1. Physical models for seismicity triggered during hydrofracture experiments Asaf Inbal Spatiotemporal distribution of induced seismicity in hydrofracture experiments will be explored via 2 models: Model #1 : Pore-pressure diffusion controls seismicity distribution Model #2 : Seismicity is triggered by stresses due to an opening fracture Shapiro et al. (1999)Fischer et al. (2008) 100 hr200 hr300 hr400 hr

2. Shapiro et al. (1999) Model #1 : Seismicity controlled by pore-pressure diffusion The pore-pressure perturbation is relaxed due to diffusion (Shapiro et al., 1999): where D is hydraulic diffusivity. For a step-function-like pore-pressure perturbation at the injection source, the triggering front is given by (Shapiro et al., 1997):

3. Model #1 : Seismicity controlled by pore-pressure diffusion Can pore-pressure diffusion explain the seismicity back-front? Parotidis et al. (2005)

4. Combining poroelastic effects and fluid leakage from the fracture may explain the temporal evolution of seismicity. The fracture half-length as a function of time is: Model #1 : Seismicity controlled by pore-pressure diffusion Shapiro et al. (2005) If fluid loss is significant (e.g. during long-term injections): Otherwise, during the initial injection phase:

5. Brief introduction to Linear Elastic Fracture Mechanics Energy balance for a static crack in an elastic medium: Griffith criteria for crack propagation: stable : unstable propagation: healing: 2aδa σ

6. Brief introduction to Linear Elastic Fracture Mechanics Energy balance for a static crack in an elastic medium: Griffith criteria for crack propagation: stable : unstable propagation: healing: 2aδa σ x σ

7. Brief introduction to Linear Elastic Fracture Mechanics Energy balance for a static crack in an elastic medium: Griffith criteria for crack propagation: stable : unstable propagation: healing: 2aδa σ x σ We relate the fracture criteria to Griffith energy balance by introducing the energy release rate:

8. Model #2 : Fluid filled crack in an elastic medium Dahm et al. (2010)

9. Phase 1 : Bidirectional growth under driving stress gradients (during injection) Crack tip velocity and crack length during phase 1:

10. Dahm et al. (2010) Phase 2 : Bidirectional growth due to decompression (post-injection) Crack growth is maintained by remaining driving pressures The post-injection length scales with the overpressure, and thus can be used to estimate K c of the formation.

11. Dahm et al. (2010) Phase 3 : Unidirectional growth (post-injection)

12. Dahm et al. (2010) Coulomb stress changes Phase 2 (post-injection, g=0) Phase 3 (post-injection, g>0) Phase 1 (during injection, g=0)

13. Application to hydrofracturing data Dahm et al. (2010)

14. Application to hydrofracturing data Dahm et al. (2010)

15. Calo et al. (2011) Is seismicity triggered by aseismic slip during the 2000 Soultz experiment?

16. Points for discussion How do we identify which physical model explains the majority of the observations? Application to natural earthquakes What happens if the stress drop is not instantaneous as assumed in the fluid filled crack model?

17. List of references used: Calo M., Dorbath C., Cornet F. H., and Cuenot, N. (2011). Large-scale aseismic motion identified through 4-D P-wave tomography, GJI, 186 (3), 1295-1314. doi: 10.1111/j.1365- 246X.2011.05108.x Dahm T., Hainzl S. and Fischer T. (2010). Bidirectional and unidirectional fracture growth during hydrofracturing: Role of driving stress gradients, JGR, 115, doi:10.1029/2009JB006817 Fischer T., Hainzl S., Eisner L., Shapiro S. A. and Le Calvez J. (2008). Microseismic signatures of hydraulic fracture growth in sedimentformations: Observations and modeling. JGR, 113(B2), doi:10.1029/2007JB005070 Parotidis M., Shapiro S.A. and Rothert E. (2005). Evidence for triggering of the Vogtland swarms 2000 by pore pressure diffusion. JGR, 110(B5), doi: 10.1029/2004JB003267 Shapiro S. A., Dinske C. and Rothert, E. (2006). Hydraulic-fracturing controlled dynamics of microseismic clouds. GRL, 33(114), doi: 10.1029/2006GL026365 Shapiro S.A., Huenges E. and Borm G (1997). Estimating the crust permeability from fluid- injection-induced seismic emission at the KTB site. GJI, 131(2). Shapiro S.A., Audigane P. and Royer J.J. (1999). Large-scale in situ permeability tensor of rocks from induced microseismicity. GJI, 137(1), 207-213, doi: 10.1046/j.1365- 246x.1999.00781.x List of references used: Calo, M., Dorbath, C., Cornet, F. H. and Cuenot, N. (2011).Large-scale aseismic motion identified through 4-D P-wave tomography, GJI, 186 (3), 1295-1314. doi: 10.1111/j.1365-246X.2011.05108.x Dahm T., Hainzl S. and Fischer T. (2010). Bidirectional and unidirectional fracture growth during hydrofracturing:Role of driving stress gradients, JGR, 115, doi:10.1029/2009JB006817 Fischer T., Hainzl, S., Eisner, L., Shapiro, S. A., Le Calvez, J. (2008) Microseismic signatures of hydraulic fracture growth in sedimentformations: Observations and modeling. JGR, 113(B2), doi:10.1029/2007JB005070 Parotidis, M and Shapiro, SA and Rothert, E (2005). Evidence for triggering of the Vogtland swarms 2000 by pore pressure diffusion. 110 (B5), doi: 10.1029/2004JB003267 Shapiro, S. A. and Dinske, C. and Rothert, E. (2006) List of references used: Calo, M., Dorbath, C., Cornet, F. H. and Cuenot, N. (2011).Large-scale aseismic motion identified through 4-D P-wave tomography, GJI, 186 (3), 1295-1314. doi: 10.1111/j.1365-246X.2011.05108.x Dahm T., Hainzl S. and Fischer T. (2010). Bidirectional and unidirectional fracture growth during hydrofracturing:Role of driving stress gradients, JGR, 115, doi:10.1029/2009JB006817 Fischer T., Hainzl, S., Eisner, L., Shapiro, S. A., Le Calvez, J. (2008) Microseismic signatures of hydraulic fracture growth in sedimentformations: Observations and modeling. JGR, 113(B2), doi:10.1029/2007JB005070 Parotidis, M and Shapiro, SA and Rothert, E (2005). Evidence for triggering of the Vogtland swarms 2000 by pore pressure diffusion. 110 (B5), doi: 10.1029/2004JB003267 Shapiro, S. A. and Dinske, C. and Rothert, E. (2006)