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 Auxiliary Channel Three Hour Release.

First, we import the TimeSeriesDict

from gwpy.timeseries import TimeSeriesDict

and then get() the data for the differential-arm length servo control loop error signal (H1:LSC-DARM_IN1_DQ) and the PSL periscope accelerometer (H1:PEM-CS_ACC_PSL_PERISCOPE_X_DQ):

data = TimeSeriesDict.get(
    ["H1:LSC-DARM_IN1_DQ", "H1:PEM-CS_ACC_PSL_PERISCOPE_X_DQ"],
    1186741560,
    1186742160,
    host="nds.gwosc.org",
)
darm = data["H1:LSC-DARM_IN1_DQ"]
acc = data["H1:PEM-CS_ACC_PSL_PERISCOPE_X_DQ"]

/home/duncan.macleod/gwpy-nightly-build/conda/envs/gwpy-nightly-3.11/lib/python3.11/site-packages/igwn_auth_utils/requests.py:46: DeprecationWarning: Support for identity-based X.509 credentials for LIGO.ORG is being dropped.
Calls to this utility will stop working on/around 20 May 2025.

For details on this change please see

https://computing.docs.ligo.org/guide/compsoft/roadmap/LVK/x509_retirement/

If you have questions about this message, or its implications, please
consider opening an IGWN Computing Help Desk ticket:

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  return func(*args, **kwargs)

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:

coh = darm.coherence_spectrogram(acc, 10, fftlength=.5, overlap=.25)

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 PSL periscope motion and LIGO-Hanford strain data",
)
ax.grid(visible=True, which="both", axis="both")
ax.colorbar(label="Coherence", clim=[0, 1], cmap="plasma")
plot.show()