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

火山内岩浆的迁移会在地球表面产生变形信号。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，控制着在火山表面可以观察到的特定变形模式。岩浆运移特征的量化是很重要的，因为岩浆的向上运移是火山喷发的前兆。该项目将开发有限元素模型（fem），这是一种数值方法，将火山模拟为一个动态系统，该系统解释了活火山复杂内部结构中迁移岩浆的相互作用。这些fem将用于逆向方法，寻求量化描述岩浆迁入或迁出岩浆库的一些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火山和厄瓜多尔的通古拉瓦火山）的背景下开发。这两座活火山的内部结构都是已知的，它们的内部结构是以断层扫描模型的形式存在的，这些模型是利用地基地震仪器的数据估计出来的，以及过去十年来用大地测量数据（例如GPS数据和卫星雷达图像）记录的地表变形历史。更具体地说，该项目将使用基于fem的大地测量数据逆分析来确定这两座活火山复杂内部结构中岩浆房的位置、形状和压力的估计和不确定性。更一般地说，这个项目将开发整合火山大地测量学和地震学这两个传统上不同的地球物理研究领域的方法。这种整合将促进对活火山的基本认识。该项目包括EPSCoR机构南达科他州矿业与技术学院（SDSMT）早期和中期职业教师和研究生教育的合作研究。SDSMT是一个科学和工程研究的区域中心，地理位置优越，可以与大量的当地印第安人社区联系。所提出的方法将提供强大的数值技术来结合不同类型的信息，这些信息通常是相互独立使用的，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活火山的内部过程提供更完整的图像，并可能导致对火山行为的更可靠的预测。该项目开发的方法将普遍适用于其他火山变形分析，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变形研究的直接相关性，地震变形是由嵌入与活动断层相关的复杂结构中的类似变形源配置驱动的。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，并可能对将来全世界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.