1 tdefnode: time dependence earth is linearly elastic (no viscous relaxation built in) all sources...

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TDEFNODE: Time dependence

• Earth is linearly elastic (no viscous relaxation built in)• All sources are super-imposed• Every datum has a time stamp (except for now the

linear velocities)• Time dependence of transients are represented by

slip rate histories• Time dependence parameterized in several ways

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QuickTime™ and a decompressor

are needed to see this picture.

From block model

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Data

GPS velocity vectors or displacements - 3 components - use East, North, Up velocities and standard errors - use NE covariance - specify time frame - psvelo and other formats

GPS time series - 3 components - E, N, U positions (in mm relative to start) - times in decimal years (e.g., 2007.3941) - standard error for each point - can be decimated by program - offsets and seasonal signals estimated

InSAR line-of-sight changes (LOS) - resampled to reduce numbers - planar frame parameters estimated - matched at times of differenced images

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Earthquake slip vectors / fault slip azimuths - specify fixed and moving blocks

Fault slip rates - specify relative blocks - can be min/max or Gaussian types - can specify azimuth of measurement (e.g., for spreading rates)

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Transients

ES: option to enter transient parametersEF: option to specify which parameters are adjustedEX: assign bounds to parametersEI: specify which transients are usedET: specify time function elementsER: specify polygon radii

EI: 1 2ES: 1 fa 1 sp 4 ts 0 to 2004.22 ln 123.3 lt 22.1 zh 10.0 xw 20.0 xx 50.0 am 500.0EX: 1 ln 123.0 123.6 lt 22.0 22.2EF: 1 ln lt zh xw xx am ES: 2 sp 10 ts 2 to 2007.95 ln 123.3 lt 22.1 zh 5.0 am 500.0EX: 2 ln 123.0 123.6 lt 22.0 22.2 zh 1.0 10.0EF: 2 ln lt zh am

Codes: 'fa' fault number 'sp' spatial transient type (0 to 11) 'ts' temporal type (0 to 6) 'sa' slip azimuth control (0 or 1) 'ln' longitude (deg) 'lt' latitude (deg) 'zh' depth (km) 'xw' along-strike width (km) 'ww' down-dip width (km) 'az' azimuth of Gaussian X-width (deg) 'am' slip rate amplitude (mm/yr) 'to' origin time (dcecimal years) 'tc' time constant (days) 'mr' migration rate (km/day) 'ma' migration azimuth (deg) 'st' strike (deg) 'dp' dip (deg) 'rk' rake or slip azimuth (deg) 'ga' 1D Gaussian amplitude (mm/yr) 'gm' 1D Gaussian mean depth (km) 'gs' 1D Gaussian sigma (km) 'rd' polygon radii (as flag in EF: ) 'ta' tau amplitude (as flag in EF: ) 'mo' moment (Nm, in EX: option)

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Arguments for sp, sa, ts

Spatial source type (sp) = 1 Independent nodes = 2 Wang exp() function for phi(z) (uses parm types 5,6,7) = 3 1D boxcar phi(z) (uses parm types 4,6,7) = 4 Gaussian phi(z) slip (uses parm types 4,8,9) = 5 not used = 6 Gaussian 2D slip source (uses parms 24, 10, 11, 12, 13,14,15,16,17) = 7 2D Boxcar slip source = 8 Polygon, uniform slip source (use ER: also) = 9 earthquake slip source (double couple not on fault) = 10 Mogi slip source (not on fault) = 11 Planar expansion source (not on fault)

Slip azimuth type (sa) = 0 if slip direction from block model (poles) = 1 if azimuth of slip specified or estimated

Time dependence type (ts) = 0 impulse = 1 Gaussian A exp( [(t-To)/Ts]**2 ) = 2 triangles (set Ntau also; use ET:) = 3 exponential = 4 boxcar = 5 negative boxcar (loading) = 6 Omori (A/(t +Ts)

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2D Gauss 1D Gauss profiles

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Time functions: Also log and Omori functions (not shown)

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COMMANDS (++ new to TDEFNODE; ** not for general use or in development; -- not used any more)

AV: ++ add block/fault surface points BC: ++ specify point within block; also name of block and pole/strain indices BL: outline of elastic rotating plate polygon BP: specify pole and strain tensor indices for a block CF: connect 2 faults (remove overlap or gap from subsurface intersection of two faults) CL: clear specified data type CO: continue reading from input file (used sith SK: option) DD: set depth and dip to nodes (use only within FA: section; similar to ZD:) DR: ++ set region for data DS: ++ displacements input file DT: ++ time interval for synthetic time series DV: ++ delete block/fault surface points EC: ++ elastic constants EF: ++ flags for the individual transient parameters EI: ++ flags to invert transient events EM: end of model input section EN: end of input data EQ: equate two nodes on different faults (set their phi's equal) ER: ++ polygon source information ES: ++ transient source parameters ET: ++ transient source time function information EX: ++ constraints on transient source parameters FA: fault geometry input FB: ++ flag faults to use to make blocks FD: -- fix depths FF: fault flags (turn faults on and off) FL: set miscellaneous flags FO: -- fault orientation FS: calculate and output relative block velocities at specified points FT: fault parameterization type FV: -- fix Xo or V for listed time series FX: specify position of a particular fault node - overrides all other specifications GD: specify Green's functions directory and other GF parameters GF: -- combined with GD: GI: GPS velocity fields (relative to reference frame) to be adjusted GP: GPS velocity input data file GR: grid of vectors to calculate GS: parameter grid search controls

