Modeling Crustal Deformation near Active Faults and Volcanic Centers—A Catalog of Deformation Models Chapter 1 of Section B, Modeling of Volcanic Processes Book 13, Volcanic Monitoring Techniques and Methods 13–B1 U.S. Department of the Interior U.S. Geological Survey Modeling Crustal Deformation near Active Faults and Volcanic Centers—A Catalog of Deformation Models By Maurizio Battaglia, Peter F. Cervelli, and Jessica R. Murray Chapter 1 of Section B, Modeling of Volcanic Processes Book 13, Volcanic Monitoring Techniques and Methods 13-B1 U.S. Department of the Interior U.S. Geological Survey U.S. Department of the Interior SALLY JEWELL, Secretary U.S. Geological Survey Suzette M. Kimball, Acting Director U.S. Geological Survey, Reston, Virginia: 2013 For more information on the USGS—the Federal source for science about the Earth, its natural and living resources, natural hazards, and the environment, visit http://www.usgs.gov or call 1–888–ASK–USGS. 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B1, 96 p., http://pubs.usgs.gov/tm/13/b1. iii Contents Abstract ...........................................................................................................................................................1 Introduction.....................................................................................................................................................1 Geodetic Transformations ............................................................................................................................2 ITRF05 to ITRF00 ....................................................................................................................................4 XYZ to LLH ..............................................................................................................................................5 LL to UTM ...............................................................................................................................................6 Local Coordinates (ENU) .....................................................................................................................8 XYZ to ENU ....................................................................................................................................8 ENU to XYZ ....................................................................................................................................8 Spherical Source (Magma Chamber) .........................................................................................................9 Volume Change ...................................................................................................................................11 Ground Tilt ............................................................................................................................................11 Internal Deformation and Strain .......................................................................................................12 Leading-Order Solution .............................................................................................................12 First Free-Surface Correction ..................................................................................................13 Higher Order Cavity Correction ...............................................................................................14 Sixth-Order Free-Surface Correction .....................................................................................15 Internal Deformation .................................................................................................................16 Strain .........................................................................................................................................16 Examples of Surface Deformation, Tilt, Internal Deformation, and Strain for a Spherical Source ...................................................................................................................19 Prolate Spheroid Source (Magma Conduit) ............................................................................................20 Coordinates and Displacement (YANGDISP) ........................................................................21 Primitive (YANGINT) ..................................................................................................................21 General Parameters (YANGPAR) .............................................................................................24 Verification ..................................................................................................................................25 Volume Change ...................................................................................................................................28 Ground Tilt ............................................................................................................................................29 Strain ..................................................................................................................................................30 Examples of Parameters Calculated for a Prolate Spheroid .......................................................30 Sill-Like Source ............................................................................................................................................31 Volume Change ...................................................................................................................................35 Ground Tilt ............................................................................................................................................35 Strain ..................................................................................................................................................36 Examples of Parameters Calculated for a Sill-Like Structure .....................................................36 Surface Deformation and Ground Tilt for Rectangular Dikes and Faults ...........................................37 Displacement .......................................................................................................................................38 Parameters for Displacements and Displacement Gradients Functions fi .............................40 Elementary Function f1 for a Strike-Slip Fault ..............................................................................42 Elementary Displacement ........................................................................................................42 Displacement Gradient .............................................................................................................42 iv Contents—Continued Surface Deformation and Ground Tilt for Rectangular Dikes and Fault—Continued Elementary Function f2 for a Dip-Slip Fault ...................................................................................42 Elementary Displacement ........................................................................................................42 Displacement Gradient .............................................................................................................43 Elementary Function f3 for a Tensile Crack .................................................................................43 Elementary Displacement ........................................................................................................43 Displacement Gradient .............................................................................................................43 Verification ...........................................................................................................................................44 Strike-Slip Fault ..........................................................................................................................44 Dip-Slip Fault...............................................................................................................................45 Tensile Crack ..............................................................................................................................46 Examples of Surface Deformation and Ground Tilt for Three Types of Faults ..........................48 Internal Deformation and Strain for Rectangular Dikes and Faults ...................................................49 Source Geometry .......................................................................................................................49 Displacement ..............................................................................................................................49 Step 1—Elementary Displacement and Gradient .......................................................50 Step