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

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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.