Mapping landforms with applications to geomorphology and earthquake geology EXERCISE

I wanted to share a project I have developed on and off for about 10 years. It is a classroom exercise for Mapping landforms with applications to geomorphology and earthquake geology. So far, it has an example for strike-slip faults (Wallace Creek along the San Andreas Fault), and blind thrust faults (Wheeler Ridge in Southern California). I have an intention to add a normal fault example but have not finished it yet.

The basic idea is that the exercises could be done "analog"--that is on paper in a classroom. They emphasize some simple morphologic and geomorphic mapping (but on high resolution topography base maps from lidar data collected by NCALM and available for download from OpenTopography), and then provide landform ages so that students can calculate slip rate or surface uplift rates. I am not sure they are so well explained so any feed back is welcome.

Exercise material:

• 2016 Mapping landforms with applications to geomorphology and earthquake geology EXERCISE pdf
• Supplemental material (for instructors)
• Wallace Creek--uses B4 lidar data
• Papers:
  
  • Wallace, R. E. (1968). Notes on stream channels offset by the San Andreas fault, southern Coast Ranges, California. In Conference on Geologic Problems of the San Andreas Fault System. Stanford University Publication in Geological Sciences (Vol. 11, pp. 6-21).
  • Sieh, K. E., & Jahns, R. H. (1984). Holocene activity of the San Andreas Fault at Wallace Creek, California. Geological Society of America Bulletin, 95, 883–896.
  • Sieh, K. E., & Wallace, R. E. (1987). The San Andreas Fault at Wallace Creek, San Luis Obispo County, California. In Geological Society of America Centennial Field Guide -- Cordilleran Section (pp. 233–238).
• Demonstrative presentation (ppt) and (pdf) and video flyover
• Pictures of the board from demonstration at U. Potsdam, 2019.
• Wheeler Ridge--uses NCALM student seed grant lidar data
• Papers:
  • Medwedeff, D. A. (1992). Geometry and kinematics of an active, laterally propagating wedge thrust, Wheeler Ridge, California. In S. Mitra & G. W. Fisher (Eds.), Structural Geology of Fold and Thrust Belts (pp. 3–28). Baltimore: Johns HOpkins University Press.
  • Mueller and Talling, Journal of Structural Geology, 1997.
  • Keller, E. A., Zepeda, R. L., Rockwell, T. K., Ku, T. L., Dinklage, W. S., Barbara, S., & Street, G. (1998). Active tectonics at Wheeler Ridge , southern San Joaquin Valley , California. Geological Society of America Bulletin, 110(3), 298–310.
  • Kleber, E. J. (2015) Surface Response to Slip Along a Propagating Blind Thrust Fault Wheeler Ridge, California. M.S. thesis: Arizona State University, 95 pp.
• Demonstrative presentation (ppt) and (pdf)

DEM grid size specification and learning a bit of TopoToolbox

I have been wanting to learn TopoToolbox for a while, and last week I had a chance to get started. Spending time at the Universität Potsdam, Institut für Erd- und Umweltwissenschaften, I have met with Wolfgang Schwanghart and Dirk Scherler occasionally. They are coauthors of TopoToolbox.

My ASU colleagues Adam Forte and Kelin Whipple have been using TopoToolbox increasingly over the last few years. Recently Kelin had a question as to why some DEMs grids were causing an error in TopoToolbox and why some were not. I dug into it and here is what I found. Projected DEMs should have EXACTLY the same x and y cell sizes and expressed in precise values (nearest meter or 10th or 100th of a meter).

DEMs (such as SRTM 30 meter) can be downloaded as geotiff formats and with geographic coordinate systems from sources such as OpenTopography: select Global Data tab.

For example, I have chosen a piece of data from Java along the Cimandiri fault (see Marliyani, et al., 2016 for example).

To be useful for most geomorphic analyses, the data should be projected to UTM so that the horizontal and vertical units are the same. Often, the projection is done in ArcGIS. And, usually it seems fine to let Arc determine the cell size automatically.

Notice how ArcGIS decided that the resolution for the cells should be: 30.8462728281739.

