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.
¥ 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.
¥ 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)
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.
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.
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.
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.
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