## Strike-slip (no gravity)

*January 28, 2008*

### Benchmark Description

Benchmark problem description. Formerly known as benchmark 4b.

### 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

#### PROBLEM GEOMETRY

- 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

- Top layer: -12 km ≤ z ≤ 0 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.

## Input Files

### PyLith-0.8 Input

Input files for PyLith-0.8.

- bmssnog_tet4_1000m.tgz

Tarball containing PyLith-0.8 input files for benchmark using linear tetrahedral elements with a 1000 m nominal node spacing.

- bmssnog_tet4_0500m.tgz

Tarball containing PyLith-0.8 input files for benchmark using linear tetrahedral elements with a 500m nominal node spacing.

- bmssnog_tet4_0250m.tgz

Tarball containing PyLith-0.8 input files for benchmark using linear tetrahedral elements with a 250m nominal node spacing.

### GeoFEST Input

Input files for GeoFEST.

- GeoFEST Linear Tet 1km resolution dt=0.1yr
- GeoFEST Linear Tet 500m resolution dt=0.1yr
- GeoFEST Linear Tet 250m resolution input file
- GeoFEST/PYRAMID 1km

PYRAMID input file for parallel 1km run.

- GeoFEST/PYRAMID 500m

PYRAMID input file for parallel GeoFEST run.

- GeoFEST/PYRAMID 250m

PYRAMID input file for parallel GeoFEST run.

- GeoFEST Linear Tet 500m dt=0.1yr NEW

The taper problem has been fixed.

- GeoFEST Linear Tet 250m dt=0.1yr NEW

The taper problem has been fixed.

## Results

Results from benchmark runs. Place tarballs containing the requested results in this folder and describe the run in the description field.

- PyLith, 1 Proc, Linear Tet, 1 km Resolution, dt=0.1yr

PyLith results run on 1 processor of a Power Mac G5. Linear tetrahedral mesh at 1 km resolution. Constant time step size of 0.1 year.

- PyLith, 1 Proc, Linear Hex, 1 km Resolution, dt=0.1yr

PyLith results run on 1 processor of a Power Mac G5. Linear hexahedral mesh at 1 km resolution. Constant time step size of 0.1 year.

- PyLith, 1 Proc, Linear Tet, 500 m Resolution, dt=0.1yr

PyLith results run on 1 processor of a Power Mac G5. Linear tetrahedral mesh at 500 m resolution. Constant time step size of 0.1 year.

- PyLith Revised Results, 500m, New BC and Split Node Input

New solution using revised BC and split node inputs. The revised BC take care of the problems of defining BC on the fault plane (or in some cases the projected fault plane). The new split node inputs no longer assume a bilinear slip distribution in the region where the fault tapers overlap, and now assumes a taper consistent with what is used for the analytical solution.

- PyLith Revised Results, 500m, Altered BC for Viscoelastic Solution

New version where BC have been altered from those of previous version to make viscoelastic results consistent with those from GeoFEST. The revised BC do not pin y-component on the y=0 plane, and no BC are applied along the intersection of the fault plane (or its projection) along y=0 and z=-24.

- PyLith, 1 Proc, Linear Tet, 250 m Resolution, dt=0.1yr

PyLith results run on 1 processor of an Opteron 2.4GHz Linux machine. Linear tetrahedral mesh at 250 m resolution. Constant time step size of 0.1 year.

- GeoFEST/PYRAMID 1km

Parallel results using 64 processors of Intel/Linux Cluster with GeoFEST-4.5 and Pyramid-2.1.3

- GeoFEST/PYRAMID 500m

Parallel results using 64 processors of Intel/Linux Cluster with GeoFEST-4.5 and Pyramid-2.1.3

- GeoFEST/PYRAMID 250m

Parallel results using 128 processors of Intel/Linux Cluster with GeoFEST-4.5 and Pyramid-2.1.3

- GeoFEST Linear Tet 1km resolution dt=0.1yr (updated)

The taper error has been fixed.

- GeoFEST Linear-Tet 500m Re-Run
- GeoFEST Linear-Tet 250m Re-Run
- Femlab 1 km resolution, t = 0 years

This model has ~162000 linear tetrahedral elements and is twice the size in y of the model description, since there is no symmetric boundary. This yields a resolution close to 1 km. The model and solver require about 800 MB and is solved in about 3 minutes on a 1.8 GHz AMD Opteron. An iterative solver was used, which uses the Incomplete LU preconditioner with a drop tolerance of 0.01. Decreasing this value has very little effect on the error but takes longer to solve.

- Femlab 1 km resolution, t = 1 year

Viscoelastic problem requires ~3.5GB and takes about 4.5 hrs to run. Drop tolerance is 0.01.

- Femlab 1 km resolution, t = 5 years

Viscoelastic problem requires ~3.5GB and takes about 4.5 hrs to run. Drop tolerance is 0.01.

- Femlab 1 km resolution, t = 10 years

Viscoelastic problem requires ~3.5GB and takes about 4.5 hrs to run. Drop tolerance is 0.01.

## Plots of Strike-Slip No Gravity Benchmark Results

Plots of global and local errors for strike-slip no gravity benchmark.

### Displacement Field

PyLith soln

GeoFEST soln

### Global Error

Plot of global error

### Local Error

#### ELASTIC SOLUTION: CODE VERSUS ANALYTIC

**250M RESOLUTION**

PyLith error

GeoFEST error

**500M RESOLUTION**

PyLith error

GeoFEST error

#### VISCOELASTIC SOLUTION: PYLITH VERSUS GEOFEST

**250M RESOLUTION**

t0yr

**500M RESOLUTION**

t0yr

t1yr

t5yr

t10yr