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

合作研究：CMG：基于小波的物理特征提取、大规模可视化和多尺度地质过程建模的统一方法

• 批准号: 0327269
• 负责人: Oleg Vasilyev
• 金额: $ 23.5万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-09-01 至 2007-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0327269&HistoricalAwards=false
• 关键词: Collaborative; Research; CMG; Wavelet; Based

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 thisproposal 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 geologicalprocesses using wavelets.We plan to apply this uni .ed approach to the analysis and simulation of thefollowing 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 structureextraction (i.e.,plumes and background thermal .uctuations)from large-scale numerical simulations,todevelop new model equations that describe their space-time evolution,taking into account the e .ect of theincoherent .eld via statistical modeling,and to develop new wavelet-based visualization tools for both featureextraction 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 rangeof scales of high-Rayleigh number geophysical .elds into their incoherent and coherent components.Modernstatistical tools,specialized to non-homogeneous processes,will be applied to the stochastic modeling of thee .ect of incoherent .elds on the evolution of coherent .elds.The governing equations will be solved using adynamically adaptive wavelet collocation algorithm.An adaptive grid will enable the coherent structures tobe resolved and their evolution followed e .ciently.Wavelet-based tools will be developed to rapidly extract and visualize the relevant features in geophysicaldata sets.Coherent structures will be extracted at multiple scales.These wavelets will be visualized usingpoint rendering techniques for fast visual displays without the need for data decompression.These tools willbe 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 phaseboundaries of n -dimensional phase diagram maps.These boundaries represent ow-dimensional features,andpose a formidable challenge to the geoscientist.Intellectual Merit.The algorithms developed herein speci .cally address problems of deterministicand/or stochastic modeling of dynamically active scales that are not explicitly resolvable,when classicalmethods have failed to yield progress in predictive modeling.These techniques have application to transportequations in other .elds of science and engineering confronted with a wide range of spatial scales.Novemethods proposed in this research will provide new insights on the internal dynamics of geosystems,willenable researchers to analyze large data sets and extract lower-dimensional features.Nove fully automatedrobust strategy of compact delineation and visualization of complicated realistic phase diagrams and relatedin 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 allowstudents from statistics,applied mathematics,computer science and geophysics to work collaboratively onthese technologically and mathematically cutting-edge areas with applied emphasis in the geosciences.

这项为期三年的建议是三位研究人员之间的合作，他们的才能涵盖了地球物理学，数学，计算。遵循地质问题的分析和模拟：1。雷利数量的热量和热化学对流在地面上，2。strong .Eld。 （即，李子和背景热.cutiation）来自大尺度数值模拟，to开发的新模型方程，这些方程描述了它们的时空演变，并考虑到通过统计建模的Incosherent .ELD的E. ect。高射线数量地球物理的范围尺度将其纳入其不连贯且相干的组件中。现代阶层工具（专门至非均匀过程）将适用于无均匀建模。自适应网格将使连贯的结构能够解决，并遵循其进化。将开发基于波浪的工具，以快速提取和可视化地球物理data集中的相关特征。编码结构将在多个尺度上提取cophysicaldata集合的相关结构，以便使用Point rendering Data Decompression以多种尺度提取这些尺度的工具，以实现可视化的工具。上面提到的地球物理问题。在最后，将开发出一种通用工具，以方向捕获，代表和可视化n维相图映射的n维相图的相位。这些界限代表OW维特征，并挑战了对地球的范围/构图。当古典方法未能在预测建模中取得进展时，动态主动的量表的动态量表。这些技术在其他.Sciency和工程中的运输方程都适用nove nove完全自动化的策略是紧凑的描绘和可视化复杂的现实阶段图和多组分系统的相关物理特性的nove nove nove nove nove n o demosics and in Comentical in Compertical and thernies intyralsics in Comentical and in ther-nin inther in Dynanctical in Dynanctical in Dynation of Dynancialsical inty.us intly inty.us。向地球科学家提供的小波。这个机会将允许统计，应用数学，计算机科学和地球物理学的学生在技术上和数学上尖端的领域进行协作，并在地球科学中进行了强调。