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

这个为期三年的计划是由三位研究人员合作完成的，他们的才能涵盖了物理学、应用数学、计算流体动力学和计算机科学。这个计划的主要目标是开发一个统一的艾德框架，用于多尺度分析、物理和统计特征提取、多组分相图的构建、我们计划将这种统一的艾德方法应用于以下地质问题的分析和模拟：1.地幔中的高瑞利数热对流和热化学对流，2.强场地球发电机（包括数值模拟和大地测量卫星数据），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旨在相干-非相干结构提取的新算法（也就是说，羽流和背景热波动），以开发描述它们的时空演化的新模型方程，通过统计建模考虑非相干场的影响，并开发新的基于小波的可视化工具，用于特征提取和多目标构建在建模和仿真领域，第二代小波将用于分离宽范围的高、低、高分辨率的组分相图。瑞利数地球物理学。将其分为非相干和相干分量。现代统计工具，专门用于非均匀过程，本文提出了一种基于自适应小波配点算法的非相干场随机模拟方法，该方法采用自适应小波配点算法求解非相干场的控制方程，自适应网格使非相干场的随机模拟成为可能。待解析的结构及其演化将被及时跟踪。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。相干结构将在多个尺度上提取。这些小波将使用点渲染技术进行可视化，以快速可视化显示，而无需数据解压缩。这些工具将应用于上述地球物理问题的分析。最后，本文提出了一种新的计算方法，它能有效地捕捉、表示和显示n维相图的相边界，这些相边界代表了低维特征，对地球科学家提出了一个巨大的挑战。当经典方法在预测建模方面未能取得进展时，这些技术可以应用于其他科学和工程领域面临广泛空间尺度的输运方程。本研究提出的新方法将为研究地球系统的内部动力学提供新的见解，将使研究人员能够分析大型数据集，并提取较低的三维特征。新的全自动化的drobust策略的紧凑描绘和可视化的复杂的现实相图和相关的多组分系统的原位物理性质是该项目将推动和促进计算、地球物理、流体动力学、非线性物理和小波在地球科学家中的一般应用的进展。这个机会将使统计学、应用数学、计算机科学和地球物理学在这些技术和数学前沿领域合作，重点放在地球科学的应用上。

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.