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

这项为期三年的计划是由三位研究人员合作完成的，他们的才华横跨地球物理学、应用数学、计算科学。Uid动力学和计算机科学。该提案的主要目标是建立一个统一。构建了多尺度分析、物理和统计特征提取、多分量相图构建、小波地质过程大尺度可视化和建模的框架。我们打算申请这所大学。对以下地质问题进行分析和模拟的方法：地球地幔的高瑞利数热与热化学对流，2。强。现场地球动力学（数值模拟和大地测量卫星数据），2。其他类型的模拟或地球物理观测。第二代小波将用于研究旨在相干-非相干结构提取（即羽流和背景热）的新算法。波动)从大规模数值模拟，发展新的模型方程，描述他们的时空演变，考虑到e。不连贯的。并开发新的基于小波的可视化工具，用于多分量相图的特征提取和构建。在建模和模拟领域，第二代小波将用于分离大范围的高瑞利数地球物理数据。分解成不连贯和连贯的成分。专门用于非同质过程的现代统计工具将应用于三次随机建模。不连贯的。Elds关于相干Elds的演化。采用动态自适应小波配置算法求解控制方程。自适应网格将使连贯结构能够被分解，并使它们的演变能够被科学地跟踪。将开发基于小波的工具来快速提取和可视化地球物理数据集中的相关特征。在多个尺度上提取相干结构。这些小波将使用点渲染技术进行可视化，以实现快速的视觉显示，而不需要对数据进行解压。这些工具将应用于上述地球物理问题的分析。最后，将开发一个通用的工具。科学地捕获，表示和可视化n维相图地图的相边界。这些边界代表了低维特征，给地球科学家带来了巨大的挑战。知识价值。本文开发的算法专门解决了当经典方法未能在预测建模方面取得进展时，无法明确解决的动态活动尺度的确定性和/或随机建模问题。这些技术在其他领域的运输过程中也有应用。科学和工程领域面临着广泛的空间尺度。本研究提出的新方法将为地球系统的内部动力学提供新的见解，使研究人员能够分析大数据集并提取低维特征。我们设想了一种能够对复杂的真实相图和多组分系统相关的原位物理性质进行紧凑描绘和可视化的全自动化稳健策略。例如地球化学和岩石学。更广泛的影响。这个项目将推动和促进计算、地球物理的进步。流体动力学、非线性物理以及小波在地球科学家中的一般应用。这个机会将允许来自统计学、应用数学、计算机科学和地球物理学的学生在这些技术和数学前沿领域进行合作，重点是地球科学的应用。

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.