フラクタルと地震の数理

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Fractal is a newly developing approach to study complex phenomena such as fracture and pattrn formation. The objuctive of the present project is to introduce the newly developed idea of fractal into seismology on one hand, and to introduce seismological problems to fractai oriented mathematicians, physicists and chenists to develop both seismolgy and fractal sciences, on the other hand. We formed several working-groups to review and discuss respective fields. The results of the working groups were then presented at symposia. In 1987 fiscal year we had 3 symposia, where a review of fractal phenomena in not only seimology but a variety of fields, such as astronomy, physics, chemistry were given. Since fractal is originally a branch of geometry, most of the presented phenomena were described commonly in the language of fractal. But this does not mean that those phenomena were dynamically equivalent. In the latter half of the project we focussed our a attention on the dynamical aspects in fractal. In 1988 fiscal year we had 2 symposia where hierarchical approach to seismic focal processes, and weve propagation problems in fractal media were discussed. The results of the project in 1987 were published in "Mathematical Seismology (III)" and the results in 1988 will be published in "Mathematical Seismology (IV)".