SCEC Award Number 08130 View PDF
Proposal Category Individual Proposal (Integration and Theory)
Proposal Title Towards A Physically Based Reduced Model for Describing Complexity Of Earthquake Rupture Process
Name Organization
Thomas Heaton California Institute of Technology
Other Participants Ahmed Elbanna (a 3rd year graduate
student in Caltech Civil Engineering)
SCEC Priorities A10, A9, A3 SCEC Groups FARM, SDOT
Report Due Date 02/28/2009 Date Report Submitted N/A
Project Abstract
This project explored the multi-scale dynamic behavior of multi-degree of freedom systems with strong rate weakening friction, a feature that has been proposed to explain the paucity of frictional melts observed in exhumed faults. In particular, we investigate the chaotic behavior of slip pulses that propagate in a spring block slider model with velocity weakening friction by numerically solving a computationally intensive set of n coupled non-linear equations, where n is the number of blocks. We observe that the system evolves into a spatially heterogeneous pre-stress after the occurrence of a sufficient number of events. We observe that, although the spatio-temporal evolution of the amplitude of a slip pulse in a single event is surprisingly complex, the geometric description of the pulses is simple and self-similar with respect to the size of the pulse. This observation allows us to write an energy balance equation that describes the evolution of the pulse as it propagates through the known prestress. The equation predicts the evolution of individual ruptures and reduces the computational time dramatically. The long time solution of the equation reveals its multi-scale nature and its potential to match many of the long time statistics of the original system, but with a much shorter computational time.
Intellectual Merit Understanding the implications of strong rate weakening friction is one of the most challenging physics problems in the earthquake sciences. In fact, dynamic systems with positive feedback that leads to chaotic behavior is one of the most challenging problems in mathematical physcis. We have discovered a remarkable difference equation that reproduces the behavior of a linear spring block slider. To our knowledge, this equation was previously unknown. While it has importantt implications in its own right, extension of this equation to a 3-d continuum could open a whole new field of earthquake mechanics.
Broader Impacts This work is a potential paradigm shift for the physics of earthquakes.
Exemplary Figure figure 2