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

小波代表了一种新的数学工具，主要是在过去十五年中发展起来的。小波的基本强度在于其固有的能力，即使用相对较少的局部函数（称为小波）就能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。在这个为期三年的项目中，一个多学科团队将运用应用数学、数值分析、流体动力学和理论地球物理学的技能，利用小波的最新工具来解决两类地球物理问题。其中包括强变粘度介质中的有限振幅粘弹性变形，其中热-机械耦合和机械压实相互作用，以及由变粘度和粘性加热引起的强热-机械耦合的二维和三维几何重力流建模。目的是将小波的应用推广到地球物理学界的前沿研究和研究生和本科生的基础教育中。

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.