Noise subtraction

Figures through show the efficacy of this simple signal to noise subtraction algorithm facilitated by the combined modeling operator inversion scheme presented here. Only the LRT model-space is forward modeled back into the data-space for subtraction from the original data. In every case the least-squares approach produces the best signal enhancement. Gather 14 produces a lot of acausal noise that could be muted, though the direct arival was the main target for this gather. That being the case, it could also be considered a poor result.

The sparesness oriented schemes produce gathers with little to no improvement in signal-to-noise ratio while altering the amplitude variation, and sometimes kinematics, of the gathers.

 

s.08
Figure 10 Signal estimate for shot-gather 08 (Panel (a) from Figure ). Panel (b) shows the BC, Panel (c) the Cauchy, Panel (d) the l₁, and Panel (d) the l₂ inversion results.

 

s.14
Figure 11 Signal estimate for shot-gather 14 (Panel (b) from Figure ). Panel (b) shows the BC, Panel (c) the Cauchy, Panel (d) the l₁, and Panel (d) the l₂ inversion results.

 

s.25r
Figure 12 Signal estimate for shot-gather 25 (Panel (c) from Figure ). Panel (b) shows the BC, Panel (c) the Cauchy, Panel (d) the l₁, and Panel (d) the l₂ inversion results.