Chapter 3 

CONCEPTS, DIMENSIONS AND SIGN CONVENTIONS

 

This chapter briefly explains the things you must understand to use the software correctly and to avoid meaningless output.

 

3.1   The crucial concept of source and receiver faults

Source faults have slip, and so they impart stress to the surrounding crust and faults. Receiver faults have no slip (slip=0.0 m in the input files). Source and receiver faults otherwise look identical in the input files. The stress imparted by source faults are resolved on the receiver faults through the command Functions > Stress > Calc. stress on faults. Further options for resolving the stress on the receiver fault are controlled by the Stress on faults control panel, which automatically appears.

 

3.2   Calculation procedure

1.     Launch Matlab; set the Matlab path to working directory ÒCoulomb 3.1 folderÓ.

2.     Type ÒcoulombÓ in Matlab Command Window.

3.     In Coulomb 3.1 window menu bar, choose Input> Open existing input file.

4.     In Coulomb 3.1 window menu bar, choose Functions > Grid, Displacements, Strain, or Stress. Many of these selections trigger requests for additional input, and let you modify the parameters in temporary windows. When you click ÒCalc. & viewÓ, calculations are performed and a new image is displayed.

5.     You can perform many operations to the image on the Coulomb 3.1 window, including Zoom In, Zoom Out, Pan, Rotate 3D, Data Cursor, Insert Color Bar, Insert Color Legend, etc. You can choose these operations either by clicking the lower menu in the Coulomb 3.1 window or the Tools pull down menu bar. While the graphic plot is open, you save this plot.

6.     To print a plot, save it as a pdf, and then print the small vector file from Acrobat Reader or an illustration program. Currently, the File > Print cmd in Matlab does not work properly.

7.     After you have finished all calculations, quit MATLAB. 

 

3.3   To change parameters interactively

Most of the settings and parameters can be changed either by modifying an input file using a text editor, or by changing them interactively within Coulomb. Choose Functions > Change parameters. Parameters changed within the software interactively are transient and will not permanently modify the input file. Every time you select Input > Save input file, all current selections will be saved in an input file. Change the name of the file if you do not want it overwritten.

 

3.4   To save, print, or modify a plot

Choose File > Save AsÉ We recommend you choose pdf, a compact vector format. Rename the file from the default Ômain_menu_window.figÕ or it will overwrite an important file. You then print the pdf from Acrobat Reader, or from an illustration program if you would like to spruce it up. Currently, the File > Print command in Matlab does not work properly.

 

 

3.5   Coordinates, units, and sign conventions

Coulomb 3.1 calculates in the (x, y, z) Cartesian coordinate system. When the lat/lon of the corner grid points are specified in the input file, it can also plot in lat/lon. In the map view projection on the monitor, x is positive from left to right, y is positive from bottom to top, z is positive upwards for displacement. DEPTH is positive downwards from the EarthÕs surface. We use the standard Aki & Richards (1980, 2002) sign conventions for fault geometry and slip. The units for the input parameters are the following (see Chapters on Input and Output files for more detail):

 

Input parameters and their dimensions (think bars and meters)

 

PR1                PoissonÕs ratio: [dimensionless, -1 to 0.5]; 0.25 is typically used, and 0.5 is an imcompressible volume, such as can be used to make balanced cross-sections.

E1                    YoungÕs modulus: [bars]; 8x105 bars is typically used

FRIC             Friction coefficient: [dimensionless; roughly 0-1]; 0.4 is often used; 0.65 is for dry ByerleeÕs law friction, 0.0-1.0 is typically considered the limits for the crust.

Sym               Obsolete legacy from Coulomb 1.0; ignore it

 

Directions, angle, and dip: [degrees; dip must be positive]

Grid and fault positions (x, y): [km]

Depth: [km] downward is positive

Displacements: [m]

Faults: Right-lateral is positive, and reverse slip is positive [m]

Dikes: Opening displacement is positive [m]

Point Source: Inflation is positive [m3]

Regional stress tensor, S1, S2, S3: positive in compression [bars]

 

Output parameters and their dimensions

 

Displacement: [m] North, East, and Up are positive

Shear Strain: [dimensionless] Right-lateral is positive

Principal Strain: [dimensionless] Extension is positive (tensor notation)

Dilatational Strain: [dimensionless] Dilatation is positive

Stress: [bars] Right-lateral and unclamping are positive

 

 

 

Shear modulus, G.  YoungÕs modulus [E] and PoissonÕs Ratio [PR] are specified in the input file. G = E/[2(1+PR)]. So the shear modulus for PR=0.25 and E=8x105 bars, G=3.2x105 bars or 3.2x1011 dyne-cm.