Simulation of hillslope processes including fault-related displacements and soil production using MATLAB

Purpose: These laboratory exercises are designed to help you gain appreciation for modeling of hillslope processes and for the power of simple tools brought together using computers to model somewhat complicated processes.

Background information for this exercise comes from Lecture12.ppt (44 Mb) and from Lecture13.ppt
Background reading is available from this document: PenckManual2006.pdf (modified from Hilley, G. E., and Arrowsmith, J R., Penck1d: Transport- and production-limited fault scarp simulation soft- ware, user's manual for software used at 2001 Geological Society of America Short-course: Tectonics and Topography: Crustal Deformation, Surficial Processes, and Landforms Cosponsored by GSA Structural Geology and Tectonics Division and taught by Dorothy Merritts and Roland Burgmann.).

Due: at the beginning of class, November 1, 2006.

Modeling to build intuition

Introduction

A former ASU student, George Hilley, and I worked together to take the theory that was presented in Lecture13.ppt and build a MATLAB-based Graphical User Interface to enable students to get a feeling for what the various parameters and process effects are like when you combine diffusion erosion with soil production. We also combined it with a model for simple faulting. Chapter 4 of this document PenckManual2006.pdf explains how to run the software for your reference.

Download this zip file to a directory of interest and unzip it: penck1D_GUI_mod.zip
Launch Matlab and then launch the program by typing:
```
>> penckgui
```
and return.
You will see this screen: I have numbered for you so we can refer to the cells easily. See also the Table 4.1 in the manual (PenckManual2006.pdf) to explain what is there.
In terms of units, it is set up now so that the length scale is in meters and the time scale is in years.
I want to emphasize about the geomorphic rates:
1. Kappa (diffusive transport rate) = 0.004 (m²/yr is the same as 4 m²/kyr as we learned from Hanks, 2000 table; cell 16)
2. Ba is maximum soil production on bare bedrock in m/yr; cell 17.
3. Bb is depth sensitivity for soil production in m^-1; see this figure for a plot of how Bb effects soil production with soil thickness; cell 18.
4. Ba and Bb are the parameters that represent how the bedrock is physically weathered to produce transportable debris.
A couple of important things to remember when running the software:
- Push enter/return after you put a number in a cell so the change will be noted by the program.
- Make sure to close each window or figure that opens before doing the next task. Leave only the main screen up all the time. Otherwise the program will get confused.
- If things are not running right, exit penck1d and start it again.

Exercise tasks

Task 1: Flat profile offset by a continuously slipping normal fault
Set these cell values (if not specified, leave as the default):

Set the profile ages to be calculated as: 10, 1000, 2500, 5000, 7500, 10000 (years; cell 3: "t (output")
Set dx (spacing between nodes) = 0.5 (cell 1)
Set nx (number of nodes) = 201 (gives 200 steps between nodes; cell 2)
Set X₀ (left side of profile) = -50 (cell 4)
Set Fault slip rate = 0.001 (1 mm/yr; cell 14) and set Fault dip = 60 (dips to right; cell 15). Use that along with the defaults of fault length = 5000 m and fault upper tip location at F_x0 = 0 (center of profile) and F_z0 = 0.001 (1 mm below the surface--does not work if this is 0, but it is close enough). It will simulate a fault that is much longer than the profile.
Set the initial topography and bedrock/soil interface:
1. Menu: Initial Conditions->Flat initial topography at z = 0
2. Menu: Initial Conditions->Copy profile to bedrock (makes the soil/bedrock interface the same elevation as the topography)
3. Menu: Initial Conditions->Offset bedrock->-1 (this pushes the soil/bedrock interface to a meter below the topography, thus making a 1 m thick soil to start).
Visualize things to make sure they look ok:
1. Menu: Plot->Initial Conditions
2. Menu: Plot->Fault displacements...
3. Menu: Plot->Fault Geometry and initial conditions...
Set the geomorphic rates:
1. Kappa (diffusive transport rate) = 0.004 (m²/yr is the same as 4 m²/kyr as we learned from Hanks, 2000 table; cell 16)
2. Ba (maximum soil production on bare bedrock) = 8e-005 (m/yr; cell 17)
3. Bb (depth sensitivity for soil production) = 0.1 (m^-1; see this figure for a plot of how Bb effects soil production with soil thickness; cell 18)
Run the transport-limited model (should basically look like your excel modeling from Monday): Menu: Run Transport-limited model. Then, Menu: Plot->Model results. Obviously, the model considered that there was always enough soil to transport.
Run the production-limited model: Menu: Run Production-limited model. Then, Menu: Plot->Model results.
Answer these questions (a couple of sentences to a paragraph each). Print out relevant plots annotated (you do not have to print every model run):
1. What is the difference between the transport-limited and production-limited results?
2. Run production-limited models for these combinations of geomorphic rates (you should not have to redo the initial conditions or the fault parameters):
  - k = 0.004 ba = 8e-005 bb = 0.1
  - k = 0.004 ba = 8e-004 bb = 0.1
  - k = 0.04 ba = 8e-004 bb = 0.1
  - k = 0.04 ba = 8e-004 bb = 1000
  - k = 0.04 ba = 8e-004 bb = 10
  - And any other combinations that might let answer: how does the fault scarp develop and what are the effects of the different geomorphic rates? Under what conditions and when does the bedrock get exposed? What is the form of the bedrock scarp? Is it always sharp or sometimes gentle?

