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名研究人员合作完成的，他们的人才横跨地球物理、应用数学、计算动力学和计算机科学。这项计划的主要目标是建立一个统一的框架，用于多尺度分析、物理和统计特征提取、多分量相图的构建、大尺度可视化和地质过程的小波模拟。我们计划将这种统一的方法应用于下列地质问题的分析和模拟：1.地幔高瑞利数热对流和热化学对流；2.强地球发电机(包括数值模拟和大地卫星数据)，3.其他类型的模拟或地球物理观测。第二代小波将用于研究从大规模数值模拟中提取相干-非相干结构(即羽流和背景热力作用)的新算法，通过统计建模考虑非相干磁场的影响，开发描述其时空演变的新的模型方程，并开发基于小波的新的可视化工具，用于特征提取和多分量相图的构建。在建模和模拟领域，第二代小波将被用于将大范围的高瑞利数地球物理场分离为非相干和相干分量。现代统计工具，针对非均匀过程，我们将把它应用于非相干域的随机建模。控制方程的求解将采用动态自适应小波配置算法。自适应网格将使相干结构得到分解，并跟踪其演化。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。将在多个尺度上提取相干结构。这些小波将利用点绘制技术可视化，无需数据解压缩。这些工具将被应用于上述地球物理问题的分析。最后，这些工具将被应用于上述地球物理问题的分析我们将开发一个通用工具来有效地捕捉、表示和可视化n维相图的相界。这些相界表示低维特征，并对地球科学家提出了巨大的挑战。本文所开发的算法特别解决了当经典方法在预测建模方面不能取得进展时，动态活动尺度的确定性和/或随机性建模的问题。这些技术可应用于面对广泛空间尺度的其他科学和工程领域的传输。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。这将使研究人员能够分析大数据集和提取低维特征。新的全自动稳健的复杂现实相图和相关多组分系统的原位物理性质的紧凑描绘和可视化策略被设想用于各种地球物理领域。例如，地球化学和岩石学。广泛的影响。这个项目将推动和促进计算、地球物理、动力学、非线性物理和小波在地球科学中的普遍应用的进步。这个机会将允许统计学、应用数学、计算机科学和地球物理的学生在这些技术和数学前沿领域合作，重点应用于地球科学。

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.