Spatially continuous slip rake angles across nonplanar fault geometry

Matthew G. Knepley, Brad T. Aagaard, & Charles A. Williams

Submitted August 30, 2026, SCEC Contribution #15492, 2026 SCEC Annual Meeting Poster #082

Accurately simulating earthquake rupture requires consistent directional conventions across a fault surface. Lateral (strike-slip) motion is measured along a fault's local strike direction, and reverse (dip-slip) motion along its local up-dip direction. Standard methods for defining the spatial variation of these directions can fail on rough or curved faults. For example, many methods break down for shallow dipping faults with saddle points, such as subduction interfaces with seamounts. The strike direction either reverses direction for portions of the surface, or some regions have small non-zero vertical components. We present an algorithm that computes these directions such that they vary smoothly across nonplanar, arbitrarily rough fault surfaces, improving the accuracy of earthquake rupture simulations. The algorithm uses a mathematical technique called parallel transport to carry a consistent horizontal strike direction across the fault surface, which is represented as a mesh of triangles or quadrilaterals. This avoids the abrupt jumps in direction and non-zero vertical components. We compute the up-dip direction as the cross product of the fault-normal direction and the strike direction. We implemented the algorithm in the Portable Extensible Toolkit for Scientific Computing (PETSc), which runs in parallel using the Message Passing Interface. We then incorporated it into the PyLith crustal deformation modeling software. We also use the algorithm to assign consistent tangential directions along a model's exterior boundaries, which are needed for Neumann (traction) boundary conditions. We demonstrate the effectiveness of this approach for fault surfaces with substantial curvature or roughness. PyLith is developed and distributed through the Computational Infrastructure for Geodynamics (https://geodynamics.org/resources/pylith). Resources include source code, binary packages, online documentation (https://pylith.readthedocs.io), and video tutorials.

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Key Words
fault geometry, slip rake, orientation

Citation
Knepley, M. G., Aagaard, B. T., & Williams, C. A. (2026, 08). Spatially continuous slip rake angles across nonplanar fault geometry. Poster Presentation at 2026 SCEC Annual Meeting.

Related Projects & Working Groups
Community Earth Models (CEM)