This electronic supplement contains a description of a theory that calculates stresses and pore pressure in the analysis. Figures S1–S7 show the coulomb stress with pore pressure at 5 km depth on different fault planes.
Cumulative values of each of the six components of stress tensor due to water loads, at any observation point, are calculated using 3D Boussinesq solutions (Jaeger and Cook, 1969, p. 281) in homogeneous, isotropic, and linear elastic half-space. These six components of the stress tensors are used to calculate normal (Δσ) and shear stress (Δτ) changes due to the reservoir on a considered plane, of given strike, dip, and rake (Jaeger and Cook, 1969). Following Biot (1941) and Rice and Cleary (1976), change in pore pressure (ΔP) due to reservoir in a water-saturated porous elastic medium is calculated by solving the following diffusion equation:
(S1)
in which c is the hydraulic diffusivity, B is the Skempton’s coefficient, Δθ/3 is the change in mean stress, and θ is the sum of normal stresses. Hydraulic properties are considered to be uniform and isotropic in the half-space. ΔP is the sum of ΔPc and ΔPd, which are the change in pore pressure due to the instant compression caused by the reservoir load (termed as compression pore pressure in the main article) and the change in pore pressure due to the diffusion of reservoir water load (termed as diffusion pore pressure in the main article), respectively (Roeloffs, 1988). Thus
(S2)
in which ΔPc can be estimated as
(S3)
To estimate ΔPd, we follow the Green’s function solution of Kalpna and Chander (2000). The initial or boundary condition, whichever is applicable for the defined problem, can be considered in terms of a source term S(x,y,z,t). Thus, the diffusion equation for ΔPd can be written as
(S4)
In our case, actual water-level time series for the Song Tranh 2 (ST2) reservoir since the impoundment of the reservoir is considered as the source term. Solution of equation (S4) can be written as
(S5)
In equation (S5), x, y, z and x′, y′, z′ refer to the observation and source points, respectively, in which the x, y, and z axes point toward north, east, and vertical downward, respectively.
Here
(S6)
Using the above method for calculating stresses and pore pressure and the concept of the coulomb stress, we analyze the effect of the ST2 reservoir impoundment on the seismicity around it.
Figure S1. Same as Figure 5 in the main article, but for c = 0.1 m2/s. In this figure, ΔS with pore pressure (all in kPa) at 5 km depth for two water stands, that is, highest and lowest water levels in the reservoir, is shown. Results in (a) and (d) correspond to fault type F4 (strike, dip, and rake as 135°, 80°, and 180°, respectively), (b) and (e) correspond to fault type F1 (strike, dip, and rake as 110°, 80°, and 180°, respectively), and (c) and (f) correspond to fault type F12 (strike, dip, and rake as 290°, 80°, and 180°, respectively). Two squares denote the locations in north and south earthquake clusters, at which calculations for Figures 3 and 4 in the main article are done. Positive ΔS corresponds to the region of destabilization due to the reservoir loading on the corresponding fault, whereas negative corresponds to stabilization.
Figure S2. Same as Figure 5 in the main article, but for c = 1.0 m2/s.
Figure S3. Same as Figure 5 in the main article, but for a different rake, considered here as −160° for all the three types of faults.
Figure S4. Same as Figure 5 in the main article, but for a different rake, considered here as 160° for all the three types of faults.
Figure S5. Same as Figure 5 in the main article, but for different dip, considered here as 60° for F4 and F1 and 90° for F12 type of faults. Results of (c) and (f) apply to F1 type of faults also, because fault is considered to be vertical.
Figure S6. Same as Figure S5, but for different rake, considered here as −160° for all the three types of faults.
Figure S7. Same as Figure S5, but for different rake, considered here as 160° for all the three types of faults.
Biot, M. A. (1941). General theory of three-dimensional consolidation, J. Appl. Phys. 12, 155–164.
Jaeger, J. C., and N. G. W. Cook (1969). Fundamentals of Rock Mechanics, Methuen, London, United Kingdom, 513 pp.
Kalpna, R. C., and R. Chander (2000). Green’s function based stress diffusion solution in the porous elastic half space for time varying finite reservoir loads, Phys. Earth Planet. In. 120, 93–101.
Rice, J. R., and M. P. Cleary (1976). Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents, Rev. Geophys. Space Phys. 14, 227–242.
Roeloffs, E. A. (1988). Fault stability changes induced beneath a reservoir with cyclic variations in water level, J. Geophys. Res. 93, 2107–2124.
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