  Gravitational waves generated by the final merger of double neutron star
(DNS) binary systems are a key target for the gravitational wave (GW)
interferometric detectors, such as LIGO, and the next generation detectors,
Advanced LIGO. The cumulative GW signal from DNS mergers in interferometric
data will manifest as "geometrical noise": a non-continuous stochastic
background with a unique statistical signature dominated by the spatial and
temporal distribution of the sources. Because geometrical noise is highly
non-Gaussian, it could potentially be used to identify the presence of a
stochastic GW background from DNS mergers. We demonstrate this by fitting to a
simulated distribution of transients using a model for the DNS merger rate and
idealized Gaussian detector noise. Using the cosmological "probability event
horizon" concept and recent bounds for the Galactic DNS merger rate, we
calculate the evolution of the detectability of DNS mergers with observation
time. For Advanced LIGO sensitivities and a detection threshold assuming
optimal filtering, there is a 95% probability that a minimum of one DNS merger
signal will be detectable from the ensemble of events comprising the stochastic
background during 12-211 days of observation. For initial LIGO sensitivities,
we identify an interesting regime where there is a 95% probability that at
least one DNS merger with signal-to-noise ratio > unity will occur during 4-68
days of observation. We propose that there exists an intermediate detection
regime with pre-filtered signal-noise-ratio less than unity, where the DNS
merger rate is high enough that the geometrical signature could be identified
in interferometer data.
