Collaborative Research: Seismic Waves from Volcanoes: Fully Coupled Time-Dependent Models of Fluid Flow Through Elastic Walled Conduits

减轻与火山有关的风险需要对岩浆通过地壳裂缝和管道的运输和喷发有详细的了解。岩浆流激发的地震波及其与弹性围岩的耦合可以用来对火山系统的某些部分施加有价值的约束，否则这些部分是无法进入的。地震观测信号的复杂性和流-固耦合系统建模的难度给该系统带来了巨大的挑战。这项合作提案的目标是建立数值模型，描述可压缩粘性流体在弹性体中通过狭窄通道的高速流动，以及地震波在固体中的传播。流体和固体响应是完全耦合的：弹性变形改变了流体流经管道的截面积，流体压力的变化推动管道壁进出，激发地震波。具体而言，该项目小组将开发一种可证明稳定和准确的数值方法，用于随时间变化的准一维流体流过固体中的导管，以及该固体的弹性动力学响应。该模型将包括可压缩性、声速、粘度和气体析出阻力的变化。该程序将首先用于探索管道壁变形对稳态喷发动力学的作用。然后，该小组将评估稳态喷发溶液的稳定性。初步分析表明，对于足够快的流动，流固系统对长波长扰动是不稳定的，这种扰动表现为管道壁振幅增长的振荡。第一个重点将是在目前实施的二维平面应变框架内从玄武岩裂缝喷发产生的地震波。然后，该小组将把该模型扩展到适用于圆柱形管道的轴对称几何结构，并研究爆炸喷发产生的地震波。最后，他们将计算远场体波和表面波，并将等效单力和矩张量表示的时间依赖性与详细的源过程联系起来。该项目由地球物理和岩石地球化学项目支持。

Mitigating the risks associated with volcanoes requires a detailed understanding of the transport and eruption of magma through cracks and conduits in Earth's crust. Seismic waves excited by magma flow and its coupling to the elastic wall rocks can be used to place valuable constraints on parts of the volcanic system that are otherwise inaccessible. The complexity of observed seismic signals and the difficulty of modeling the coupled fluid-solid system present a formidable challenge. The objective of this collaborative proposal is to develop numerical models describing the high-speed flow of compressible, viscous fluids through narrow channels in elastic bodies, together with the propagation of seismic waves through the solid. The fluid and solid response is fully coupled: elastic deformation changes the cross-sectional area of the conduit through which fluid flows, and changes in fluid pressure push the conduit walls in and out, exciting seismic waves.Specifically, the project group will develop a provably stable and accurate numerical method for time-dependent quasi-one-dimensional fluid flow through conduits in a solid body, together with the elastodynamic response of that solid. The model will include changes in compressibility, sound speed, viscosity, and drag from gas exsolution. The code will be used first to explore the role of conduit wall deformation on steady state eruption dynamics. The group will then assess the stability of steady state eruption solutions. Preliminary analyses indicate that for sufficiently rapid flows, the fluid-solid system is unstable to long wavelength perturbations that appear as conduit wall oscillations of growing amplitude. One first focus will be on seismic waves from basaltic fissure eruptions within the currently implemented two-dimensional plane-strain framework. The group will then extend the model to the axisymmetric geometry appropriate for cylindrical conduits, and study seismic waves from explosive eruptions. Finally, they will calculate far-field body and surface waves and link the time dependence of equivalent single force and moment tensor representations to detailed source processes.This project is supported by the Geophysics and Petrology & Geochemistry Programs.