フラクタルと地震の数理

分形是研究裂缝和图案形成等复杂现象的一种新方法。本项目的目的是一方面将分形的新思想引入地震学，另一方面向分形的数学家、物理学家和化学家介绍地震学问题，以发展地震学和分形科学。我们成立了几个工作组来审查和讨论各自的领域。工作组的结果随后在专题讨论会上提出。在1987财政年度，我们举行了3次专题讨论会，讨论了分形现象在地震学和天文学、物理学、化学等各个领域的应用。由于分形最初是几何学的一个分支，所以大多数出现的现象通常用分形的语言来描述。但这并不意味着这些现象是动态等效的。在项目的后半部分，我们将注意力集中在分形的动态方面。在1988财政年度，我们举行了两次专题讨论会，讨论了地震震源过程的分层方法和分形介质中的波传播问题。1987年的成果发表在《数学地震学（III）》上，1988年的成果将发表在《数学地震学（IV）》上。

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)".