SCEC Award Number 16037 View PDF
Proposal Category Collaborative Proposal (Integration and Theory)
Proposal Title Precision Tests of Stress Transfer Calculations in Earthquake Simulators
Investigator(s)
Name Organization
Michael Barall Invisible Software, Inc. Terry Tullis Brown University
Other Participants
SCEC Priorities 2e, 4e, 3f SCEC Groups CS, WGCEP, Simulators
Report Due Date 03/15/2017 Date Report Submitted 03/03/2017
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. 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 follow a curved surface without gaps while rectangles cannot, one intuitively expects that stress calculations performed with triangles should be more accurate than stress calculations done with rectangles. In a previous SCEC project, we performed accuracy tests for rectangular and triangular fault elements, on negatively-curved and positively-curved fault surfaces. Our surprising result was that triangles are not superior to rectangles. In this SCEC project, we expanded the number of test cases to include triangulations composed mainly of nearly-equilateral triangles (previously we used right triangles), to include both edge and screw dislocations (previously we only tested edge dislocations), and to include a cylindrical (zero-curvature) fault surface. For each test case, we measured three kinds of error: the error when a fault element acts as a dislocation source; the error when a fault element acts as a target; and the error in propagating a rupture from a slipping region into the immediately adjacent fault elements. These new tests confirm our previous results: 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.
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 recently, it has been unknown whether the use of triangular fault elements would improve the accuracy of simulators. This research confirms our earlier results, which demonstrate 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 C3: Approximation errors in propagating a rupture from a slipping region into the immediately adjacent fault elements. This test is performed on a negatively-curved fault surface, for three different shapes of fault elements: rectangles (“rectangle-2”), right triangles (“triangle-5”), and equilateral triangles (“triangle-6”). For shear stress, the rectangles and equilateral triangles perform about equally well, and both are better than right triangles. For normal stress, rectangles are better than equilateral triangles, which in turn are better than right triangles.

Credit: Michael Barall and Terry Tullis.