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*January 28, 2008*

Benchmark problem description. Formerly known as benchmark 4b.

Viscoelastic (Maxwell) relaxation of stresses from a single, finite, strike-slip earthquake in 3-D without gravity. Evaluate results with imposed displacement boundary conditions on a cube with sides of length 24 km. The displacements imposed are the analytic elastic solutions. Anti-plane strain boundary conditions are imposed at y = 0, so the solution is equivalent to that for a domain with a 48 km length in the y direction.

- Model size
- 0 km ≤ x ≤ 24 km; 0 km ≤ y ≤ 24 km; -24 ≤ z ≤ 0 km
- Top layer
- -12 km ≤ z ≤ 0 km
- Bottom layer
- -24 km ≤ z ≤ -12 km

- Material properties
- The top layer is nearly elastic whereas the bottom layer is viscoelastic.
- Elastic
- Poisson solid, G = 30 GPa
- Viscoelasticity
- Maxwell linear viscoelasticity
- Top layer
- η = 1.0e+25 Pa-s (essentially elastic)
- Bottom layer
- η = 1.0e+18 Pa-s

- Type
- Vertical right-lateral strike-slip fault.
- Location
- Strike parallel to y-direction at center of model (x = 12km) 0 km ≤ y ≤ 16 km; -16 km ≤ z ≤ 0 km Slip distribution: 1 m of uniform strike slip motion for 0 km ≤ y ≤ 12 km and -12 km ≤ z ≤ 0 km with a linear taper to 0 slip at y = 16 km and z = -16 km.
- Slip distribution
- 1 m of uniform strike slip motion for 0 km ≤ y ≤ 12 km and -12 km ≤ z ≤ 0 km with a linear taper to 0 slip at y = 16 km and z = -16 km. In the region where the two tapers overlap, each slip value is the minimum of the two tapers (so that the taper remains linear).

Bottom and side displacements are set to the elastic analytical solution, and the top of the model is a free surface. There are two exceptions to these applied boundary conditions. The first is on the y=0 plane, where y-displacements are left free to preserve symmetry, and the x- and z-displacements are set to zero. The second is along the line segment between (12, 0, -24) and (12, 24, -24), where the analytical solution blows up in some cases. Along this line segment, all 3 displacement components are left free.

The model should be discretized with nominal spatial resolutions of 1000 m, 500 m, and 250 m. If possible, also run the models with a nominal spatial resolution of 125 m. Optionally, use meshes with variable (optimal) spatial resolution with the same number of nodes as the uniform resolution meshes.

Linear and/or quadratic and tetrahedral and/or hexahedral.

Displacements at all nodes at times of 0, 1, 5, and 10 years as well as the mesh topology (i.e., element connectivity arrays and coordinates of vertices) and basis functions.

- June 30, 2006
- Use ASCII output for now. In the future we will switch to using HDF5 files.

- CPU time
- Wallclock time
- Memory usage
- Compiler and platform info

Okada routines are available to generate an elastic solution. The ‘best’ viscoelastic answer will be derived via mesh refinement. Analytical solutions to the viscoelastic solution are being sought if anyone has information.