Paradox of Modeling Curved Faults Revisited with General Non-Hypersingular Stress Green's Functions

TL;DR

This paper revisits the paradox in modeling curved faults by developing a new non-hypersingular stress Green's function, demonstrating that previous functions were incorrect and establishing equivalence between smooth and segmented faults.

Contribution

It introduces a compact, general expression for non-hypersingular stress Green's functions applicable to curved faults in elastic media, resolving previous inaccuracies.

Findings

Previous Green's functions for curved faults were incorrect.

Smooth and infinitesimally segmented faults are equivalent.

The new functions bridge analytical and numerical modeling methods.

Abstract

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.