Supplementary Materials for: Superposition Approach ...

2 downloads 0 Views 1MB Size Report
This supplement analyzes the sensitivity of failure conditions to the shape of the slip dis- tribution. Given the uncertainty about the profile of cumulative slip in ...
Supplementary Materials for: Superposition Approach to Understand Triggering Mechanisms of Post-Injection Induced Seismicity Silvia De Simonea,b,c,∗ , Jes´ us Carreraa,c and V´ıctor Vilarrasaa,c

a

Institute of Environmental Assessment and Water Research (IDAEA), CSIC, c/ J. Girona 18, 08034 Barcelona, Spain b

Department of Civil and Environmental Engineering, Universitat Politcnica de Catalunya (UPC), c/ J. Girona 1-3, 08034 Barcelona, Spain c

Associated Unit: Hydrogeology Group (UPC-CSIC)



Corresponding author (email: [email protected])

Reservoir response after application of a slip distribution with elliptical profile This supplement analyzes the sensitivity of failure conditions to the shape of the slip distribution. Given the uncertainty about the profile of cumulative slip in induced seismicity, we have also analyzed the response of the reservoir to an elliptical slip distribution, which is typically assumed in natural seismology (Pollard and Segall, 1987). To this end, we have considered an elliptical slip distribution with the same total slipped length that the constant slip distribution assumed in the paper, L, and with maximum slip, uc =0.39 m, such that the two R cumulative earthquakes are equivalent in L

magnitude (i.e, with the same integral area

−L

u(x)dx, where u(x) is the slip value).

Figure S1 displays the stress perturbation caused by the activation of the slip movements with elliptical profile. Stress variation is smaller than in the case of constant slip distribution, for both shear and normal stresses (compare with Fig. 6). Shear stress drop is constant along the slipped surface, whereas it is variable and maximum near the tips in the case of constant slip distribution. At the tips, both distributions provoke a large increase in shear stress. 1

2

Figure S1: Variation of (a) shear and compressive (b) x- and (c) y-stress fields driven by shear slip with elliptical profile. The blue line inside (a) represents the spatial distribution of the imposed slip, with the orientation indicated by the yellow arrows.

Compared to the constant slip distribution assumed in the main body of the paper, a elliptical slip distribution provokes a smaller rotation of the stress tensor in the compression zones, but in the extensional zones the rotation is similar to the case of constant slip (compare Figs. 7b and S2).

Figure S2: Stress field rotation caused by shear slip with elliptical profile. The regional (initial) and perturbed stress tensor orientations are also shown. Note that we assume the convention of positive clockwise angle and rotation.

3 The failure conditions after superposition of hydraulic, thermal and slip movements with elliptical profile are similar to the case with constant slip, but the maximum values of the CF S are smaller, especially for fractures oriented like the y-axis (compare Figs. 10 and S3). This difference is localized at the tips, where the values are large, but the superposition of three effects at the observation regions H, J and W gives almost the same results for the two slip profiles considered (compare Figs. 11 and S4).

Figure S3: CF S due to the superposition of hydraulic, thermal and elliptical slip effects 33 days after shut-in in the (a) x- and (b) y-directions. The dashed lines indicate fractures whose stability is analyzed in detail.

4

Figure S4: CF S as a function of orientation for a point a) within region J (x=700, y=70), b) within region H (x=-540, y=70) and c) within region W (x=300, y=100), after 7 days of injection (dashed lines) and at 33 days after shut-in (solid lines). Grey lines refer to THM effects, whereas black lines refer to the superposition of THM and shear slip (elliptical profile) effects. The shadowed areas identify orientations that fail after shut-in, but not during injection.

Bibliography Pollard, D. and Segall, P. (1987). Theoretical displacements and stresses near fractures in rock: with applications to faults, joints, veins, dikes, and solution surfaces, volume 277, pages 277–349. edited by B.K. Atkinson, Academic Press, London.

5