Excitation and resonance of acoustic-gravity waves in a column of stratified, bubbly magma
Excitation and resonance of acoustic-gravity waves in a column of stratified, bubbly magma
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层状气泡岩浆柱中声重力波的激发和共振
DOI：
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发表时间：
2016
影响因子：
3.7
通讯作者：
E. Dunham
中科院分区：
文献类型：
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作者：
L. Karlstrom;E. Dunham
火山导管中岩浆的振荡被认为是在活火山附近观测到的某些地震和次声信号的来源。然而，管道内岩浆的多相和分层性质使解释观测所需的共振模式的计算复杂化。在这里，我们提出了一个线性化的数学框架来描述具有无牵引力上表面（熔岩湖）的两相岩浆（液体熔体和气泡）的稳定分层柱中的小振幅振荡和波。我们探讨了在一个轴对称的垂直管道中，阶段之间随时间的质量交换，深度变化的流体性质和重力对无粘性岩浆振荡模式的作用。非平衡相交换，我们称之为气泡生长和再吸收（BGR），通过引入一个动力学时间尺度来量化液相和气相之间的质量交换，使混合物发展到热力学平衡状态，从而参数化。利用可证明的稳定有限差分方法，我们求解了导管本征模的共振频率、衰减率和空间结构的本征值问题。然后将数值方法扩展到由导管内体积源激发的波或施加于熔岩湖表面的力的时域模拟。我们通过识别由代表性激励过程激发的主模态，将时变波传播模拟与模态分析联系起来。波在气泡岩浆中传播是弥散的，它们的行为是由三维参数决定的。其中一个量化了浮力和重力恢复力相对于可压缩性的重要性，第二个量化了平衡和非平衡条件下流体性质（例如混合物可压缩性）之间的差异，第三个将波浪周期与BGR时间尺度进行比较。背景流体性质的明显深度变化，例如从深部高压下溶解挥发物的液体熔体到气体析出深度以上的气泡岩浆的转变，将管道分割成不同的区域。对于典型的激发过程，以最大振幅表示的最长周期模态对气泡区域的长度和气泡岩浆的性质最为敏感。虽然管道底部的边界条件决定了基模态是否受管道总长度的影响，但位于出溶深度以上的模态对管道总长度明显不敏感。分析表明，影响火山喷发方式的参数，如总挥发分含量和BGR的动力学时间尺度，以及激发源特征，都印记在活火山的长周期地震和次声信号上。
Oscillations of magma in volcanic conduits are thought to be the source of certain seismic and infrasonic signals observed near active volcanoes. However, the multiphase and stratified nature of magma within the conduit complicates the calculation of resonant modes that is required to interpret observations. Here we present a linearized mathematical framework to describe small-amplitude oscillations and waves in a stably stratified column of two-phase magma (liquid melt and gas bubbles) with a traction-free upper surface (a lava lake). We explore the role of time-dependent mass exchange between the phases, depth-varying fluid properties and gravity on the modes of oscillation of inviscid magma within an axisymmetric, vertical conduit. Non-equilibrium phase exchange, which we refer to as bubble growth and resorption (BGR), is parameterized by introduction of a kinetic time scale quantifying mass exchange between the liquid and gas phases that evolves the mixture towards a state of thermodynamic equilibrium. Using a provably stable finite difference method, we solve the eigenvalue problem for the resonance frequencies, decay rates, and spatial structure of the conduit eigenmodes. The numerical method is then extended to time-domain simulations of waves excited by internal volumetric sources in the conduit or forces applied to the surface of the lava lake. We connect time-dependent wave propagation simulations to the modal analysis by identifying the primary modes that are excited by representative excitation processes. Waves propagating through bubbly magma are dispersive, and their behaviour is determined by three dimensionless parameters. One quantifies the importance of buoyancy and gravitational restoring forces relative to compressibility, the second quantifies differences between fluid properties (e.g. mixture compressibility) under equilibrium and non-equilibrium conditions, and the third compares the wave period to the BGR time scale. Pronounced depth variations in background fluid properties, such as the transition from liquid melt with dissolved volatiles at the high pressures at depth to bubbly magma above the gas exsolution depth, segment the conduit into distinct regions. The longest-period modes, which are expressed with the largest amplitudes for typical excitation processes, are most sensitive to the length of the bubbly region and properties of the bubbly magma within it. While the boundary condition at the bottom of the conduit determines whether the fundamental mode is affected by the total conduit length, modes localized above the exsolution depth are remarkably insensitive to the overall conduit length. Our analysis suggests that parameters affecting eruption style, such as total volatile content and kinetic time scales of BGR, along with excitation source characteristics, are imprinted on long-period seismic and infrasonic signals at active volcanoes.