Modeling fast and slow earthquakes at various scales.

Earthquake sources represent dynamic rupture within rocky materials at depth and often can be modeled as propagating shear slip controlled by friction laws. These laws provide boundary conditions on fault planes embedded in elastic media. Recent developments in observation networks, laboratory experiments, and methods of data analysis have expanded our knowledge of the physics of earthquakes. Newly discovered slow earthquakes are qualitatively different phenomena from ordinary fast earthquakes and provide independent information on slow deformation at depth. Many numerical simulations have been carried out to model both fast and slow earthquakes, but problems remain, especially with scaling laws. Some mechanisms are required to explain the power-law nature of earthquake rupture and the lack of characteristic length. Conceptual models that include a hierarchical structure over a wide range of scales would be helpful for characterizing diverse behavior in different seismic regions and for improving probabilistic forecasts of earthquakes.