Collaborative Research: FEM-based inverse methods to estimate nonlinear geometric source parameters of volcano deformation from geodetic data

火山内岩浆的迁移在地球表面产生了变形特征。岩浆室的位置、形状和压力，以及岩浆室周围岩石的内部结构，控制着在火山表面可以观察到的特定变形模式。量化岩浆迁移的特征很重要，因为岩浆向上迁移是火山喷发的前兆。该项目将开发有限元模型(FEMS)，这是一种数值方法，将火山模拟为一个动态系统，说明在活火山复杂的内部结构中迁移的岩浆之间的相互作用。这些FEM将用于反向方法，寻求量化描述岩浆流入或流出岩浆室的几个特征参数的估计和不确定性。这些方法将在作为自然实验室的两座火山(阿拉斯加的奥克莫克和厄瓜多尔的通古拉瓦)的背景下开发。这两座活火山都有已知的内部结构，其内部结构是用地面地震仪器的数据估计的层析成像模型，以及过去十年用大地测量数据(如全球定位系统数据和卫星雷达图像)记录的地表形变历史。更具体地说，该项目将使用基于有限元的大地测量数据逆向分析，以确定嵌入这两个活火山复杂内部结构中的岩浆室的位置、形状和压力的估计和不确定性。更广泛地说，该项目将开发整合火山大地测量学和地震学的方法，这两个传统上截然不同的地球物理研究领域。该项目包括职业生涯初期和职业生涯中期的教师之间的合作研究，以及南达科他州矿产与技术学院(SDSMT)的研究生教育，这是EPSCoR的一个机构。SDSMT是一个地区性的科学和工程研究中心，地理位置优越，可以与当地大量的美洲原住民社区建立联系。拟议的方法将提供强大的数字技术，将不同类型的信息结合起来，这些信息通常相互独立地使用，以评估火山危险。这种同时分析不同类型信息的能力将为给定的活火山提供更完整的内部过程图景，并可能导致对火山行为的更可靠预测。该项目开发的方法将被设计成一般适用于火山变形的其他分析，并最终为更可靠的自然灾害评估提供重要的社会效益。该项目的另一个影响是它与地震形变研究直接相关，地震形变研究是由与活动断裂相关的复杂结构中嵌入的形变源的类似配置驱动的。因此，为该项目开发的技术可以很容易地扩展到地震形变的研究，并可能对未来世界范围内的地震和海啸灾害的分析产生重要影响。

The migration of magma within a volcano produces a deformation signature at the Earth's surface. The location, shape, and pressurization of the magma chamber, as well as the internal structure of the rocks surrounding the magma chamber, control the specific deformation pattern that can be observed at the surface of the volcano. Quantifying the characteristics of magma migration is important, because the upward migration of magma is a precursor to volcanic eruptions. This project will develop finite element models (FEMs), a type of numerical method, to simulate volcanoes as a dynamic system that accounts for the interaction of migrating magma within the complex internal structure of an active volcano. These FEMs will be used in inverse methods that seek to quantify estimates and uncertainties of a few characteristic parameters that describe magma migration into, or out of, a magma chamber. These methods will be developed in the context of two volcanoes (Okmok, Alaska, and Tungurahua, Ecuador) that will serve as natural laboratories. Both of these active volcanoes have known internal structures in the form of tomography models estimated using data from ground-based seismic instruments, as well as surface deformation histories that were recorded with geodetic data (e.g., GPS data and satellite radar imagery) over the past decade. More specifically, this project will use FEM-based inverse analyses of geodetic data to determine estimates and uncertainties for the location, shape, and pressurization of magma chambers embedded in the complex internal structures of these two active volcanoes. More generally, this project will develop methods to integrate volcano geodesy and seismology, two traditionally disparate geophysical fields of study. This integration is poised to advance the fundamental understanding of active volcanoes.This project comprises collaborative research among early-career and mid-career faculty and graduate education at the South Dakota School of Mines and Technology (SDSMT), an EPSCoR institution. SDSMT is a regional center for science and engineering research and is ideally located to interface with a substantial local Native American community. The proposed methods will provide powerful numerical techniques to combine different types of information that are customarily used independently from one another to assess volcano hazards. This ability to simultaneously analyze different types of information will provide a more complete picture of the internal processes for a given active volcano and will likely lead to more reliable predictions of volcanic behavior. The methods developed by this project will be designed to be generally amenable for other analyses of volcano deformation and ultimately provide important societal benefits of more reliable natural hazards assessments. Another impact of this project is its direct relevance to studies of earthquake deformation, which are driven by analogous configurations of deformation sources embedded in complex structures associated with active faults. Thus, the techniques developed for this project may be readily extended to studies of earthquake deformation and may have important implications for future analyses of seismic and tsunami hazards worldwide.