  The temperature and field dependences of the site-selective nuclear spin
relaxation time T_1 around vortices are studied comparatively both for s-wave
and d-wave superconductors, based on the microscopic Bogoliubov-de Gennes
theory. Reflecting low energy electronic excitations associated with the vortex
core, the site selective temperature dependences deviate from those of the
zero-field case, and T_1 becomes faster with approaching the vortex core. In
the core region, T_1^{-1} has a new peak below the superconducting transition
temperature T_c. The field dependence of the overall T_1(T) behaviors for
s-wave and d-wave superconductors is investigated and analyzed in terms of the
local density of states. The NMR study by the resonance field dependence may be
a new method to probe the spatial resolved vortex core structure in various
conventional and unconventional superconductors.
