Filtering and pattern recognition - I do not believe that "classic" time series approaches get the job done. Years ago I spent time looking at  actual filter operators from time series deconvolution programs. I found that all their significant "multipliers" were clustered right at the front. This troubled me because I had an instinctive feeling that such filters should have a "Pattern recognition" capability.  No matter the design technique, to do this the filter action would have to be spread over the wavelet length. The same applies to  band pass filters. They are what I call "frequency sensitive". That is to say they ignore event shape.

The subject of the composition of a wavelet is very complex. When we are trying to discriminate against particular wavelets (such as the shear waves I am suggesting), doing it just on the basis of dominant frequency is simplistic. Pattern recognition capability is essential, and non-linear techniques are good at this.
The "wiggle" plot below comes from the area shown in the last slide. "A" points to what I say is a shear wave, "B" to what I say is a real event, and "C" to where they are conflicting. "D" points to another noise event, probably another shear wave. You can see the conflict when it approaches "A".

 

what we as the filter to do is to remove the effect of "A" without disturbing the shape of "B"-

Not an easy task, since the two spectra have overlapping frequencies. This is where pattern recognition becomes a necessity.

When the independent waves arrive at the surface, the recording devices do  algebraic additions. The higher frequency arrivals appear to ride on top of the lower frequency ones (piggy back, as the picture to the right implies). A low-cut band pass filter will have trouble with this. In this plot the low frequency is at a low amplitude. The "pickable" peaks on the reflection events will be shifted by this algebraic addition. You can see this within the circle (C) above. 

I hasten to say here that this reasoning is based on old observations, and that I am open to being proven wrong. In any case, in an attempt to improve the chances I turned to non-linear logic that predicts on the basis of pattern recognition. In essence this logic looks for specific wavelet forms, than tries to gently lift off the offending energy. There are times when it works very well, as we will see below, and times that it only helps by better defining the trouble spots. The next picture shows the logic in action (as did the similar one used in the intro to random noise). The process is described in more detail later.

Consider this an introduction to the non-linear procedures I have used in my inversion logic, since the reasons for choosing this direction are similar.
Obviously the non linear, predictive filter logic worked well here. However no comparison with conventional band pass filtering is available.

Over the course of the large data set there are many similar examples, but there are also places it did not work this well. Of course a lot of work remains to be done on the concept.

The important thing is to recognize the problem.