Multiphysics and multiscale earthqauke modeling

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1 Multiphysics and multiscale earthqauke modeling C. Meng B. Hager ERL, MIT May 29, 2017

2 Multiphysics Poro(visco-)elasticity, (quasi-)static and dynamic processes. ground overburden reservoir producer reservoir underburden Static equation apple KU = F, apple Ke H where K = H T, F = tk c + S p Dynamic equation Mü + C u + K e u = f. f Q tk c p.

3 Multi(temporal-)scale Implicitly solving the (quasi-)static equation, although expensive, one can take long time step hours, days... U = K 1 F Explicitly solving the dynamic equation, although cheap, one has to take short time step (CFL condition). u n = M 1 t 2 (f n Ku n 1 ) tc (u n 1 u n 2 ) +2u n 1 u n 2

Multi(spatial-)scale ground or ocean bottom FD FE absorbing PML High order explicit FE methods (SEM, DG) suffer strict CFL condition, and do not solve

4 Multi(spatial-)scale ground or ocean bottom FD FE absorbing PML High order explicit FE methods (SEM, DG) suffer strict CFL condition, and do not solve (quasi-)static equations. Linear FE can solve both the static and dynamic equations, but suffers strict CFL condition, i.e. expensive for field scale ground motions.

5 Why a new code? this Pylith SPECFEM Seissol Comsol method FE-FD FE SEM DG FE static X X X dynamic X X X X X hybrid X? poroelastic X? X multiscale X open X X X X

6 Pore pressure stabilization Smith and Griffiths (1982) provide the FE formulation for poroelasticity. Bochev and Dohrmann (2006) provide a pore pressure stabilization method. For Maxwell power law viscoelasticity, the deformation has affect on both the stiffness matrix K and the RHS function F, Melosh and Raefsky (1980).

7 Fault constrain equations 2 3 nx nz 0 nx nz 0 4 t x t z 0 t x t z u (1) x u (1) z p (1) u (3) x u (3) z p (3) 3 = I, 7 5 apple T K G G 0 apple U n n apple = f n I n. is a fault stress proxy. Constraint I can be solved for dynamic rupture. Bartolomeo et al. (2010) provide an explicit routine to model the fault constraint in 2D. Defmod (Meng 2016) has made the method for 3D and general constitutive laws.

8 Implicit explicit hybrid solver

9 Introduction Proe(visco-)lasticity Fault Hybridization Model examples FE-FD direct binding... j vi,j = P3 i... k =1 N(x(i, j), k )ve,k Discussion Backups

10 Splay fault rupture

11 Introduction Proe(visco-)lasticity Fault Dipping and curved fault height height height height reservoir depletion induced rupture, curved fault. Hybridization Model examples Discussion Backups

12 Summary This work has resulted a multipysics and multiscale earthquake simulation tool, defmod-swpc. Temporally, it covers both the (quasi-)static and dynamic processes. Spatially, it covers both the near source/fault motions and far field ground motions.

13 Heterogeneous fault rupture v [m/s] Defmod EqSim Rot en 1.0 t [s] Defmod EqSim Rot en v [m/s] Defmod 0.3 EqSim Rot en t [s] z [km] v [m/s] Defmod EqSim 0.3 Rot en 0.5 t [s] y [km] SCEC205 z km y 3 4 x 3km v [m/s] Defmod EqSim Rot en t [s]

14 Dipping fault rupture SCEC10 z 1 12km 3 3km 2 y 4 x

251 679 560 45 rank 0 rank 3 3 0 458 1022 0 4 0 0 0 0 5 107 45 315

15 FE-FD parallel connection FD partitions rank 1 rank 2 fault grid points held by FE/FD ranks FD FE rank 0 rank rank 0 rank 1 rank 2 FE partitions rank 3 rank 4 fault z x y rank 5

16 FE-FD verification SCEC 205, pure FD by Cui et al. (2010)

17 FE-FD verification SCEC 10, pure FD by Andrews (1999)

Defmod, an earthquake simulator that adaptively switches between quasi-static and dynamic states

Defmod, an earthquake simulator that adaptively switches between quasi-static and dynamic states C. Meng (cmeng@mit.edu) B. Hager ERL, MIT May 16, 2016 Reservoir production/injection induced seismicity