Chapter 6

DEFORMATION, GPS DISPLACEMENT AND STRAIN

Here we guide you in calculating deformation caused by an earthquake and display the results graphically.

6.1 To display horizontal displacement vectors

1. Input > Preferences and change Coordinates from Cartesian to Lon. & Lat. Input > Open existing input file > ‘Example-2(LL)-lonlat.inp’. Then, Functions > Displacements > Horizontal displ. (vectors). You will see a dense vector image in the Coulomb 3.1 window. To plot fewer vectors, Functions > Change parameters > Grid size, and change it from 0.06° x 0.04° to 0.12° x 0.08°, and hit OK. Now repeat Functions > Displacements > Horizontal displ. (vectors). After you’ve seen the plot, return the coordinate system to (x, y) by Input > Preferences and change Coordinates from Lon. & Lat. to Cartesian, and click OK.

No reference point Reference point by mouse click

2. To change vector scale and reference frame: In the Displacement control panel, either move the slider (which rescales the vectors on the fly) or type in a number (try 10,000) in the text field (these means the vector scale is 10,000 x the distance scale). Then click on Fixed point, hit the Mouse click button and click on a point to the SE of the fault, and hit “Calc. & view.” You should now see a plot like that above right, with the reference point indicated by a red circle.

3. Numerical output files are created every time you make a run. Every time when you click “Cal. & View” in the Displacement control panel, a text output file called “Displacement.cou” will be created or updated and saved in a sub-folder called “Output files” within the “Coulomb 3.1 folder”. When you want to save your latest runs, remember to rename the “Displacement.cou” file; otherwise it will be overwritten by your next displacement calculations. Below left is an excerpt of a “Displacement.cou” text output file.

Coordinates Displacements

4. Change sampling depth of calculation: In the Displacement control panel, type your desired value after “Depth”. Most often for displacements, one sets DEPTH to 0.0 to compare the results to geodetic data.

5. Make a displacement cross-section: Choose Input > Open existing input file > Example-2(TH).inp. Next, Functions > Displacements > Horizontal displ (vectors). In the Displacement control panel, choose “Cross section”. Change the increments to 2 km by 2 km. This is a reverse fault; the dashed blue line in the plot below is the depth of the vectors in the map view plot. The cross-section line was included in the input file (this optional information is shown above right). You can change the cross-section line interactively in the Cross section control panel. Use the left mouse button to click the start (A) point, and the right mouse button to click the end (B) point, and make sure that the starting point is to the left of the ending point. If you do not have a two-button mouse, use ctrl+click for the right button. To save the changes, choose Input > Save input file as ascii with a new file name.

For displacement plots, the dip of the cross section is always vertical. Within the Cross section window, you can chose items on the menu bars to Zoom In, Zoom Out, Pan, and 3D Rotate.

6.2 To display observed and modelled GPS vectors

1. You can create a GPS file with five columns: lon.°, lat.°, dx, dy, dz (m), in space delimited format. If easier, prepare the file in Excel and then save as ‘Formatted text (space delimited)’. An example of the format is shown below. Also, see ‘gps_example.dat’ in the GPS_data folder.

2. After you have plotted a figure, choose Overlay > GPS stations, and select the file you created. If you did not set ‘Depth’ in the input file to zero, choose Functions > Change Parameters > Calculation depth. If the input file has a source fault, you will see a plot like the one below for the observed and modelled vectors (no error ellipses; the circles mark the stations) and a meter scale bar. Here we saved the file as a pdf and added the legend in Illustrator.

3. To output a numerical file of the observed and modelled displacements, follow the instructions in the command window (reproduced below). The GPS_DATA file can be opened in Excel for further calculations of residuals. The example below uses the input file, Niigata-Chuetsuoki-2007.may and the GPS file ‘Niigata-Chuetsuoki-2007-GPS.dat.

6.3 To display crustal deformation as wireframe images

1. Using Example-2(TH).inp, Choose Functions > Displacements > Horizontal displ. (wireframe). The undistorted grid is in yellow and the distorted grid in blue. For a cross-section, use the default cross-section line, but change the horizontal and depth increments to 2 km in the Cross section control panel to see the images below. These cross-sections conserve area (they are ‘retrodeformable’ in geological jargon) if you set Possion’s ratio to 0.5 by Functions > Change Parameters >All input parameters:

2. The wireframe cross-sections are useful to illustrate deformed strata associated with thrust and normal faults and ramp-thrusts. You can pop them into Illustrator and color the layering so it appears like strata.

6.4 To display the vertical displacement by color gradients and contours

1. Choose Input > Open an existing file ‘Example-2(LL)-latlon.inp’; then Functions > Displacements > Vertical displ. (color & contours). You will see the following left image in the Coulomb 3.1 window.

Tiled Interpolated

2. Data smoothing and color scale options: In the Vertical displ. control panel, you can choose either Mosaic, i.e., un-interpolated data (left image shown above) or Interp., i.e., interpolated (right image shown above). Color saturation: You can adjust color scale by moving the slider bar under “Color saturation” or type the value in the box, hit return, and then click ‘Calc. & View” in the Displacement control panel (below left).

3. Contours: In the Displacement control panel, choose “Contours” and click “Calc. & View”. Contours showing vertical displacements are superimposed on the color image (image above right). You can choose the contour interval.

4. Cross section: Choose “Cross section” in the Displacement control panel. The methods of making cross sections are similar to those described in previous sections.

6.5 To display the vertical displacement as a 3D image drape

1. Choose Functions > Displacements > 3D image drape. The color scale is controlled by the parameter in your input file.

2. To control the amount of vertical exaggeration (the “m” factor in the screen images), choose Functions > Change parameters > Vertical, and you will see a pop-up Vertical exaggeration window, in which you can change vertical exaggeration by entering a new value and then clicking “OK”.

3. In the Coulomb 3.1 window, you can use options of Zoom In, Zoom Out, Pan, 3D Rotate, Insert/Remove ColorBar, and Insert/Remove Legend, as described in previous sections.

6.6 To display the vertical displacement as 3D image wireframed surface

1. Choose Functions > Displacements > 3D image wireframed surface. The color scale is controlled by the parameter in your input file.

2. You can use options of Zoom In, Zoom Out, Pan, 3D Rotate, Insert/Remove ColorBar, and Insert/Remove Legend, as described in previous sections. Now try changing the vertical exaggeration by choosing Functions > Change parameters > Vertical exaggeration > 8000. Then, again choose Functions > Displacements > 3D image wireframed surface. Now change the azimuth to 10° and Elevation to 40° in the Viewpoint window by hitting tab after each number and the screen will redraw:

6.7 To display and output the horizontal and vertical surface deformation in cross-section

Both ‘Horizontal Displ. (vectors)’ and ‘Horizontal displ. (wireframe)’ provide cross-section outputs. These also produce numerical output files of the ground surface deformation components, Ux, Uy, and Uz.

6.8 To display any component of the strain field

1. Choose Functions > Strain. A Strain control panel will appear (below right).

2. In the Strain control panel, choose the type of strain you want to calculate. For example, choose Eyy and you will see the image above right.

3. Numerical output files. Every time you click “Cal. & View” in the Strain control panel, an output file called “dilatation_section.cou” will be created or updated. When you want to save your latest runs, remember to rename the “dilatation_section.cou” file within the “output files” sub-folder; otherwise it will be written over by your future displacement calculations. Here is an example of “dilatation_section.cou” output file:

4. By choosing parameters in the Strain control panel, you have the options to switch between the tiled versus interpolated data grid, change color saturation, and contours, as explained in previous sections.