INTRODUCTION

 

1.1   Why Coulomb? The rationale and philosophy of this program

 

Coulomb is intended both for publication-directed research and for college and graduate school classroom instruction. It is designed to let one calculate static displacements, strains, and stresses caused by fault slip, magmatic intrusion or dike expansion/contraction. The displacements, strains, and stresses can be on calculated at any surface at any depth. 

 

There is now abundant evidence to support the hypothesis that faults interact by the transfer of stress; this is evident on the short time scales of earthquake sequences and aftershocks, and on longer time scales associated with the inter-event time of the largest shocks that occur in a given region. Key review papers include: Harris, R.A. (1998), Introduction to special section: Stress triggers, stress shadows, and implications for seismic hazard, J. Geophys. Res., 103, 24,347–24,358; Stein, R.S. (1999), The role of stress transfer in earthquake occurrence, Nature, 402, 605–609; King, G.C.P., and M. Cocco (2000), Fault interaction by elastic stress changes: New clues from earthquake sequences, Adv. Geophys., 44, 1–36; Freed, A.M. (2005), Earthquake triggering by static, dynamic, and postseismic stress transfer, Ann. Rev. Earth Planet. Sci. 33:335–67, doi: 10.1146/annurev.earth.33.092203.122505; Steacy, S., J. Gomberg, and M. Cocco (2005), Introduction to special section: Stress transfer, earthquake triggering, and time-dependent seismic hazard, J. Geophys. Res., 110, B05S01, doi:10.1029/2005JB003692. There is also evidence that faults and magmatic systems interact as well, and that static stress changes influence intrusions and eruptions. Undoubtedly, other processes not included in Coulomb are also important, such as dynamic stresses, pore fluid diffusion, and viscoelastic rebound. Further, basins and crustal layering modify the stresses in comparison to the elastic halfspace implemented in Coulomb. Nevertheless, we believe that a simple tool that permits exploration of a key component of earthquake interaction has great value for understanding and discovery.

 

Coulomb 3.1 is designed to investigate Coulomb stress changes on mapped faults and earthquake nodal planes, and is intended both for publication-directed research and for university teaching and instruction. One can calculate static displacements (on a surface or at GPS stations), strains, and stresses caused by fault slip, magmatic intrusion or dike expansion. Problems such as how an earthquake promotes or inhibits failure on nearby faults, or how fault slip or dike expansion will compress a nearby magma chamber, are germane to Coulomb. Geologic deformation associated with strike-slip faults, normal faults, or fault-bend folds is also a useful application. Calculations are made in an elastic halfspace with uniform isotropic elastic properties following Okada [1992].

We believe that one learns best when one can see the most and can explore alternatives quickly. So the principal feature of Coulomb is ease of input, rapid interactive modification, and intuitive visualization of the results. The program has menus, sub-menus, check-items, and dialogue boxes to ease operation. The internal graphics are suitable for publication, and can be easily imported into illustration or animation programs for further enhancements.

 

1.2   Hardware/software requirements:

¥      Macintosh OSX, Windows PC, or UNIX computer

         Note: We have not yet tested Coulomb 3.1 on Unix machines or the Vista operating system, but it does run on Intel MacÕs.

¥      Matlab 7.X or higher is required. There are a few Matlab functions that work on PCs but not MacÕs. Matlab 7.5 is not advised; its full of bugs.

¥      A color monitor of at least 600 x 400 pixel resolution. A laptop screen (1024 x 768 pixels) is fine.

¥      A text editor to modify ascii input files, and a spreadsheet to read tab-delimited text files. Some output files are created as .csv (Excel-friendly) files.

 

1.3   Recommended extras:

¥      A vector illustration program, such as Adobe Illustrator, is strongly recommended.

¥      When editing input files, we recommend that you use a text editor that allows you to distinguish spaces from tabs, such as BBEdit (BBEdit Lite is free from http://www.barebones.com/) or Notepad on a Windows PC. Regardless of the editor, use a non-kerning (uniform-spacing) font, such as Monaco, so that numbers stay aligned.

¥      Google Earth (which is free)

 

1.4   UserÕs Guide Alerts

Any words of wisdom in the manual are printed in red!

The images used in the manual to show you what you will see on the screen were captured at low resolution (72 dpi). But donÕt worry: you will save full-resolution vector files.

 

1.5   Help menu

This can be useful; there is a search command.