Task 2: Scarp erosion without any continuous fault slip
It is a good idea to exit penck1d and start it again. Set these cell values (if not specified, leave as the default). Many of the cell values are the same as above:

Set the profile ages to be calculated as: 10, 1000, 2500, 5000, 7500, 10000 (years; cell 3: "t (output")
Set dx (spacing between nodes) = 0.5 (cell 1)
Set nx (number of nodes) = 201 (gives 200 steps between nodes; cell 2)
Set X₀ (left side of profile) = -50 (cell 4)
Set Fault slip rate = 0.0000001 (1 mm/yr; cell 14). This will make it effectively 0 slip.
Set the initial topography and bedrock/soil interface. This is what is different from task 1. Follow these instructions carefully and if you have to, quit and start again. In the directory with the software should be a small file called "scarp.xz". It is a list of x, z data that lets us make a little scarp:
```
-50 7
-1 7
1 -15
50 -15
```
1. Menu: File->Import x-z data->choose scarp.xz
2. Menu: Edit->sort and grid import data->profile import data.
3. Menu: Initial conditions->Apply gridded profile data to initial condition (topography)--if you get an error that says something about Interpolation problem, and it gives you the choices to assign elevations of bedrock to topography or vice versa, then you definitely need to quit and start over.
4. Menu: Initial conditions->Copy profile to bedrock
5. Menu: Initial conditions->Offset bedrock (-1)

Set the geomorphic rates:

Kappa (diffusive transport rate) = 0.004 (m²/yr is the same as 4 m²/kyr as we learned from Hanks, 2000 table; cell 16)
Ba (maximum soil production on bare bedrock) = 8e-005 (m/yr; cell 17)
Bb (depth sensitivity for soil production) = 0.1 (m^-1; see this figure for a plot of how Bb effects soil production with soil thickness; cell 18)

Run the transport-limited model (should basically look like your excel modeling from Monday): Menu: Run Transport-limited model. Then, Menu: Plot->Model results. Obviously, the model considered that there was always enough soil to transport.

Run the production-limited model: Menu: Run Production-limited model. Then, Menu: Plot->Model results.

Answer these questions (a couple of sentences to a paragraph each). Print out relevant plots annotated (you do not have to print every model run):

What is the difference between the transport-limited and production-limited results?
Run production-limited models for these combinations of geomorphic rates (you should not have to redo the initial conditions or the fault parameters):
- k = 0.004 ba = 8e-005 bb = 0.1
- k = 0.004 ba = 8e-004 bb = 0.1
- k = 0.04 ba = 8e-004 bb = 0.1
- k = 0.04 ba = 8e-004 bb = 1000
- k = 0.04 ba = 8e-004 bb = 10
- And any other combinations that might let answer: how does the scarp develop and what are the effects of the different geomorphic rates? Under what conditions and when does the bedrock get exposed? What is the form of the bedrock scarp? Is it always sharp or sometimes gentle?

GLG362/598 Geomorphology

Last modified: November 1, 2006