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Open-File Report 2015-1028

Strike-Parallel and Strike-Normal Coordinate System Around Geometrically Complicated Rupture Traces—Use by NGA-West2 and Further Improvements

By Paul Spudich and Brian Chiou


We present a two-dimensional system of generalized coordinates for use with geometrically complex fault ruptures that are neither straight nor continuous. The coordinates are a generalization of the conventional strike-normal and strike-parallel coordinates of a single straight fault. The presented conventions and formulations are applicable to a single curved trace, as well as multiple traces representing the rupture of branching faults or noncontiguous faults. An early application of our generalized system is in the second round of the Next Generation of Ground-Motion Attenuation Model project for the Western United States (NGA-West2), where they were used in the characterization of the hanging-wall effects. We further improve the NGA-West2 strike-parallel formulation for multiple rupture traces with a more intuitive definition of the nominal strike direction. We also derive an analytical expression for the gradient of the generalized strike-normal coordinate. The direction of this gradient may be used as the strike-normal direction in the study of polarization effects on ground motions.

First posted February 10, 2015

For more information concerning the research in this report, contact:
Earthquake Science Center — Menlo Park
U.S. Geological Survey
345 Middlefield Road, MS 977
Menlo Park, CA 94025

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Suggested citation:

Spudich, Paul and Chiou, Brian, 2015, Strike-parallel and strike-normal coordinate system around geometrically complicated rupture traces—Use by NGA-West2 and further improvements: U.S. Geological Survey Open-File Report 2015-1028, 20 p.,

ISSN 2331-1258 (online)




Generalized Coordinate System for a Single Rupture Trace

Generalized Coordinate System for Multiple Rupture Traces

Strike-Normal Direction Defined by ∇T


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