Stochastic Models for Earthquake Sequences

Although my title refers specifically to earthquake sequences, I would like to use this topic to illustrate some aspects of a more general theme, the roleof stochastic models in a science such as geophysics. One reason for pursuing such generalities, even at a Conference where I know the main interest will be on new discoveries and techniques, is a concern that the role of stochastic models is not well understood, and that this feature itself may be a brake on progress in this area. I refer in my abstract to the almost paradoxical situation that, whereas most geophysical data presents an extremely random appearance, there can be few sciences other than geophysics where mathematical models remain so firmly deterministic in character. I think it is important to ask how far this is due to the nature of the subject matter, and how far to matters of style and tradition. And to resolve this question one needs to have some idea of what stochastic models are for, in general terms, and when they are likely to be useful. Another reason for my choice is that, in my own work also, I have felt a desire to examine more critically the role of stochastic models and the general principles underlying their development and use. Ten years ago, when I first became involved with problems of statistical seismology, I was prepared to take on any geophysicist who dared to suggest that statistical ideas were less than central to the development of geophysical theory. Now I am more cautious. Although the last few years have shown a continuing increase in the application of statistical techniques in geophysics, as well as a sprinkling of papers on stochastic models, there has been no really definitive progress in this field; no outstanding instances where one can feel that the understanding of geophysical phenomena has been substantially advanced by the application of stochastic ideas; no convincing resolutions to long standing problems. Again one would like to know more about the reasons for this situation; is it expecting too much to look for advances of this kind, or are there particular reasons why stochastic models are hard to develop in geophysics ?