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

袁Vasilyev小波代表了一种新的数学工具，主要是在过去的15年里发展起来的。小波的基本优势在于其固有的能力，即使用相对较少的局部化函数(称为小波)在局部获得非常高的分辨率。然而，它在固体地球物理中的应用仍然相对有限。在这份为期三年的提案中，一个精通应用数学、数值分析、流体力学和理论地球物理技能的多学科团队将使用小波的最新工具来解决两类地球物理问题。其中包括在强变粘度介质中的有限幅粘弹性变形，其中热力耦合和机械压实起相互作用，以及由变粘度和粘性加热产生的具有强热力耦合的2D和3D几何中的重力流的建模。其目的是在研究生和本科生的前沿研究和基础教育中向地球物理界传播小波的使用。

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.