It will be noted that because the ground roll is very aliased and dispersive in these gathers, the linear radon operator has great difficulty describing these events with a single kernel in the model domain. While the least squares inversion will introduce energy into the model-space to combine these events, as well as cancel acausal energy above the direct arrival in the data-space, the sparse inversions are not capable of stopping events that do not cross the entire data-space. For this reason, only one-sided gathers have been used for this analysis.

These techniques are particularly sensitive to noisy, unbalanced traces. For this reason all gathers have been trace-balanced, gained as a function of time, and noisy traces zeroed. Last, it should be noted that CMP-gathers should be used for this analysis instead of shot-gathers to insure that all of the subsurface hyperbolas do not have an apex shift.

While the bound-constrained, Cauchy, and *l _{1}* inversion schemes
produce a more pleasing model-space, this investigation shows it is of
limited use in this application of separating the linear from
hyperbolic events in a CMP gather. While the
least-squares inversion does allow the introduction of cross-talk
between the two model-spaces, the noise subtraction technique is
better implemented within this framework. This conclusion can be
evaluated in terms of the sometimes disparate goals of analysis versus
synthesis. If analysis is the goal, the sparseness optimized
inversion schemes clearly outperform the least-squares model product.
Velocity picking would be much better performed with these results.
Of the three, this exploration shows the

For the purpose of removing linear events with a combined HRT-LRT inversion scheme a data-space solution is required. For this problem, the extra expense of fine-tuning the model-space is wasted.

5/3/2005