フラクタルと地震の数理

分形和地震的数学

• 批准号: 62300007
• 负责人: SAITO Masanori
• 金额: $ 3.2万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Co-operative Research (A)
• 财政年份: 1988
• 资助国家: 日本
• 起止时间: 1988 至 1989
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-62300007/
• 关键词: fractal; earthquake; focal mechanism; rock fracture; chaos; パターン形成

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)".

分形是一种新开发的方法，用于研究断裂和图案形成等复杂现象。本项目的目的是一方面将新发展的分形思想引入地震学，另一方面向面向分形的数学家、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。随后，各工作组的成果在研讨会上进行了介绍。 1987财年我们举办了3次研讨会，不仅回顾了地震学中的分形现象，还回顾了天文学、物理、化学等各个领域的分形现象。由于分形最初是几何学的一个分支，因此大多数所呈现的现象都是用分形语言来描述的。但这并不意味着这些现象在动态上是等效的。在项目的后半部分，我们将注意力集中在分形的动力学方面。在 1988 财年，我们举办了两次研讨会，讨论了地震震源过程的分层方法以及分形介质中的传播问题。 1987年该项目的成果发表在《数学地震学（III）》上，1988年的成果将发表在《数学地震学（IV）》上。

项目成果

高安秀樹 他: "フラクタル科学" 朝倉書店, 1-258 (1987)

高安秀树等：《分形科学》朝仓书店，1-258（1987）

Masanori SAITO (Ed.): Mathematical Seismology (III). Institute of M Statistical Mathematics, 1-380 (1988)

Masanori SAITO（主编）：数学地震学（III）。

斎藤正徳: "数理地震学(III)" 統計数理研究所, 1-380 (1988)

Masanori Saito：《数学地震学（III）》统计数学研究所，1-380（1988）