Three dimensional non-singular mollified elastic dislocation theory for extended width fault zones and inhomogeneous boundary element models
Abstract
Classical elastic dislocation theory (CEDT) has two challenges when applied to faulting problems: 1) fictitious on-fault stresses not defined by ordinary integration and 2) the geometric unreality of infinitely thin fault zones. We show that both can be resolved by a mollified elastic dislocation theory (MEDT) built on Cortez blob (Cortez, 2001) mollified displacement discontinuity Green's functions, which represent deformation across spatially distributed fault zones of finite scale epsilon and produce singularity-free displacements and stresses everywhere. Analytical integration of the mollified source solution over arbitrary planar triangular elements is done with AI, and the resulting closed-form solutions allow for the calculation of non-singular stresses across geometrically complex fault systems. Further, we demonstrate the decoupling of the fault-zone width scale epsilon from the mesh length scale h, the elasticity analog of a result established for regularized viscous flow Stokeslets (Ferranti and Cortez, 2024). We use these mollified kernels to demonstrate numerically stable collocation boundary element models including spatially extended fault zones, material property variations and non-planar topography.
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BibTeX
@misc{meade2026three,
title = {{Three dimensional non-singular mollified elastic dislocation theory for extended width fault zones and inhomogeneous boundary element models}},
author = {Brendan Meade},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15601},
eprint = {2609.15601},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15601},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Three dimensional non-singular mollified elastic dislocation theory for extended width fault zones and inhomogeneous boundary element models
AU - Brendan Meade
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15601
UR - https://arxiv.org/abs/2609.15601
AB - Classical elastic dislocation theory (CEDT) has two challenges when applied to faulting problems: 1) fictitious on-fault stresses not defined by ordinary integration and 2) the geometric unreality of infinitely thin fault zones. We show that both can be resolved by a mollified elastic dislocation theory (MEDT) built on Cortez blob (Cortez, 2001) mollified displacement discontinuity Green's functions, which represent deformation across spatially distributed fault zones of finite scale epsilon and produce singularity-free displacements and stresses everywhere. Analytical integration of the mollified source solution over arbitrary planar triangular elements is done with AI, and the resulting closed-form solutions allow for the calculation of non-singular stresses across geometrically complex fault systems. Further, we demonstrate the decoupling of the fault-zone width scale epsilon from the mesh length scale h, the elasticity analog of a result established for regularized viscous flow Stokeslets (Ferranti and Cortez, 2024). We use these mollified kernels to demonstrate numerically stable collocation boundary element models including spatially extended fault zones, material property variations and non-planar topography.
ER -