TDEFNODE:%20Time%20dependence

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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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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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ES option to enter transient parameters EF
option to specify which parameters are
adjusted EX assign bounds to parameters EI
specify which transients are used ET specify
time function elements ER specify polygon
radii EI 1 2 ES 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
500.0 EX 1 ln 123.0 123.6 lt 22.0 22.2 EF 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 500.0 EX 2 ln 123.0
123.6 lt 22.0 22.2 zh 1.0 10.0 EF 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)
Transients
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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)/Ts2 ) 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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COMMANDS ( new to TDEFNODE not for general
use or in development -- not used any more)
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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COMMANDS ( new to TDEFNODE not for
general use or in development -- not used any
more) 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 invert PI 1 2 SI Strain
tensors to invert SI 1 14 RE reference frame
block RE Blk1 GD Greens functions GD gf1 2 1
0 1.0 1.0 2000 PF Parameter file PF mod1/pio
3 GP GPS vector files GP NORA "nora_2003.vec"
2 1 0 0 0 1900 3000 0 0 0 1 1 0 GI rotate GPS
files GI 2 SV slip vector data SV cr.svs FORE
COCO 5.0 SVd Tual BHed 133.96 -4.07 286 15
C20040207E SR fault slip rate data SR
saf_rate.dat NOAM PACI 1 0 0
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Input PO Pole of rotation PO 1 43.2 237.1
-0.7 ST Strain rate tensor ST 2 -1.2 2.1 0.3
237.0 43.0 FL set flags FL 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
controls SA 0 80 GS grid search controls GS
30 0.1 7 2 3 IC iteration control (1SA,
2-GS) IC 1 2 1 2
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Input RM remove site from velocity field RM
PNW1 TILL DAYV MV move node to new position MV
237.0 43.0 237.5 43.3 TS time series data
file TS 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
chi2 (weighted data misfit) and penalties for
parameter constraints Simulated annealing or
grid search - both methods require many solutions
to forward model Uses Greens functions for
elastic deformation convolve locking or slip
distribution with GFs SA 0.0 20 500 GS 30 1.0
5 2 3
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Iteration controls

• SA 0.0 20 500
• Simulated Annealing control
• Temperature
• Number of iterations
• Number of calls to amoeba for each iteration
• GS 30 1.0 5 2 3
• Grid Search control
• Number of steps away from current value
• Nominal size of step (in parameters units)
• Number of times to run through each parameter
• Grid search type
• Decrease in step size for each run through
• IC 1 2 1 2
• Iteration Control

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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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