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A finite difference method for earthquake sequences in poroelastic solids

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Abstract

Induced seismicity (earthquakes caused by injection or extraction of fluids in Earth’s subsurface) is a major, new hazard in the USA, the Netherlands, and other countries, with vast economic consequences if not properly managed. Addressing this problem requires development of predictive simulations of how fluid-saturated solids containing frictional faults respond to fluid injection/extraction. Here, we present a finite difference method for 2D linear poroelasticity with rate-and-state friction faults, accounting for spatially variable properties. Semi-discrete stability and accuracy are proven using the summation-by-parts, simultaneous-approximation-term (SBP-SAT) framework for discretization and boundary condition enforcement. Convergence rates are verified using the method of manufactured solutions and comparison to the analytical solution to Mandel’s problem. The method is then applied to study fault slip triggered by fluid injection and diffusion through high-permeability fault damage zones. We demonstrate that in response to the same, gradual forcing, fault slip can occur in either an unstable manner, as short-duration earthquakes that radiate seismic waves, or as stable, aseismic, slow slip that accumulates over much longer time scales. Finally, we use these simulation results to discuss the role of frictional and elastic properties in determining the stability and nature of slip.

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Acknowledgements

Discussions with Ossian O’Reilly on numerical methods and assistance from Kali Allison on the PETSc implementation are gratefully acknowledged.

Funding

This work was supported by the Stanford Consortium for Induced and Triggered Seismicity and by a scholarship to K.T. and V.S. from the Anna Whitlocks minnesfond.

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Authors and Affiliations

  1. Department of Information Technology, Uppsala University, Uppsala, Sweden

    Kim Torberntsson, Vidar Stiernström & Ken Mattsson

  2. Department of Geophysics, Stanford University, Stanford, CA, USA

    Kim Torberntsson, Vidar Stiernström & Eric M. Dunham

  3. Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA

    Eric M. Dunham

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  1. Kim Torberntsson
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  2. Vidar Stiernström
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  4. Eric M. Dunham
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Correspondence to Eric M. Dunham.

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Torberntsson, K., Stiernström, V., Mattsson, K. et al. A finite difference method for earthquake sequences in poroelastic solids. Comput Geosci 22, 1351–1370 (2018). https://doi.org/10.1007/s10596-018-9757-1

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  • DOI: https://doi.org/10.1007/s10596-018-9757-1

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