Parameters for signal enhancement by prediction

The predictions in Figure 12 were derived from prediction errors computed from subroutine lopef2() , seen earlier in another application. The prediction is simply the data minus the prediction error.

Data is analyzed in many overlapping windows which are then merged. Because the quality of the results depends on the window sizes, I report here the reasoning behind my choices. First, the Canales process is generally applied in the temporal frequency domain. The number of coefficients on the space axis for the predictions is generally taken much larger than the wave-slope count in a typical window. This is common practice and I explain the larger size by saying that because the prediction of the data is based on noisy data itself, the process needs a sizeable window in which to do statistical averaging.

To match the stepout of the dominant wave (an around-world Rayleigh wave) I took the filter length and width to be a1=27 and a2=7. Then for statistical smoothing I chose fitting windows to be ten times as large as the filter in both directions. Obviously, the statistics could be gathered in different amounts on the two axes and averaging differently could give significantly different results. Anyway, the result for my choices is that the entire page is divided into four windows horizontally and three vertically.

The temporal (half) extent of the filter is evident by the strong character change at the top and bottom. The spatial extent is not revealed in this way because of the vanishing traces (empty bins) along the edges.

I notice a disturbing darkness at late times and wide offsets. This is energy at zero frequency, a highly predictable frequency, that might have crept in because I used medians on bins with small numbers of traces, perhaps an even number so the median had a consistent bias.

Overall, the prediction process performs as expected. It is disappointing, however, in that it tends to swamp weak events in the ``side lobes'' of strong events. I believe the widespread acceptance of this process arises from its use on data of very low quality. Where there is barely one perceptible event, a process that strengthens that event is a welcome process.