  The detection of gravitational waves (GWs) from binary black holes (BBHs) has
allowed the theory of general relativity to be tested in a previously unstudied
regime: that of strong curvature and high GW luminosities. One distinctive and
measurable effect associated with this aspect of the theory is the nonlinear GW
memory effect. The GW memory effect is characterized by its effect on freely
falling observers: the proper distance between their locations differs before
and after a burst of GWs passes by their locations. Gravitational-wave
interferometers, like the LIGO and Virgo detectors, can measure features of
this effect from a single BBH merger, but previous work has shown that it will
require an event that is significantly more massive and closer than any
previously detected GW event. Finding evidence for the GW memory effect within
the entire population of BBH mergers detected by LIGO and Virgo is more likely
to occur sooner. A prior study has shown that the GW memory effect could be
detected in a population of BBHs consisting of binaries like the first GW150914
event after roughly one-hundred events. In this paper, we compute forecasts of
the time it will take the advanced LIGO and Virgo detectors (when the detectors
are operating at their design sensitivities) to find evidence for the GW memory
effect in a population of BBHs that is consistent with the measured population
of events in the first two observing runs of the LIGO detectors. We find that
after five years of data collected by the advanced LIGO and Virgo detectors the
signal-to-noise ratio for the nonlinear GW memory effect in the population will
be about three (near a previously used threshold for detection). We point out
that the different approximation methods used to compute the GW memory effect
can lead to notably different signal-to-noise ratios.
