10:15 AM - 10:30 AM
[SVC32-15] Physical process of the onset event of volume increase in magma reservoir leading to the 2011eruption of Shinmoe-dake in Kirishima Volcano, Japan
Keywords:Shinmoe-dake in Kirishima Volcano, magma reservoir, volcanic crustal deformation, magma ascent and intrusion
The volcanic activities of Shinmoe-dake are caused by the supply of magma from a magma reservoir located about 8 km northwest of Shinmoe-dake, at a depth of 8 to 9 km. The first inflation of the magma reservoir was detected in December 2009. This study focuses on the beginning of the inflation event and models the magma reservoir to understand the magma intrusion processes.
The upper panel in Fig. 1 shows the timing of eruption event (red arrow) and the daily frequency of volcanic earthquakes that occurred directly beneath Shinmoe-dake from July 2007 to February 2011. The horizontal axis is the date, and the vertical axis is the daily frequency. The lower panel of Fig.1 shows the temporal change in the baseline length (in meters) between the two GNSS stations of the Geospatial Information Authority of Japan, located on either side of the magma reservoir of the Kirishima volcano. As interpreted from Fig.1, the magma reservoir turned into inflation in December 2009, accompanied by the increase of eruptive frequency and volcanic earthquakes. Subsequently, the deflation of the reservoir was observed after the eruption in January 2011. Fig. 2 shows the temporal change of the volume of the magma reservoir (in x103m3) for the period encircled in Fig.1, calculated by comparing the change in baseline length and the volume of the magma reservoir, as estimated by Ozawa and Munekane (2023). The rapid volume increase was detected in the first three days from December 15th.
In this study, we considered the following model as a magma supply system that explains this phenomenon (Fig. 3).
1. Assuming the magma reservoir to be a sphere, the changes in the pressure and the volume of the reservoir (Pm and Vm) satisfy the following equation:
dVm = (πR3(3K+4μ)/3μK)・dPm = A・dPm.
where R is the radius of magma reservoir, μ is the rigidity of the surrounding rock, and K is the bulk modulus of the magma.
2. Magma is supplied to the magma reservoir from the deep reservoir (pressure is constant at Pdm). For simplicity, assuming a laminar flow in a cylindrical vent, with length L and radius a. Assuming a laminar flow, the volumetric flow velocity J is as follows:
J = (πa4/8η)x(Pdm-Pm)/L = B・(Pdm-Pm).
3. The following relationship exists between the volumetric flow velocity of the vent and the volumetric change of the magma reservoir:
J = dVm/dt.
Solving these equations under the conditions Vm=0 at t=0 and Vm=Vmi (a constant) at t→∞, Vm is expressed as:
Vm = Vmi(1-e-bt).
Here, as we have a relationship of
b = B / A,
using the least squares method to find the best parameters to fit the observation (Fig. 2) with December 15 as t=0, we obtained
Vmi=2.5x106 [m3], b = 0.4[1/day].
As shown in Fig.4, our theoretical calculations (circle) successfully explain the observed rapid response (triangle).
Since B = (πa4)/(8ηL) and A = (πR3(3K+4μ))/(3μK), b is expressed by the following equation.
b = (3a4μK )/(8ηLR3(3K+4μ)).
Here, given the physical properties of magma and surrounding rock to beη≈102 [Pa•s], μ≈K≈109[Pa], and substitute b=0.4[1/day]=4.8x10-6[1/s], and the following equation is obtained:
LR3/a4 = 1.1x1011.
Now, we have successfully obtained an equation linking the geometries of the magma reservoir and plumbing vent. While it is impossible to determine these parameters independently, this equation allows us to roughly estimate the realistic values for plumbing systems, for example, L=1000m and a=1m, R=460m.
