Collaborative Research: Application of Wavelets in Modelling and Visualizing Multiscale Phenomena in Geophysics

合作研究：小波在地球物理多尺度现象建模和可视化中的应用

• 批准号: 0106276
• 负责人: David Yuen
• 金额: $ 15万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-15 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0106276&HistoricalAwards=false
• 关键词: Collaborative; Research; Application; Wavelets; Modelling

Yuen Vasilyev Wavelets represent a new mathematical tool, developed mostly over the last fifteen years. The fundamental strength of wavelets lies in its inherent ability to achieve very high resolution locally using relatively few localized functions, called wavelets. However, its application in solid-earth geophysics has remained relatively limited. In this three-year proposal a multidisciplinary team, steeped in the skills of applied mathematics, numerical analysis, fluid dynamics and theoretical geophysics, will employ the latest tools from wavelets to address two classes of geophysical problems. These include finite-amplitude viscoelastic deformation in strongly variable viscosity media where thermo-mechanical coupling and mechanical compaction play mutually interacting roles, and modeling of gravity currents in both 2D and 3D geometries with strong thermo-mechanical coupling from variable viscosity and viscous heating. The aim is to disseminate the use of wavelets to the geophysical community in frontier research and basic education of graduate and undergraduate students.

Yuen Vasilyev Wavelet是一种新的数学工具，主要是在过去的15年中开发的。小波的基本优势在于其固有的能力，实现非常高的分辨率局部使用相对较少的本地化功能，称为小波。然而，它在固体地球物理学中的应用仍然相对有限。在这个为期三年的提案中，一个多学科团队，沉浸在应用数学，数值分析，流体动力学和理论物理学的技能，将采用小波的最新工具来解决两类地球物理问题。 这些包括有限振幅的粘弹性变形在强烈的变粘度介质中的热机械耦合和机械压实发挥相互作用的作用，并在2D和3D的几何形状与强烈的热机械耦合从可变粘度和粘性加热的重力流建模。其目的是在前沿研究和研究生和本科生的基础教育中向地球物理界传播小波的使用。