(* Let's have some fun with LIGO data (motivated by https://arxiv.org/pdf/1706.04191.pdf). 
First download the raw strain data from the LIGO website: 
https://losc.ligo.org/events/GW150914/
In the section "Strain Data at 4096 Hz" select the 32s sample from Livingston in hdf5 frormat. This fortunately can be read by mathematica *)

lowstrain = Import["~/Downloads/L-L1_LOSC_4_V2-1126259446-32.hdf5",{"Datasets","/strain/Strain"}]

(* ... and compute its spectrum. *)
lowspectrum = Fourier[lowstrain]

(* To get some idea what the power spectrum looks like *)
ListPlot[Abs[lowspectrum]]

(* Right in the middle is the interesting low frequency part. You can see that the noise is smallest there but there are some sigificant narrow lines *)

(* But we want to see the phase as well. So encode it in the color of the plot. And zoom in to the central region *)

bunt[z_] := Style[Abs[z], Hue[Arg[z/2/Pi]]]

innerspectrum[list_] :=ListPlot[Map[bunt,Take[list,{Length[list]/2 - 15000,Length[list]/2+15000}]]]

innerspectrum[lowspectrum]

(* You can see around the center (which correponds to the lowest frequencies), there is an almost constant residual at the order of 10^-22 and it is predominantly red, i.e. the phase is constant.

It is important to note that the original signal was real. So the Fourier transform obeys F(-ω) = F(ω)^*. This is compatible with constant phase only for phase 0 or π. Turning this argument around, this corresponds to a signal that is either the same under time reversal or minus the same. So let's test that: *)
revlowstrain = Reverse[lowstrain]

summe = revlowstrain + lowstrain

summespectrum = Fourier[summe]

innerspectrum[summespectrum]

(* Obviously, this operation almost eliminated the noise at low frequencies. Or whatever it was. Let me be clear: This is not about the signal. That is not visible in this representation since the surrounding noise is much stronger. It only becomes visible after some filtering is applied. But the fact that you can remove the "noise" by adding the time inverted signal should make you wonder if that can realy be noise. Note also that all this depends on the time window selected by the original data. If you shift that by a bit "time reversal" means a different thing and you would be adding other samples together. So this is something peculiar to this time window which as I understand is centered around the event. *)