  Measurements of the luminosity distance of propagating gravitational waves
can provide invaluable information on the geometry and content of our Universe.
Due to the clustering of cosmic structures, in realistic situations we need to
average the luminosity distance of events coming from patches inside a volume.
In this work we evaluate, in a gauge-invariant and fully-relativistic
treatment, the impact of cosmological perturbations on such averaging process.
We find that clustering, lensing and peculiar velocity effects impact estimates
for future detectors such as Einstein Telescope, Cosmic Explorer, the Big Bang
Observer and DECIGO. The signal-to-noise ratio of the angular power spectrum of
the average luminosity distance over all the redshift bins is 17 in the case of
binary black holes detected by Einstein Telescope and Cosmic Explorer. We also
provide fitting formulas for the corrections to the average luminosity distance
due to general relativistic effects.
