RESONANCE OF A FLUID-DRIVEN CRACK - RADIATION PROPERTIES AND IMPLICATIONS FOR THE SOURCE OF LONG-PERIOD EVENTS AND HARMONIC TREMOR
RESONANCE OF A FLUID-DRIVEN CRACK - RADIATION PROPERTIES AND IMPLICATIONS FOR THE SOURCE OF LONG-PERIOD EVENTS AND HARMONIC TREMOR
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DOI：
10.1029/jb093ib05p04375
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发表时间：
1988-05-10
期刊：
影响因子：
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通讯作者：
CHOUET, B
中科院分区：
文献类型：
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作者：
CHOUET, B
提出了一种动态源模型，其中包含粘性可压缩流体的三维裂纹被施加在裂纹表面小面积ΔS上的脉冲压力瞬态激励进入共振。裂纹的激发主要取决于两个无量纲的参数，即裂纹刚度C=（B/μ）（L/d）和粘性阻尼损失F=（12ηL）/（ρ <$d ~ 2 α），式中，α是体积模量，η是粘度，ρ <$是流体密度，μ是刚度，α是固体的压缩速度，L是裂纹长度，δ是裂纹厚度。第一个参数表征的能力的裂缝振动和形状的频谱签名的源，和第二个量化的效果的流体粘度上的持续时间的共振。共振是由一个非常慢的波被困在充满流体的裂缝。这种导波，称为裂纹波，类似于在充满流体的钻孔中传播的管波;它是反向色散的，显示出随波长增加而减小的相速度，并且其波速总是低于流体的声速，随着裂纹刚度的增加而迅速减小。源频谱显示出许多尖锐的峰值特征的裂纹的振动的各个模式的频谱形状的变化，无论是在峰的数量和宽度，是令人惊讶的复杂，反映了横向和纵向模式的共振之间的干扰，以及这些模式的节点。远场频谱由窄带主峰和次主峰标记，其反映了各种源模式的相互作用。由源辐射的主谱峰的频率与辐射方向无关。共振峰的频率、带宽和间距强烈依赖于裂纹刚度，刚度因子的较大值将这些峰移到较低频率并减小其带宽。特定模式的激发取决于触发器的位置和受压力瞬变影响的裂纹表面的程度。流体粘度降低了主要频谱峰值的幅度，模糊了频谱的精细结构，并大大减少了辐射信号的持续时间。辐射造成的能量损失在高频率下更强，产生的地震特征在信号开始附近以高频成分为标志，在信号尾波中以持续时间更长的较长周期成分为主。这种特征与在活火山和水力压裂实验中观察到的长期事件所显示的特征相一致。在高刚度（C≥ 100）的裂纹中可能存在的极低速度也为诸如日本阿索火山的2型震颤等极长周期震颤提供了有吸引力的解释，而不需要不切实际的大岩浆容器。在裂纹表面上的驻波图案成立的持续共振的流体中是可观察到的裂纹的近场，这表明源的位置和范围可以估计从映射的模式的节点和腹看到在其附近。根据该模型，长周期事件和谐波震颤共享相同的源，但在流体流动的边界条件和建立源的共振的触发机制方面不同，前者被视为震颤生成系统的脉冲响应，后者表示由于更复杂的强迫函数而引起的激励。
A dynamic source model is presented, in which a three‐dimensional crack containing a viscous compressible fluid is excited into resonance by an impulsive pressure transient applied over a small area ΔS of the crack surface. The crack excitation depends critically on two dimensionless parameters called the crack stiffness,C= (b/μ)(L/d), and viscous damping loss,F= (12ηL)/(ρƒd2α), wherebis the bulk modulus, η is the viscosity, ρƒis the density of the fluid, μ is the rigidity, α is the compressional velocity of the solid,Lis the crack length, anddis the crack thickness. The first parameter characterizes the ability of the crack to vibrate and shapes the spectral signature of the source, and the second quantifies the effect of fluid viscosity on the duration of resonance. Resonance is sustained by a very slow wave trapped in the fluid‐filled crack. This guided wave, called the crack wave, is similar to the tube wave propagating in a fluid‐filled borehole; it is inversely dispersive, showing a phase velocity that decreases with increasing wavelength, and its wave speed is always lower than the acoustic velocity of the fluid, decreasing rapidly as the crack stiffness increases. The source spectrum shows many sharp peaks characterizing the individual modes of vibration of the crack; the variation of spectral shape, both in the number and width of peaks, is surprisingly complex, reflecting the interference between the lateral and longitudinal modes of resonance, as well as nodes for these modes. The far‐field spectrum is marked by narrow‐band dominant and subdominant peaks that reflect the interaction of the various source modes. The frequency of the dominant spectral peak radiated by the source is independent of the radiation direction. The frequency, bandwidth, and spacing of the resonant peaks are strongly dependent on the crack stiffness, larger values of the stiffness factor shifting these peaks to lower frequencies and decreasing their bandwidth. The excitation of a particular mode depends on the position of the trigger and on the extent of the crack surface affected by the pressure transient. Fluid viscosity decreases the amplitudes of the main spectral peaks, smears out the finer structure of the spectrum, and greatly reduces the duration of the radiated signal. The energy loss by radiation is stronger for high frequencies, producing a seismic signature that is marked by a high‐frequency content near the onset of the signal and dominated by a longer‐period component of much longer duration in the signal coda. Such signature is in harmony with those displayed by long‐period events observed on active volcanoes and in hydrofracture experiments. The very low velocity which is possible in a crack with high stiffness (C≥ 100) also provides an attractive explanation for very long period tremor, such as type 2 tremor at Aso volcano, Japan, without the requirement of an unrealistically large magma container. The standing wave pattern set up on the crack surface by the sustained resonance in the fluid is observable in the near field of the crack, suggesting that the location and extent of the source may be estimated from the mapping of the pattern of nodes and antinodes seen in its vicinity. According to the model, the long‐period event and harmonic tremor share the same source but differ in the boundary conditions for fluid flow and in the triggering mechanism setting up the resonance of the source, the former being viewed as the impulse response of the tremor generating system and the latter representing the excitation due to more complex forcing functions.