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

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。

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.