Over the years, I have maintained a steady obsession with fault scarps. For my Ph.D., I worked on a few aspects of fault-scarp development: Arrowsmith, J R., Pollard, D. D., and Rhodes, D. D., Hillslope development in areas of active tectonics, *Journal of Geophysical Research*, *101*, B3, 6,255--6,275, 1996. Correction: *Journal of Geophysical Research*, *104*, B1, 805, 1999. Since then, I have kept the work going along, mostly with teaching applications. In this blog post, I wanted to share some of the presentations and tools that are available to explore, learn about, perform one dimensional morphological modeling of transport and production-limited fault scarps.

** A few definitions**:

- One dimensional--means elevation (
*H*) as a function of distance along a profile (*x*).
- Transport-limited--there is enough transportable material available for any erosion that comes from the application of the mass continuity equation. In this case, the transport capacity is equal to the sediment supply.
- Production-limited--there is insufficient transportable material (regolith=material between topographic surface and top of bedrock) for erosion. In this case, the transport capacity exceeds the sediment supply locally.
- Diffusion erosion--transport capacity is scaled by local slope and a constant k. The consequence of this transport rate choice and the application of continuity for transport-limited conditions yields a diffusion-like or heat-conduction-like behavior.

This presentation (PPT and PDF) provides a bit of a review of fault scarp research as I saw it mostly about 5-10 years ago. This PPT has two embedded movies which illustrate this basic behavior: PPT. Transport-limited scarp movie; Production-limited scarp movie

**Transport-limited models**:

This web page from my

Computers in Earth and Space Exploration class lays out the main derivation and numerical implementation:

Lecture 8: Exploring diffusion using Excel. This older page has some Matlab and Excel implementations of 1D transport-limited linear diffusion:

Scarp diffusion exercise. Finally, here is a 2D version of transport-limited non-linear diffusion in a paper by Mattia de Michieli Vitturi and me: de Michieli Vitturi, M. and Arrowsmith, J R., Two dimensional nonlinear diffusive numerical simulation of geomorphic modifications to cinder cones,

*Earth Surface Processes and Landforms*, doi:10.1002/esp.3423, 2013.

**Production-limited models**:

George Hilley significantly updated my original code and produced the Penck1D imlpementation in MATLAB:

zip file. Here is an older version of the MATLAB (no gui):

zip file.

The software is delicate in some ways so you may have to try it a few times! If it crashes, just start over. One important thing is that it works best if downhill is to the right.

Note in particular the

user's manual we wrote in 2006: Hilley, G. E., and Arrowsmith, J R.,

*Penck1d: Transport- and production-limited fault scarp simulation software*, 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 Bürgmann.