Calculating the time-dependent coherence between two channels

The standard coherence calculation outputs a frequency series (FrequencySeries) giving a time-averaged measure of coherence. See Calculate the coherence between two channels for an example.

The TimeSeries method coherence_spectrogram() performs the same coherence calculation every stride, giving a time-varying coherence measure.

These data are available as part of the O3 Auxiliary Channel Data Release.

First, we import the TimeSeries

from gwpy.timeseries import TimeSeries

and then get() the LIGO-Hanford strain data, and the mains power monitor data, for a 20 minute (1200 second window near the end of the O3 Auxiliary Channel Data Release:

start = 1389410000
end = 1389411200
strain = TimeSeries.get("H1", start, end)
mains = TimeSeries.get(
    "H1:PEM-EY_MAINSMON_EBAY_1_DQ",
    start,
    end,
    frametype="H1_AUX_AR1",
)

error authenticating against nds.ligo.caltech.edu, attempting Kerberos kinit()
error authenticating against nds.ligo-wa.caltech.edu, attempting Kerberos kinit()

Data are accessed separately

We could have used TimeSeriesDict.get to access both channels in a single call - that method would first try to find a single dataset that contain both of them, then automatically fall back to separate calls if that fails.

But, since we know that these channels are in different datsets, we access them separately here for clarity and speed.

Calculating coherence

We can then calculate the coherence() of one TimeSeries with respect to the other, using an 2-second Fourier transform length, with a 1-second (50%) overlap, and a stride of 10:

coh = strain.coherence_spectrogram(mains, 20, fftlength=2, overlap=1)

Finally, we can plot() the resulting data

plot = coh.plot()
ax = plot.gca()
ax.set_ylabel("Frequency [Hz]")
ax.set_yscale("log")
ax.set_ylim(10, 2000)
ax.set_title("Coherence between Power mains and LIGO-Hanford strain data")
ax.grid(visible=True, which="both", axis="both")
ax.colorbar(label="Coherence", clim=[0, 1], cmap="plasma")
plot.show()

This shows the time-dependent coherence between the two channels. The 60 Hz power mains frequency and its harmonics are clearly visible, but the coherence is variable over time, demonstrating the varying fidelity of the incoming mains signal.