10:15 AM - 10:30 AM
[SVC31-06] A fluid flow model of N-type earthquakes
Keywords:volcanic earthquake, fluid flow
In active andesitic volcanoes, we occasionally observe a remarkable earthquake characterized by gradually attenuating long-tail oscillation containing a harmonic spectrum structure. These events are called N-type earthquake naming after non-dumping oscillation. One of the most reliable models of N-type earthquake is a fluid-filled crack model proposed by Chouet (e.g, Chouet, 1986; Chouet, 2003). Chouet’s studies showed that the fluid-filled crack generates a very slow wave propagating along the crack wall, which he called the “crack wave”. The crack wave leads to more realistic estimates of the resonator size relative to a spherical resonator. Chouet’s model consists of a single isolated fluid-filled crack in an infinite elastic solid body, and no external mass transfer into and/or out of the crack is taken into consideration. Based on this model, a high-frequent occurrence of N-type earthquakes suggests that a blockage in the source area had been progressing and the fluid had been kept in the cracks. However, we sometimes observe high-frequent occurrences of N-type earthquakes associated with an expansion of geothermal anomaly. This fact suggests an exitance of alternative source model of N-type earthquake.
In this paper, we discuss another source model of N-type earthquake caused by a fluid flow. Takeo (2021) proposes that harmonic tremors are excited by a non-linear instability that arises when viscous fluid flows through a partially constricted flexible channel, and develops a simple lumped-parameter model of the process. Figure 1 schematically depicts a system consisting of a flexible channel mounted between upstream and downstream cylindrical tubes. Changing only a reservoir pressure of this model, Takeo (2021) succeeds in simulating a harmonic tremor which has the same topological characteristics (phase portrait) with the largest observed harmonic tremor. When the reservoir pressure exceeds a critical value, the stationary point becomes unstable and the trajectory moves away from the stationary point, exhibiting a self-sustained oscillation. When the stationary point is a stable focus, the trajectories spiral into the stationary point. Thus, a transient disturbance of the reservoir pressure holds a potential for exciting a transient oscillation. Figure 2 shows two examples of transient pressure change in the reservoir. These pressure changes produce gradually attenuating long-tail oscillations like the N-type earthquake as shown in Figure 3. In this case, the oscillating duration is controlled by a level of bottom pressure in the reservoir (see #1 and #2 in Fig. 3) and/or a configuration of the channel (see #1 and #3 in Fig. 3). The characteristic period of oscillation also depends on the channel configuration (see #1, #2 and #4 in Fig. 3). These long tail oscillations contain harmonic spectrum structures due to slightly distorted waveform caused by the non-linear instability. A general tube law (pressure-area curve relation) for the flexible channel will affect waveforms of long-tail oscillation. The detail will be discussed in the presentation. This result implies that the N-type earthquake can be excited in two conflicting physical conditions: one is the single isolated fluid-filled crack in an elastic solid and the other is the fluid flow through a flexible channel.
In this paper, we discuss another source model of N-type earthquake caused by a fluid flow. Takeo (2021) proposes that harmonic tremors are excited by a non-linear instability that arises when viscous fluid flows through a partially constricted flexible channel, and develops a simple lumped-parameter model of the process. Figure 1 schematically depicts a system consisting of a flexible channel mounted between upstream and downstream cylindrical tubes. Changing only a reservoir pressure of this model, Takeo (2021) succeeds in simulating a harmonic tremor which has the same topological characteristics (phase portrait) with the largest observed harmonic tremor. When the reservoir pressure exceeds a critical value, the stationary point becomes unstable and the trajectory moves away from the stationary point, exhibiting a self-sustained oscillation. When the stationary point is a stable focus, the trajectories spiral into the stationary point. Thus, a transient disturbance of the reservoir pressure holds a potential for exciting a transient oscillation. Figure 2 shows two examples of transient pressure change in the reservoir. These pressure changes produce gradually attenuating long-tail oscillations like the N-type earthquake as shown in Figure 3. In this case, the oscillating duration is controlled by a level of bottom pressure in the reservoir (see #1 and #2 in Fig. 3) and/or a configuration of the channel (see #1 and #3 in Fig. 3). The characteristic period of oscillation also depends on the channel configuration (see #1, #2 and #4 in Fig. 3). These long tail oscillations contain harmonic spectrum structures due to slightly distorted waveform caused by the non-linear instability. A general tube law (pressure-area curve relation) for the flexible channel will affect waveforms of long-tail oscillation. The detail will be discussed in the presentation. This result implies that the N-type earthquake can be excited in two conflicting physical conditions: one is the single isolated fluid-filled crack in an elastic solid and the other is the fluid flow through a flexible channel.