Here I set the cell size to exactly 30 m

Turning to TopoToolbox, as we compute drainage network properties, including contributing area, there is a check that the cell sizes are the same (inside the GRIDobj.m function):

if abs(abs(dx)-abs(dy))>1e-9;
    error('TopoToolbox:GRIDobj',...
    'The resolution in x- and y-direction must be the same');
    end

The 1e-9 is a somewhat arbitrarily small number which one would think would not cause a problem.

I looked into this problem tracking along with the TopoToolbox processing and some of the MATLAB built in tools.

1. Read the geotiff using MATLAB's geotiffread:

   [demdata, R] = geotiffread(filename);
   geotiffreaddifference = R.CellExtentInWorldX-R.CellExtentInWorldY;
   

   The R object has a number of values including the cell size of the geotiff:
   

   R.CellExtentInWorldX= 30.79776426908749800
   R.CellExtentInWorldY= 30.79776426908791000
   R.CellExtentInWorldX-R.CellExtentInWorldY= -4.12115e-13
   

2. Read the geotiff into the DEM object in TopoToolbox and do a similar check as above (refmat is similar to R):
   

   DEM = GRIDobj(filename);
   refmatdifference = abs(DEM.refmat(2,1))-abs(DEM.refmat(1,2));
   

   Again we see the same very small grid size difference:
   

   abs(DEM.refmat(2,1))-abs(DEM.refmat(1,2))= -4.12115e-13
   

3. The problem comes in a calculation that builds out the x and y vectors that includes a cumulative multiplication from the grid sizes inside a TopoToolbox function refmat2XY:
   

   nrrows = siz(1);
   nrcols = siz(2);
   
   x = [ones(nrcols,1) (1:nrcols)' ones(nrcols,1)]*R;
   x = x(:,1)';
   
   y = [(1:nrrows)' ones(nrrows,2)]*R;
   y = y(:,2);
   

   R is the refmat object. But, here we get the error:
   

   dx=x(1)-x(2)= -30.79776426916942000
   dy=y(1)-y(2)= 30.79776426777243600
   abs(dx)-abs(dy)= 1.39698e-09
   

   Which then would fail the GRIDobj test.
If I run the same set of checks on the file I projected with exactly 30 m grid cell size (recall above), I don't get the problem:


geotiffread:
R.CellExtentInWorldX= 30.00000000000000000
R.CellExtentInWorldY= 30.00000000000000000
R.CellExtentInWorldX-R.CellExtentInWorldY= 0
refmat difference as produced from GRIDobj:
abs(DEM.refmat(2,1))-abs(DEM.refmat(1,2))= 0
Difference after GRIDobj2mat:
dx=x(1)-x(2)= -30.00000000000000000
dy=y(1)-y(2)= 30.00000000000000000
abs(dx)-abs(dy)= 0

I think what is happening is a bit of roundoff error (see this link for detailed discussion: What Every Computer Scientist Should Know About Floating-Point Arithmetic, by David Goldberg): "Therefore the result of a floating-point calculation must often be rounded in order to fit back into its finite representation." MATLAB does all of its calculations by default in double precision, so we should have access to 16 decimal digits (e.g., https://en.wikipedia.org/wiki/IEEE_754-1985). So, why we loose precision up to 10^-9 at times is a little surprising to me, but it can obviously happen.

Thus there are a couple of workarounds:

1. Comment out the dx and dy check in GRIDobj:

   %if abs(abs(dx)-abs(dy))>1e-9;
   %    error('TopoToolbox:GRIDobj',...
   %    'The resolution in x- and y-direction must be the same');
   %    end
   

   Or make the threshold larger.
2. Explicitly set the grid resolution to a round number when projecting in ArcGIS or other software.
3. Use the reproject2utm.m command to project dems before using other TopoToolbox operations. It sets the resolution to be exactly the same for x and y

Here is a script to run these calculations: DEM_cell_size_Script.m

Thanks to Chris Crosby, Benjamin Gross, Wolfgang Schwanghart, Kelin Whipple, and Mike Zoldak for discussions.

