Collaborative Research: CMG: Wavelet-Based Unified Approach for Physical Feature Extraction, Large-Scale Visualization, and Modeling of Multiscale Geological Processes

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

This three-year proposal is a collaboration between three researchers whose talents span geophysics, applied mathematics,computational .uid dynamics,and computer science.The main objective of this proposal is to develop a uni .ed framework for multiscale analysis,physical and statistical feature extraction, construction of multi-component phase diagram maps,large-scale visualization and modeling of geological processes using wavelets.We plan to apply this uni .ed approach to the analysis and simulation of the following geological problems: 1.High Rayleigh number thermal and thermo-chemical convection in Earth mantle, 2.Strong .eld geodynamo (both numerical simulations and geodetical satellite data), 3.Other kinds of simulations or geophysical observations. Second generation wavelets will be used to investigate new algorithms aimed at coherent-incoherent structure extraction (i.e.,plumes and background thermal .uctuations)from large-scale numerical simulations,to develop new model equations that describe their space-time evolution,taking into account the e .ect of the incoherent .eld via statistical modeling,and to develop new wavelet-based visualization tools for both feature extraction and construction of multi-component phase diagram maps. In the area of modeling and simulation second generation wavelets will be used to separate the wide range of scales of high-Rayleigh number geophysical .elds into their incoherent and coherent components.Modern statistical tools,specialized to non-homogeneous processes,will be applied to the stochastic modeling of the e .ect of incoherent .elds on the evolution of coherent .elds.The governing equations will be solved using a dynamically adaptive wavelet collocation algorithm.An adaptive grid will enable the coherent structures to be resolved and their evolution followed e .ciently. Wavelet-based tools will be developed to rapidly extract and visualize the relevant features in geophysical data sets.Coherent structures will be extracted at multiple scales.These wavelets will be visualized using point rendering techniques for fast visual displays without the need for data decompression.These tools will be applied to the analysis of the aforementioned geophysical problems. Finally,a general purpose tool will be developed to e .ciently capture,represent and visualize the phase boundaries of n -dimensional phase diagram maps.These boundaries represent ow-dimensional features,and pose a formidable challenge to the geoscientist. Intellectual Merit.The algorithms developed herein speci .cally address problems of deterministic and/or stochastic modeling of dynamically active scales that are not explicitly resolvable,when classical methods have failed to yield progress in predictive modeling.These techniques have application to transport equations in other .elds of science and engineering confronted with a wide range of spatial scales.Nove methods proposed in this research will provide new insights on the internal dynamics of geosystems,will enable researchers to analyze large data sets and extract lower-dimensional features.Nove fully automated robust strategy of compact delineation and visualization of complicated realistic phase diagrams and related in situ physical properties of multicomponent systems are envisioned to be used in a variety of geophysical .elds such as geochemistry and petrology. Broader Impact.This project will drive and promote progress in computation,geophysical .uid dynam- ics,nonlinear physics and in the general application of wavelets to geoscientists.This opportunity will allow students from statistics,applied mathematics,computer science and geophysics to work collaboratively on these technologically and mathematically cutting-edge areas with applied emphasis in the geosciences.