  GW170817 is the unique gravitational-wave (GW) event that is associated to
the electromagnetic (EM) counterpart GRB 170817A. NGC 4993 is identified as the
host galaxy of GW170817/GRB 170817A. In this paper, we particularly focus on
the spatially resolved properties of NGC 4993. We present the photometric
results from the comprehensive data analysis of the high spatial-resolution
images in the different optical bands. The morphological analysis reveals that
NGC 4993 is a typical early-type galaxy without significant remnants of major
galaxy merger. The spatially resolved stellar population properties of NGC 4993
suggest that the galaxy center has passive evolution with the outskirt formed
by gas accretion. We derive the merging rate of the compact object per galaxy
by a co-evolution scenario of supermassive black hole and its host galaxy. If
the galaxy formation is at redshift 1.0, the merging rate per galaxy is
$3.2\times 10^{-4}$ to $7.7\times 10^{-5}$ within the merging decay time from
1.0 to 5.0 Gyr. The results provide the vital information for the ongoing GW EM
counterpart detections. The HST data analysis presented in this paper can be
also applied for the Chinese Space Station Telescope (CSST) research in the
future.
