Six tests of sparse log decon

Spectral plots

The spectrum calculation in all the cases (except for DATA4) is based on gaining the output by $t^{tpow}$ . The value of $tpow$ was chosen to balance amplitudes throughout the section. With the sparse decon, that gain is done after filtering. We have since decided a more appropriate gain function is $t^2/t_0(x)$ where $t_0(x)$ is water depth, but our software to do it requires completion and more testing.

Unexpectedly, we found that sparse decon yields nearly white output for all six datasets. Its whiteness is comparable to that of the Burg decon. We had hoped it would drop off naturally at high and low frequencies as those frequencies should contribute little to sparseness. This observation was another prod to Jon Claerbout to revise the current sparseness theory to an augmented theory found elsewhere in this report. This augmented theory provides those ``bad frequencies'' another place to go besides the decon output.

Six tests of sparse log decon