Automatic FEAVO detection

The automatic FEAVO-discriminating procedure outlined in the previous section offers a ready solution to an older problem: FEAVO detection. Until now, the only way to find whether the amplitudes at the reflector were corrupted by focusing effects was the method used by Kjartansson (1979). First, the interpreter would have to become suspicious that the AVO in his region of interest exhibited variations too strong and abrupt to be due to the rock properties expected at that interface. The dataset would be sent back to processing, which would sum the absolute values of the samples in the 2-D prestack line along time, and examine the midpoint-offset image looking for the specific ``V'' shapes of the anomalies. Since it is not to be expected that such a labor-intensive, custom procedure was undertaken routinely, compromised AVO measurements were the likely result.

FEAVO, however, can be detected and flagged automatically during processing in a much simpler way. Figure 2 depicts the removal of a linear trend from FEAVO-affected data. If the same workflow is applied to data that is not affected by FEAVO, the residual after subtraction of the trend will be very close to zero everywhere. High values in the variance of the residuals will therefore flag the presence of FEAVO. Figure 5 shows the result of automatic FEAVO detection, which is no longer a 5-D cube, but a 3-D one, reducing the volume of data to be examined by orders of magnitude through elimination of the offset axes. The presence of FEAVO anomalies is highly visible. I need not even do a good job of finding the values of the intercept and gradient. All that matters for detection is that the amplitude values in focusing-affected areas do not vary linearly with the squared sine of offset, and therefore no straight line whatsoever will approximate them well. The procedure is also quite cheap computationally.

 

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Figure 5 FEAVO anomalies flagged in the midpoint-depth space by the automatic detection procedure. The stars denote the location of the lenses causing the focusing.

I could build an ``anomaly locator'' by summing Radon-transform-style the output of the FEAVO detector inside the bounds of precomputed, velocity-dependent, FEAVO-effect paths. That, however, would not give the magnitude of the velocity anomalies, so it would be of little use in eliminating the amplitude effects in the prestack volume.