versus angle estimates for images obtained using wave-equation migration.

As mentioned earlier, we compute the image-gathers either in the image space, or in the data space via Fourier-domain radial-trace transforms. Analysis of our procedure reveals four major sources of distorsion of the amplitude response which are: (1) the limited offset and depth wavenumber bandwidths, (2) the limited temporal frequency bandwidth, (3) the incorrect implementation of RTT, and (4) the unweighted imaging condition. In the next four subsections, we discuss each of these sources of error, and refer to image gathers in the angle domain, although the discussion is fully applicable to offset ray-parameter, as well.

We demonstrate the various transformations and sources of inaccuracy using a very simple synthetic model (Figure 3), which is a perfectly focused image (a spike in the offset domain).

 

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Figure 3 Synthetic offset-gather. From left to right, Fourier-domain representation, space-domain representation, and amplitude response. The image is represented by one single perfectly focused event at a depth of 0.5 km.