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GW: -- global weight HC: hard constraints IN: interpolation lengths for fault segments between nodes (for final forward run) IS: ++ Insar data input file LA: ** layered structure LL: ** line length data MF: merge faults at T-junction MM: range of seismic moments allowed for a fault MO: model experiment name, used for output filenames MS: ++ merge two time series MV: move block/fault surface points NI: number of iterations NN: node parameter index numbers (same as old NF:) NV: node values (same as old NO:) NX: indices of fixed nodes OP: ** output poles relative to a block PE: scaling factors for penalty functions PF: parameter and model I/O file PG: initialize pole of rotation for GPS vector file PI: block poles to be adjusted PM: parameter min and max values allowed PN: node z-profile parameter index numbers PO: block pole of rotation values PR: surface profile line PT: ** file of lon,lat points to compute displacements PV: node z-profile parameter values PX: fix node z-profile parameters RC: remove sites within a specified circular area (e.g., volcanic region) RE: reference block for vectors RF: rotate reference frame for vector output RM: remove named GPS sites or blocks from data RO: rotation rates input data file

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RQ: remove equates with list of names to use RS: reference site for GPS vectors SA: simulated annealing inversion controls SE: ++ select sites from GPS file SI: strain rates tensors to be adjusted SK: skip following lines of input data until a CO: line is encountered SM: apply smoothing to fault locking SN: snap block boundary points together SR: fault slip rate / spreading rate data file SS: strain rate tensor data file ST: initialize strain rate tensor values and origin SV: slip vector / transform azimuth data file TI: tilt rate data file TS: ++ time series input file UP: -- uplift rate data file (see GP:) ZD: set depth and dip to nodes (use only within FA: section); similar to DD:

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Input

PI: Poles to invertPI: 1 2

SI: Strain tensors to invertSI: 1 14

RE: reference frame blockRE: Blk1

GD: Green’s functionsGD: gf1 2 1 0 1.0 1.0 2000

PF: Parameter filePF: “mod1/pio” 3

GP: GPS vector filesGP: NORA "nora_2003.vec" 2 1 0 0 0 1900 3000 0 0 0 1 1 0

GI: rotate GPS filesGI: 2

SV: slip vector dataSV: cr.svs FORE COCO 5.0SVd: Tual BHed 133.96 -4.07 286 15 C20040207E

SR: fault slip rate dataSR: saf_rate.dat NOAM PACI 1 0 0

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Input

PO: Pole of rotationPO: 1 43.2 237.1 -0.7

ST: Strain rate tensorST: 2 -1.2 2.1 0.3 237.0 43.0

FL: set flagsFL: +mkb -cov

FF: fault flags (turns on/off elastic strain)FF: +1 -2 +3 +4 -13

FB: fault flag (removes fault from blocks)FB: -1 -13

SA: simulated annealing controlsSA: 0 80

GS: grid search controlsGS: 30 0.1 7 2 3

IC: iteration control (1=SA, 2-GS)IC: 1 2 1 2

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Input

RM: remove site from velocity fieldRM: PNW1 TILL DAYV

MV: move node to new positionMV: 237.0 43.0 237.5 43.3

TS: time series data fileTS: PBO1 "PNW.gts ” 3 1.0 25.0 30.0 50.0 2004.0 2010.5 2 2 2 3 3 3

DS: Displacement data file

SM: Smoothing fault slip

SE: Select specific sites from file, use with GP:, RM:, TS: component flags to select site-components

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Inversion:

Minimize penalty function: sum of chi**2 (weighted data misfit) and penalties for parameter constraints

Simulated annealing or grid search - both methods require many solutions to forward model

Uses Green’s functions for elastic deformation; convolve locking or slip distribution with GFs

SA: 0.0 20 500GS: 30 1.0 5 2 3

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SA: 0.0 20 500

Simulated Annealing control: 1. Temperature2. Number of iterations3. Number of calls to ‘amoeba’ for each iteration

GS: 30 1.0 5 2 3

Grid Search control:1. Number of steps away from current value2. Nominal size of step (in parameter’s units)3. Number of times to run through each parameter4. Grid search type5. Decrease in step size for each run through

IC: 1 2 1 2

Iteration Control:• Run simulated annealing• Run grid search

Iteration controls

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While iterating press:

‘q’ - quit iterating and finish program‘s’ - go to next step in IC: sequence‘n’ - if in GS: to go to next run through parameters

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Example: Costa Rica



Cocos Plate subducts beneath the forearc. Forearc sliver moves to NW along possible strike-slip fault near arc. Use defnode to solve for locking on subduction thrust and motion of forearc.

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Strike-slip

Subduction

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crc0 - solve for block model

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Planar slip source; using offset picks for 2007 SSE

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2D Gaussian slip source; fit picks and time series

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1D Gaussian

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1 tdefnode: time dependence earth is linearly elastic (no viscous relaxation built in) all sources...

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