Tests on real data

Figure 8 shows the input for the real data example. These data are contaminated with a low velocity/low frequency noise crossing the main signal. The Huber threshold and the damping paramater for IRLS are equal and obey the empirical choice that we gave above. Figure 8 details the least-squares result. The velocity panel (middle) shows some horizontal stripes that severely blur the main velocity fairway; in addition, because no strong event appears below 1s., a poor resolution is achieved. In regard to the l² result, we might note that the remodeled data (right panel of Figure 8) exhibit some artifacts in the top part that shows the limitations of the least-squares inversion in this case. Figure 10 displays the ``l¹'' inversion results with the Huber solver and IRLS. Again, because we are able to pick up a velocity fairway all the way down, both results are very comparable. Moreover, the remodeled data (Figure 9) show fewer artifacts than they do in the l² case.

 

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Figure 8 From left to right: 1) Input data. 2) velocity domain, l² inversion result. 3) remodeled data from the l² result

 

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Figure 9 From left to right: 1) Remodeled data with l². 2) Remodeled data with the Huber solver. 3) Remodeled data using IRLS

 

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Figure 10 From left to right: 1) l² velocity space. 2) Huber velocity space. 3) IRLS velocity space