Paradox of modelling curved faults revisited with general non-hypersingular stress Green’s functions

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 2-D and 3-D 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.