In this paper, I present another method for solving the two-slope estimation problem. It is a nonlinear extension of Claerbout's methodology, and differs from Fomel's in the sense that it is a strictly local method. Because mine is a local method, it runs much faster than Fomel's. Theoretically, my method is sensitive to aliased data, unlike Fomel's. Like Fomel's, the estimated slope depends on the starting guess. The existence of local minima appears to be an inherent weakness of the two-slope estimation problem in general.

Fomel successfully applies ``plane-wave destructor'' filters, derived from estimated slopes, to the signal/noise separation problem. Analogously, I use the estimated slopes to construct ``steering filters'' of a form derived by Clapp et al. (1997). Like Fomel, I find that when the signal and noise slopes are too similar, my method converges to (incorrect) local minima, unless the slope estimation is ``guided'' with a prior model of the signal or the noise. Using this constrained approach, I obtain excellent separation results on three different real data examples. Most encouragingly, in all cases, very simple, easily-obtained prior models sufficed.

11/11/2002