SCEC Award Number 14090 View PDF
Proposal Category Collaborative Proposal (Integration and Theory)
Proposal Title Performance of Triangular Fault Elements in Earthquake Simulators
Investigator(s)
Name Organization
Terry Tullis Brown University Michael Barall Invisible Software, Inc.
Other Participants
SCEC Priorities 2e, 4e, 3f SCEC Groups CS, USR, SIV
Report Due Date 03/15/2015 Date Report Submitted N/A
Project Abstract
 Most of the computational effort in an earthquake simulator goes into computing how slip on one part of a fault affects stresses on other parts of the fault, and on other faults. The simulator discretizes the fault system into a large number of fault elements, and uses Greens functions to determine how slip on some fault elements affects the stresses on all the fault elements. Because triangles can represent curved fault geometry more accurately than rectangles, one intuitively expects that stress calculations performed with triangles should be more accurate than stress calculations done with rectangles. To test this expectation, we performed accuracy tests using both rectangular and triangular fault elements, on two curved fault surfaces: a negatively-curved fault in the shape of a helicoid, and a positively-curved fault in the shape of an ellipsoid. We performed three kinds of tests: a source test that measures the errors when a fault element acts as a dislocation source, a target test that measures the errors when a fault element acts as a target, and a propagation test that measures the errors in propagating a rupture from a slipping region into the immediately adjacent fault elements. Our results are contrary to the intuitive expectation: triangles are not superior to rectangles. One or the other may be superior in a particular case, but, overall, rectangles perform as well as triangles. Another unexpected result is that one triangulation of a fault surface may perform significantly better than another triangulation with a different pattern of triangles.
Intellectual Merit The development of earthquake simulators is a SCEC research objective. Traditionally, earthquake simulators have used rectangular fault elements, chosen so that the Okada Greens functions can be used. Recently, due to the development of new Greens functions for triangular dislocations, it has become practical to use triangular fault elements. Triangular fault elements are appealing because they can represent curved fault surfaces without the gaps and overlaps that are unavoidable when rectangular fault elements are used. Until now, it has been unknown whether the use of triangular fault elements would improve the accuracy of simulators. This research demonstrates that, contrary to what might be intuitively expected, rectangular and triangular fault elements overall provide the same level of accuracy.
Broader Impacts Earthquake simulators are likely to become an important tool in seismic hazard assessment. This project is one step on the way to developing simulators that are capable of larger and more accurate simulations.
Exemplary Figure Figure 7. Source Test: Negatively Curved Fault Configuration N1. For shear stress, rectangle and triangle-4 perform about equally well, and both are better than triangle-2. For normal stress, triangle-4 is a little better than rectangle, which in turn is much better than triangle-2.

Credit: Michael Barall and Terry Tullis.