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U.S. Geological Survey Open-File Report 2011–1060

Coulomb 3.3 Graphic-Rich Deformation and Stress-Change Software for Earthquake, Tectonic, and Volcano Research and Teaching—User Guide

By Shinji Toda, Ross S. Stein, Volkan Sevilgen, and Jian Lin

Thumbnail of and link to report PDF (18.5 MB)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. 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 and check-items, and dialogue boxes to ease operation. The internal graphics are suitable for publication, and can be easily imported into Illustrator, GMT, Google Earth, or Flash for further enhancements.

Coulomb is designed to let one calculate static displacements, strains, and stresses at any depth caused by fault slip, magmatic intrusion, or dike expansion/contraction. 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)—see list of key papers in section 1.9.

There is substantial evidence to support the hypothesis that faults interact by the transfer of stress, both on the time scales of earthquake sequences and aftershocks and on longer time scales associated with the interevent time of the largest shocks that occur in a given region. There is also evidence that faults and magmatic systems interact as well, and that static stress changes influence intrusions and eruptions. Processes not included in Coulomb are also important, such as dynamic stresses, pore-fluid diffusion, and viscoelastic rebound. Further, elastic stiffness differences between 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.

To download the software (a MATLAB application) and tutorial files, please go to

  • This report is available only on the Web.

For additional information:
Contact Information, Earthquake Science Center, Menlo Park Science Center
U.S. Geological Survey
345 Middlefield Road, MS 977
Menlo Park, California 94025

This report is presented in Portable Document Format (PDF); the latest version of Adobe Reader or similar software is required to view it. Download the latest version of Adobe Reader, free of charge.

Suggested citation:

Toda, Shinji, Stein, R.S., Sevilgen, Volkan, and Lin, Jian, 2011, Coulomb 3.3 Graphic-rich deformation and stress-change software for earthquake, tectonic, and volcano research and teaching—user guide: U.S. Geological Survey Open-File Report 2011–1060, 63 p., available at


What’s New in Coulomb 3.3

Chapter 1. Introduction

Chapter 2. The Keys to the City, and a Quick Tour

Chapter 3. Concepts, Dimensions, and Sign Conventions

Chapter 4. Building Input Files

Chapter 5. Earthquake, Fault, Coastline Overlays, and Seismicity RateChanges

Chapter 6. Deformation, GPS Displacement and Strain

Chapter 7. Coulomb Stress Calculations

Chapter 8. Magmatic Sources, Google Earth Displays, Polygon Digitizing

Chapter 9. Input File Structure

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