  Gravitational memory is an important prediction of classical General
Relativity, which is intimately related to asymptotic symmetries at null
infinity and the so-called soft graviton theorem first shown by Weinberg. For a
given transient astronomical event, the angular distributions of energy and
angular momentum flux uniquely determine the displacement and spin memory
effect in the sky. We investigate the possibility of using the binary black
hole merger events detected by Advanced LIGO/Virgo to test the relation between
source energy emissions and gravitational memory measured on earth, as
predicted by General Relativity. We find that while it is difficult for
Advanced LIGO/Virgo, one-year detection of a third-generation detector network
will easily rule out the hypothesis assuming isotropic memory distribution. In
addition, we have constructed a phenomenological model for memory waveforms of
binary neutron star mergers, and use it to address the detectability of memory
from these events in the third-generation detector era. We find that measuring
gravitational memory from neutron star mergers is a possible way to distinguish
between different neutron star equations of state.
