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

火山内部岩浆的迁移在地球表面产生了变形的特征。岩浆房的位置、形状和压力，以及岩浆房周围岩石的内部结构，控制着火山表面可以观察到的特定变形模式。对岩浆迁移的特征进行量化很重要，因为岩浆的向上迁移是火山爆发的前兆。本项目将开发有限元模型（FEM），这是一种数值方法，将火山模拟为一个动态系统，说明活动火山复杂内部结构内迁移岩浆的相互作用。这些有限元法将用于逆方法，寻求量化的估计和不确定性的一些特征参数，描述岩浆迁移到，或出，岩浆房。这些方法将在两座火山（阿拉斯加的奥克莫克和厄瓜多尔的通古拉瓦）的自然实验室范围内开发。这两座活火山都具有已知的内部结构，其形式为使用地面地震仪器数据估计的层析成像模型，以及使用大地测量数据记录的表面变形历史（例如，全球定位系统数据和卫星雷达图像）。更具体地说，该项目将使用基于有限元法的大地测量数据的逆分析，以确定嵌入这两座活火山复杂内部结构中的岩浆房的位置、形状和加压的估计值和不确定性。更一般地说，该项目将制定方法，将火山大地测量学和地震学这两个传统上完全不同的地球物理学研究领域结合起来。该项目包括南达科他州矿业与技术学院（SDSMT）的早期和中期教师和研究生教育之间的合作研究，EPSCoR机构。SDSMT是科学和工程研究的区域中心，地理位置优越，可以与当地大量的美洲原住民社区进行交流。所提出的方法将提供强大的数值技术，以联合收割机结合不同类型的信息，通常独立使用彼此评估火山的危险。这种同时分析不同类型信息的能力将为特定活火山的内部过程提供更完整的画面，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为一般适用于火山变形的其他分析，并最终提供更可靠的自然灾害评估的重要社会效益。该项目的另一个影响是它与地震变形研究的直接相关性，这是由嵌入与活动断层相关的复杂结构中的变形源的类似配置驱动的。因此，为这个项目开发的技术可以很容易地扩展到地震变形的研究，并可能有重要的影响，为未来的分析，地震和海啸的危害世界各地。

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.