Techniques and Methods 13-B1
This manual provides the physical and mathematical concepts for selected models used to interpret deformation measurements near active faults and volcanic centers. The emphasis is on analytical models of deformation that can be compared with data from the Global Positioning System (GPS) receivers, Interferometric synthetic aperture radar (InSAR), leveling surveys, tiltmeters and strainmeters. Source models include pressurized spherical, ellipsoidal, and horizontal penny-shaped geometries in an elastic, homogeneous, flat half-space. Vertical dikes and faults are described following the mathematical notation for rectangular dislocations in an elastic, homogeneous, flat half-space. All the analytical expressions were verified against numerical models developed by use of COMSOL Multyphics, a Finite Element Analysis software (http://www.comsol.com). In this way, typographical errors present were identified and corrected. Matlab scripts are also provided to facilitate the application of these models.
First posted July 8, 2013
dMODELS (version 1.0, June 2013)
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Battaglia, Maurizio, Cervelli, P.F., and Murray, J.R., 2013, Modeling crustal deformation near active faults and volcanic centers—A catalog of deformation models: U.S. Geological Survey Techniques and Methods, book 13, chap. B1, 96 p., https://pubs.usgs.gov/tm/13/b1.
Geodetic Transformations Function
Spherical Source (Magma Chamber)
Prolate Spheroid Source (Magma Conduit)
Surface Deformation and Ground Tilt for Rectangular Dikes and Faults
Internal Deformation and Strain for Rectangular Dikes and Faults
Smoothing Operator D
Appendix 1. Mathematical Methods for Computing Displacement