  In a dislocation problem, a paradoxical discordance is known to occur between
an original smooth curve and an infinitesimally discretized curve. To solve
this paradox, we have investigated a non-hypersingular expression for the
integral kernel (called the stress Green's function) which describes the stress
field caused by the displacement discontinuity. We first develop a compact
alternative expression of the non-hypersingular stress Green's function for
general two- and three-dimensional infinite homogeneous elastic media. We next
compute the stress Green's functions on a curved fault and revisit the paradox.
We find that previously obtained non-hypersingular stress Green's functions are
incorrect for curved faults, and that smooth and infinitesimally segmented
faults are equivalent. Their compatibility bridges the gap between analytical
methods featuring curved faults and numerical methods using subdivided flat
patches.
