Benchmark Description

Summary

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.

Problem Specification

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

Fault specifications

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).

Boundary conditions

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.

Discretization

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.

Element types

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

Requested Output

Solution

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.

Performance

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

"Truth"

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.