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研究复杂现象，例如断裂和pattrn形成。本项目的讨论是将新成立的分形概念一方面引入地震学，并向面向面向面向的数学家，物理学家和Chenists引入地震学问题，以开发地震和分形科学。我们组建了几个工作组来审查和讨论各自的领域。然后将工作组的结果呈现在研讨会上。在1987财年，我们进行了3次研讨会，其中对分形现象的回顾不仅在表现学中，而且对各种领域（例如天文学，物理，化学）进行了综述。由于分形最初是几何的分支，因此大多数提出的现象通常用分形语言描述。但这并不意味着这些现象在动态上等效。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，我们讨论了两次座谈会，在其中讨论了地震焦点过程的等级方法，并讨论了分形培养基中的传播问题。该项目在1987年的结果发表在“数学地震学（III）”中，1988年的结果将发表在“数学地震学（IV）”中。

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）