## Reverse Slip (no gravity)

### Benchmark Description

*January 25, 2007*

Benchmark problem description. Formerly known as benchmark 5b.

### Summary

Viscoelastic (Maxwell) relaxation of stresses from a single, finite, reverse-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. Symmetry 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

- Maxwell linear viscoelasticity
- Top layer: η = 1.0e+25 Pa-s (essentially elastic)
- Bottom layer: η = 1.0e+18 Pa-s

#### FAULT SPECIFICATIONS

- Type
- 45 degree dipping reverse fault.
- Location
- Strike parallel to y-direction with top edge at x = 4 km and bottom edge at x = 20 km. 0 km ≤ y ≤ 16 km; -16 km ≤ z ≤ 0 km
- Slip distribution
- 1 m of uniform thrust 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 set to analytic solution. (Note: the side at y = 0 km has zero y- displacements because of symmetry.) Top of the model is a free surface.

#### 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
- v 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

- Temporary holding pen for files from Charles (DO NOT USE)
- Temporary holding pen for some files from Charles. This folder will be deleted in the very near future!
- bmrsnog_hex8_1000m.tgz
- Tarball containing PyLith-0.8 input files for benchmark using linear hexahedral elements with a 1000m nominal node spacing.
- bmrsnog_tet4_1000m.tg
- Tarball containing PyLith-0.8 input files for benchmark using linear tetrahedral elements with a 1000m nominal node spacing.
- bmrsnog_tet4_0500m.tgz
- Tarball containing PyLith-0.8 input files for benchmark using linear tetrahedral elements with a 500m nominal node spacing.
- bmrsnog_tet4_0250m.tgz
- Tarball containing PyLith-0.8 input files for benchmark using linear tetrahedral elements with a 250m nominal node spacing.
- reverse slip (no grav), refined grid 01, no smoothing
- Carl Gable’s mesh, see http://meshing.lanl.gov/proj/crustal_dyn_reverse_fault_bm/catalog.html
- reverse slip (no grav), refined grid 02, no smoothing
- Carl Gable’s mesh #2, see http://meshing.lanl.gov/proj/crustal_dyn_reverse_fault_bm/catalog.html

### GeoFEST Input

Input files for GeoFEST.

- bmrsnog_tet4_1000m.gft.gz
- Gzipped GeoFEST input file for benchmark using linear tetrahedral elements with a 1000 m nominal node spacing.
- bmrsnog_tet4_0500m.gft.gz
- Gzipped GeoFEST input file for benchmark using linear tetrahedral elements with a 500 m nominal node spacing.
- reverse slip (no grav), refined grid 01, no smoothing (GeoFEST 4.5)
- Carl Gable’s mesh, see http://meshing.lanl.gov/proj/crustal_dyn_reverse_fault_bm/catalog.html
- reverse slip (no grav), refined grid 02, no smoothing (Geofest 4.5)
- Carl Gable’s variable resolution mesh #02, see http://meshing.lanl.gov/proj/crustal_dyn_reverse_fault_bm/catalog.html

## Results

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

- GeoFEST reverse fault results – 1 km
- Tarball contains input and output files as well as text file containing run time information.
- GeoFEST reverse fault results – 500 m
- Tarball contains input and output files as well as text file containing run time information.
- Geofest_reverse_slip_var_res_mesh_01_soln
- fixed the BCs, Geofest 4.5, dt=0.1 constant
- 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, 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 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, 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.
- tet_var_res_01_pylith_soln.tgz
- PyLith-0.8 results for Carl Gable’s variable resolution (no smoothing) mesh 01 for the reverse slip benchmark – constant dt=0.1 yr.
- Femlab 2 km resolution, elastic
- This model has 19544 quadratic 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 2 km. The model and solver require about 800 MB and is solved in about 10 minutes on a 1.8 GHz AMD Opteron.
- 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.
- 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 Reverse-Slip No Gravity Benchmark Results

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

### Displacement Field

PyLith soln

GeoFEST soln

### Global Error

Plot of global error

### Local Error

#### zELASTIC SOLUTION: CODE VERSUS ANALYTIC

**1000M RESOLUTION**

PyLith error

GeoFEST error

COMSOL error

**500M RESOLUTION**

PyLith error

GeoFEST error

**VISCOELASTIC SOLUTION: PYLITH VERSUS GEOFEST**

t0yr

t1yr

t5yr