Field trip in NW Himalaya (Himachal Pradesh)

I just returned from a very interesting and pleasant field trip in Himachal Pradesh (India) to examine the major elements of the frontal portion of the NW Himalaya. The trip was lead by Dr. Rasmus Thiede of the University of Potsdam (UP). This was my third trip to the Himalayas (the first in 2001 to the Sutlej and Spiti Rivers with UP colleagues including Rasmus and Bodo Bookhagen when they were starting their Ph.D.s under the supervision of Professor Manfred Strecker; the second was in 2010 with Dr. Wendy Bohon in the Ladakh region to contribute to her work along the Karakoram Fault in the Pangong Range area). We joined two UP students (Katharina Kretzschmar and Markus Nennewitz) who had been working in the area for two weeks already, focusing on developing a structural profile across the principal faults of the NW Himalaya in the region. I overlapped for a day with Dr. Saptarshi Dey who worked on his Ph.D. with Rasmus in the Kangra reentrant (see Dey, et al., 2016a,b). And, it was a pleasure to meet Professor Vikrant Jain from IIT Gandhinagar and his Ph.D. students. I did not (yet) get their last names but they were Ramindran, Sonam, and Pritha. Tashi Gyatseo is a long-time guide and friend of Rasmus who was chief of logistics for the trip. It was fun to meet everyone and to discuss the geology and geomorphology as well as learn a bit more of eachother's cultures.

Along with strengthening the collaborations among the groups, there were a couple of scientific targets of the trip. They build to a large degree from the Ph.D. work of Saptarshi Dey and focus on:

1. The role of climate modulation of the sediment supply and transport capacity along the major river systems and the development (and removal) of fluvial fills and terraces.
2. The activity of the major faults of the system, including the Himalayan Frontal Thrust and out of sequence faulting (activity higher in the tectonic wedge) possibly influenced by load variation from changes in sediment storage in the orogenic wedge.

So, we looked at a lot of interesting fluvial terraces mostly along the Ravi River system as well as reviewed the major structural elements of the system: HFT, Siwaliks, Main Boundary Thrust (MBT), and the Main Central Thrust (MCT).

Overview figure of the region from Gavillot, et al., 2016. The box shows the location of our trip and the map shown below.

Overview of the field trip with the orange-red line showing most of our tracks and the yellow points my main obversation locations. I am using the GaiaGPS app for my mapping. It seems ok but I might look for a more geologically oriented app for the next trip.

Panorama and annotated overlay showing the major structures and bounded rock units

Pictures

View of the nice mountains (Dhaula Dhar Range) from the Kangra airport--a nice way to start the trip!

Katharina, Markus, and Rasmus with the impressive Dhaula Dhar Range behind as seen from the Kangra area.

Most of the group at a stop along the Main Boundary Thrust where a spring may indicate increased permeability along the fault zone (yellow-white material at left is travertine).

Upper Siwaliks at sunset

Katharina in the MCT mylonites.

Chambo Town--built on an important probably 10 ka terrace. We spent a pleasant cool night there.

Pretty agricultural terraces on a high terrace south of Chamba.

Nice terraces near the Chemera Reservoir.

Stair step terraces in a tributary a few km below the Chemera Reservoir.

Rasmus is a great teacher and it was wonderful to learn from him. Here he is near some fine grained schists discussing their reflection of the overall deformation in the MCT zone.

References cited
Dey, S., Thiede, R., Schildgen, T., Wittmann, H., Bookhagen, B., Scherler, D., and Strecker, M. Holocene internal shortening within northwest Sub-Himalaya: Out-of-sequence faulting of the Jwalamukhi Thrust, India: Tectonics, 2016a.

Dey, S., Thiede, R. C., Schildgen, T. F., Wittmann, H., Bookhagen, B., Scherler, D., … Strecker, M. R. (2016b). Climate-driven sediment aggradation and incision since the late Pleistocene in the NW Himalaya, India. Earth and Planetary Science Letters, 449, 321–331. https://doi.org/10.1016/j.epsl.2016.05.050

Gavillot, Y., Meigs, A., Yule, D., Heermance, R., Rittenour, T., Madugo, C., & Malik, M. (2016). Shortening rate and Holocene surface rupture on the Riasi fault system in the Kashmir Himalaya: Active thrusting within the Northwest Himalayan orogenic wedge. Bulletin of the Geological Society of America, 128(7), 1070–1094. https://doi.org/10.1130/B31281.1