Tests on synthetic data: groundroll

In this example, we contaminated the data with a low frequency/low velocity linear event that simulates, to some extent, groundroll (Figure 5, left). Because the operator A models only hyperbolas, the simulated groundroll introduces some inconsistent data. It is therefore interesting to test the sensitivity of our inversion schemes (l² and l¹) for this new problem. The l² inversion of the data leads to a fairly noisy model where the five expected events are difficult to pick (Figure 5). However, without groundroll and only a few artifacts, the remodeled l² data does not display so dramatic effects. With a ``l<sup>1</sup>'' inversion, the model space is more accurately resolved, as shown in Figure 7. Again, there are few differences between IRLS and the Huber solver, and it looks like the ``l¹'' norm copes more easily with inconsistent events than l² (groundroll in this case).

 

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Figure 5 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 6 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 7 From left to right: 1) l² velocity space. 2) Huber velocity space. 3) IRLS velocity space