Acknowlegements: We used GNSS baseline length data from the Geospatial Information Authority of Japan. We would like to thank Dr. Shinzaburo Ozawa and Dr. Hiroshi Munekane of the Geospatial Information Authority of Japan for providing us with data on the volume changes of the magma reservoir in Kirishima, as well as for their useful discussions. We would also like to thank Dr. Yosuke Aoki of the Earthquake Research Institute, University of Tokyo, for his advice on physical properties around volcanic belts and for his discussions on the model. We would like to express our gratitude to them here.
The upper panel in Fig. 1 shows the timing of eruption event (red arrow) and the daily frequency of volcanic earthquakes that occurred directly beneath Shinmoe-dake from July 2007 to February 2011. The horizontal axis is the date, and the vertical axis is the daily frequency. The lower panel of Fig.1 shows the temporal change in the baseline length (in meters) between the two GNSS stations of the Geospatial Information Authority of Japan, located on either side of the magma reservoir of the Kirishima volcano. As interpreted from Fig.1, the magma reservoir turned into inflation in December 2009, accompanied by the increase of eruptive frequency and volcanic earthquakes. Subsequently, the deflation of the reservoir was observed after the eruption in January 2011. Fig. 2 shows the temporal change of the volume of the magma reservoir (in x103m3) for the period encircled in Fig.1, calculated by comparing the change in baseline length and the volume of the magma reservoir, as estimated by Ozawa and Munekane (2023). The rapid volume increase was detected in the first three days from December 15th.
In this study, we considered the following model as a magma supply system that explains this phenomenon (Fig. 3).
1. Assuming the magma reservoir to be a sphere, the changes in the pressure and the volume of the reservoir (Pm and Vm) satisfy the following equation:
dVm = (πR3(3K+4μ)/3μK)・dPm = A・dPm.
where R is the radius of magma reservoir, μ is the rigidity of the surrounding rock, and K is the bulk modulus of the magma.
2. Magma is supplied to the magma reservoir from the deep reservoir (pressure is constant at Pdm). For simplicity, assuming a laminar flow in a cylindrical vent, with length L and radius a. Assuming a laminar flow, the volumetric flow velocity J is as follows:
J = (πa4/8η)x(Pdm-Pm)/L = B・(Pdm-Pm).
3. The following relationship exists between the volumetric flow velocity of the vent and the volumetric change of the magma reservoir:
J = dVm/dt.
Solving these equations under the conditions Vm=0 at t=0 and Vm=Vmi (a constant) at t→∞, Vm is expressed as:
Vm = Vmi(1-e-bt).
Here, as we have a relationship of
b = B / A,
using the least squares method to find the best parameters to fit the observation (Fig. 2) with December 15 as t=0, we obtained
Vmi=2.5x106 [m3], b = 0.4[1/day].
As shown in Fig.4, our theoretical calculations (circle) successfully explain the observed rapid response (triangle).
Since B = (πa4)/(8ηL) and A = (πR3(3K+4μ))/(3μK), b is expressed by the following equation.
b = (3a4μK )/(8ηLR3(3K+4μ)).
Here, given the physical properties of magma and surrounding rock to beη≈102 [Pa•s], μ≈K≈109[Pa], and substitute b=0.4[1/day]=4.8x10-6[1/s], and the following equation is obtained:
LR3/a4 = 1.1x1011.
Now, we have successfully obtained an equation linking the geometries of the magma reservoir and plumbing vent. While it is impossible to determine these parameters independently, this equation allows us to roughly estimate the realistic values for plumbing systems, for example, L=1000m and a=1m, R=460m.
Acknowlegements: We used GNSS baseline length data from the Geospatial Information Authority of Japan. We would like to thank Dr. Shinzaburo Ozawa and Dr. Hiroshi Munekane of the Geospatial Information Authority of Japan for providing us with data on the volume changes of the magma reservoir in Kirishima, as well as for their useful discussions. We would also like to thank Dr. Yosuke Aoki of the Earthquake Research Institute, University of Tokyo, for his advice on physical properties around volcanic belts and for his discussions on the model. We would like to express our gratitude to them here.