 

1.6   Cover images

The full-page cover page was designed by Serkan Bozkurt (now at Geomatrix Consulting) by importing Coulomb numerical output into ArcGIS. All of the interior cover images were made exclusively from Coulomb 3.1.

 

1.7   Acknowledgements

We are grateful for generous support by the Office of Foreign Disaster Assistance (OFDA) of the U.S. Agency for International Development (USAID) to code, test, and calibrate Coulomb 3.1.  Geoffrey C.P. KingÕs 1995 GEN inspired Coulomb 1.0. We thank many users for testing the functions, finding errors and suggesting improvements.

 

1.8   Citing Coulomb

 

 

Coulomb is intended for teaching and research. If you use Coulomb in research you submit for publication, we ask only that you cite these two papers:

 

Toda, S., R. S. Stein, K. Richards-Dinger and S. Bozkurt (2005), Forecasting the evolution of seismicity in southern California: Animations built on earthquake stress transfer, J. Geophys. Res., B05S16, doi:10.1029/2004JB003415.

 

Lin, J. and R.S. Stein (2004), Stress triggering in thrust and subduction earthquakes, and stress interaction between the southern San Andreas and nearby thrust and strike-slip faults, J. Geophys. Res., 109, B02303, doi:10.1029/2003JB002607.

 

 

1.9   Some key papers that explain and use Coulomb

 

Introduction without jargon or math:

            Stein, R.S., Earthquake conversations, Scientific American, 288 (1), 72-79, January 2003. (http://quake.wr.usgs.gov/research/deformation/modeling/refs/ross_refs.html)

 

Coulomb stress change concepts (for strike-slip faults):

            King, G.C.P., R.S. Stein, and J. Lin, Static stress changes and the triggering of earthquakes, Bull. Seismol. Soc. Amer., 84 (3), 935-953, 1994.

              (http://quake.wr.usgs.gov/research/deformation/modeling/papers/landers.html)

 

Coulomb stress concepts (for thrust faults and interaction between thrust and strike-slip faults):

            Lin, J., and R.S. Stein, Stress triggering in thrust and subduction earthquakes, and stress interaction between the southern San Andreas and nearby thrust and strike-slip faults, J. Geophys. Res., 109, B02303, doi:10.1029/2003JB002607, 2004.

             (http://quake.usgs.gov/research/deformation/modeling/papers/jlin/lin_stein04.html

 

Dislocation solution formulae:

            Okada, Y., Internal deformation due to shear and tensile faults in a half-space, Bull. Seismol. Soc. Amer., 82 (2), 1018-1040, 1992.

 

Application of Coulomb to seismic hazard:

            Toda, S., R.S. Stein, P.A. Reasenberg, and J.H. Dieterich, Stress transferred by the Mw=6.5 Kobe, Japan, shock: Effect on aftershocks and future earthquake probabilities, J. Geophys. Res., 103, 24,543-24,565, 1998.

               (http://quake.usgs.gov/research/deformation/modeling/papers/kobe.html)

            Toda, S., and R.S. Stein, Response of the San Andreas fault to the 1983 Coalinga-Nu–ez Earthquakes: An application of interaction-based probabilities for Parkfield, J. Geophys. Res., 107, 10.1029/2001JB000172, 2002.

                  (http://quake.wr.usgs.gov/research/deformation/modeling/papers/parkfield/parkfield.html)

Toda, S., R. S. Stein, K. Richards-Dinger and S. Bozkurt (2005), Forecasting the evolution of seismicity in southern California: Animations built on earthquake stress transfer, J. Geophys. Res., B05S16, doi:10.1029/2004JB003415.

http://quake.wr.usgs.gov/research/deformation/modeling/papers/2005/summaries/landers05JGR.html

 

Application of Coulomb to dike inflation:

            Toda, S., R.S. Stein and T. Sagiya, Evidence from the 2000 Izu Islands swarm that seismicity is governed by stressing rate, Nature, 419, 58-61, 2002.

                  (http://sicarius.wr.usgs.gov)

 

Application of Coulomb to earthquake-volcano interaction:

Nostro, C., R. S. Stein, M. Cocco, M. E. Belardinelli and W. Marzocchi, Two-way coupling between Vesuvius eruptions and southern Apennine earthquakes (Italy) by elastic stress transfer, J. Geophys. Res., 103, pp. 24,487-24,504, 1998.

http://quake.wr.usgs.gov/research/deformation/modeling/papers/nostro.html