The geometry of fault systems and the spatial and temporal distribution of quakes along them are extremely complex. Geometrical complexity arises at a variety of scales, from the rough geometry of an individual fault (Dieterich, Ben-Zion, Ando), to larger irregularities on the scale of entire fault systems (Shaw, Harris, Rundle). Complex temporal correlations in the forms of aftershocks and foreshocks appear to occur across a wide range of time scales from seconds to years (Rundle, Sornette, Jordan, Helmstetter, Turcotte). Some of the fundamental questions addressed in the program were how this complexity is generated and what physical features must be included in theoretical models of earthquakes. For example, what roles do inertial dynamics, frictional properties, fault heterogeneity and long-range coupling between fault segments play in determining observed behavior. The discussions of friction and fracture described above, provide important input into modeling this behavior. Another question was whether there are fundamental connections to complex behavior in other systems where scaling relations and renormalization group methods have provided powerful insights (Dahmen, Wiese, Zapperi, Pastor-Satorras).

Participants from other areas were introduced to the nomenclature, phenomenology and statistical behavior of earthquakes through a tutorial by Archuletta and an overview talk by Carlson. One central observation is the power law distribution of earthquake sizes known as the Gutenberg-Richter law. Similar power law scaling can be generated in simple models of planar faults with inertia and friction instabilities (Zoeller), but also in overdamped motion of elastic systems with disorder (Carlson, Dahmen, Wiese). Some discussions focused on which mechanisms were at work in real fault systems.

One thrust of participants was to build detailed models of specific fault systems and examine the correlations of their geometry with quake statistics (Rundle, Jordan, Harris, Helmstetter). Isolating statistics from specific regions reveals deviations from simple power law behavior that constrains models. There appear to be large, fault-spanning quakes that are statistically independent from smaller, localized quakes. In addition to elastic coupling between different regions of faults, the coupling of pore fluid pressures to the passage of seismic waves can be important in triggering quakes in distant regions (Brodsky).

A second approach was to analyze statistics of real earthquake events to see whether correlations could be identified and used to make useful predictions (Rundle, Turcotte, Sornette, Helmstetter). Correlations, like those between aftershocks, also place important constraints on the physics in earthquake models (Sornette, Helmstetter, Jordan, Turcotte, Zoeller, Brodsky).

A related focus of research was to examine simple models that generate complex statistics. The goal is to understand the connection between features in the model and the statistics of earthquake-like events. Substantial progress has been made in understanding quakes in dislocation patterns (Miguel), fracture propagation (Zapperi, Wiese), magnetic domain wall motion (Robbins and Dahmen) and other physical systems (Pastor-Satorras, Zapperi, Wiese). Participants explored how the knowledge gained from these studies informs us about the crucial physics underlying earthquake observations (Carlson, Dahmen, Dieterich, Shaw, Zoeller). Some parallels include the emergence of structures with fractal scaling and power law distributions of events, as well as detailed features of the dynamics of individual events.

19 Talks in this area

8/15, 10:00am
John Rundle (UC Davis)
Relating Observable Earthquake Pattern Formation to Unobservable Earthquake Physics: Implications for Earthquake Forecasting
8/15, 11:05am
Karin Dahmen (UIUC)
Statistics of Earthquakes in Inhomogeneous Faults
8/15, 11:40am
Yehuda Ben-Zion (USC)
Analysis of Aftershocks in a Continuum Damage Rheology Model
8/15, 2:00pm
Susan Coppersmith (Wisconsin)
Computational Complexity and Predictability of Chaotic Dynamical Systems
8/15, 2:35pm
Bruce Shaw (Columbia)
Dynamical, Material, and Geometrical Heterogeneities in Earthquake Models: Similarities, Differences, and Observable Consequences
8/15, 4:15pm
Didier Sornette (UCLA)
Multifractal Scaling of Thermally-Activated Rupture Processes: Prediction and Observation of a Magnitude-Dependent Temporal Power Law for Aftershocks
8/15, 4:50pm
Tom Jordan (USC)
Earthquake Prediction: Guide to a Gambler's Game
8/19, 2:00pm
Ruth Harris (USGS)
The Earthquake Probabilities and Occurrence (EQPRO) Megaproject
9/01, 10:30 a.m.
Dr. Agnes Helmstetter (Columbia)
Earthquake Triggering: Observations, Models, and Application for Earthquake Forecasting
9/06, 3:30 p.m.
Discussion Leader Y. Ben-Zion
Discussion: Geometric Complexity
9/29, 10:30 a.m.
Dr. Donald Turcotte (UC Davis)
What Aftershock and Recurrence Interval Statistics Tell Us About the Physics of Earthquakes
10/11, 10:30 a.m.
Dr. Gert Zoeller (University of Potsdam)
Quasidynamic Simulations of Long Deformation Histories on a Heterogeneous Fault
10/14, 10:30 a.m.
Dr. Ryosuke Ando (Columbia University)
How Can We Connect the Scales of Earthquakes and Laboratories? Introduction of Multi-Hierarchy into Earthquake Rupture Models
10/19, 12:00 p.m.
Discussion Leaders: D. Turcotte and K. Dahmen
Discussion: Recurrence and Interevent Times in Complex Systems
10/20, 10:30 a.m.
Dr. Stefano Zapperi (Sapienza)
Inertial Effects in Crackling Noise: From Magnets to Granular Media
10/28, 12:00 p.m.
Dr. Emily Brodsky (UCLA)
Long-Range Earthquake Triggering
11/22, 10:30 a.m.
Dr. Romualdo Pastor-Satorras (Universitat Politecnica de Catalunya)
Avalanches in Complex Systems: From Sandpiles to Internet Storms
11/30, 12:00 p.m.
Dr. James Dieterich (UC Riverside)
Slip and Seismicity of Faults with Fractal Roughness
12/01, 10:30 a.m.
Evolution of Faults