Introduction Stochastic models with an increasing component of physical reasoning have been slowly gaining acceptance over the last two decades. The subject of statistical seismology aims to bridge the gap between physics-based models without statistics, and statistics-based models without physics. This volume, which is based largely on papers presented at the 3rd International Workshop on Statistical Seismology, held in Juriquilla, Mexico in May 2003, may serve to illustrate the range of

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... now coming under the statistical seismology heading. While the papers presented may not solve the problem of bridging the gap, they indicate routes by which it is being approached. Several driving forces can be recognized behind the development of statistical seismology. One is idealistic in character, and based on attempts to emulate for seismology the success of classical models in continuum mechanics, statistical mechanics and turbulence theory. Although progress has been made, seismology has proved a difficult subject in which to make a breakthrough. Appealing analogies such as the approach to a phase change can be made, and general models such as selforganized critically can provide valuable insights into the processes at work. However, converting such broad insights into tractable explicit models, that can be fitted to a specific data set and used to provide quantitative predictions, is an altogether more difficult issue, and only partially resolved. On the physical side, there is a long history of attempts to model the processes of rupture and fault propagation. Earthquake models that represent faults as dislocation surfaces in a surrounding elastic solid capture important aspects of the process, as is evident by the success of such models to fit a variety of seismological