Filtering High Frequency Channel Noise
Looks like you actually have pretty good signal to noise ratio, and the noise that is there seems to be largely above the major frequency components of the signature you are looking for.  Looking at the noise at this level is not meaningful.  You want to see how much signal to noise headroom you have after proper detection of your doublet (some sort of echo chirp?).

The obvious detection procedure is too convolve the input signal with the signature from your first plot.  That should give you a nice single spike when the signature is detected.  The width of the filter kernel (the fixed waveform you are convolving the input with, which is the first plot) indicates that much of the high frequency hash will be removed.  This is a necessary step in detecting the signature anyway.  Try that first and then see what the signal to noise ratio is.  If the data you show is representative, then there will be a quite healthy signal to noise ratio.  Detecting the chirp from the background and determining the chirp's center time should work very nicely.