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
4
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)
5
Transients
ES:
EF:
EX:
EI:
ET:
ER:
option to enter transient parameters
option to specify which parameters are adjusted
assign bounds to parameters
specify which transients are used
specify time function elements
specify polygon radii
EI:
ES:
EX:
EF:
ES:
EX:
EF:
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1
1
1
2
2
2
Codes:
2
fa
ln
ln
sp
ln
ln
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
123.0 123.6 lt 22.0 22.2
lt zh xw xx am
10 ts 2 to 2007.95 ln 123.3 lt 22.1 zh 5.0 am 500.0
123.0 123.6 lt 22.0 22.2 zh 1.0 10.0
lt zh am
'fa'
'sp'
'ts'
'sa'
'ln'
'lt'
'zh'
'xw'
'ww'
'az'
'am'
'to'
'tc'
'mr'
'ma'
'st'
'dp'
'rk'
'ga'
'gm'
'gs'
'rd'
'ta'
'mo'
fault number
spatial transient type (0 to 11)
temporal type (0 to 6)
slip azimuth control (0 or 1)
longitude (deg)
latitude (deg)
depth (km)
along-strike width (km)
down-dip width (km)
azimuth of Gaussian X-width (deg)
slip rate amplitude (mm/yr)
origin time (dcecimal years)
time constant (days)
migration rate (km/day)
migration azimuth (deg)
strike (deg)
dip (deg)
rake or slip azimuth (deg)
1D Gaussian amplitude (mm/yr)
1D Gaussian mean depth (km)
1D Gaussian sigma (km)
polygon radii (as flag in EF: )
tau amplitude (as flag in EF: )
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
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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:
BC:
BL:
BP:
CF:
CL:
CO:
DD:
DR:
DS:
DT:
DV:
EC:
EF:
EI:
EM:
EN:
EQ:
ER:
ES:
ET:
EX:
FA:
FB:
FD:
FF:
FL:
FO:
FS:
FT:
FV:
FX:
GD:
GF:
GI:
GP:
GR:
GS:
++ add block/fault surface points
++ specify point within block; also name of block and pole/strain indices
outline of elastic rotating plate polygon
specify pole and strain tensor indices for a block
connect 2 faults (remove overlap or gap from subsurface intersection of two faults)
clear specified data type
continue reading from input file (used sith SK: option)
set depth and dip to nodes (use only within FA: section; similar to ZD:)
++ set region for data
++ displacements input file
++ time interval for synthetic time series
++ delete block/fault surface points
++ elastic constants
++ flags for the individual transient parameters
++ flags to invert transient events
end of model input section
end of input data
equate two nodes on different faults (set their phi's equal)
++ polygon source information
++ transient source parameters
++ transient source time function information
++ constraints on transient source parameters
fault geometry input
++ flag faults to use to make blocks
-- fix depths
fault flags (turn faults on and off)
set miscellaneous flags
-- fault orientation
calculate and output relative block velocities at specified points
fault parameterization type
-- fix Xo or V for listed time series
specify position of a particular fault node - overrides all other specifications
specify Green's functions directory and other GF parameters
-- combined with GD:
GPS velocity fields (relative to reference frame) to be adjusted
GPS velocity input data file
grid of vectors to calculate
parameter grid search controls
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COMMANDS (++ new to TDEFNODE; ** not for general use or in development; -- not used any more)
GW:
HC:
IN:
IS:
LA:
LL:
MF:
MM:
MO:
MS:
MV:
NI:
NN:
NV:
NX:
OP:
PE:
PF:
PG:
PI:
PM:
PN:
PO:
PR:
PT:
PV:
PX:
RC:
RE:
RF:
RM:
RO:
-- global weight
hard constraints
interpolation lengths for fault segments between nodes (for final forward run)
++ Insar data input file
** layered structure
** line length data
merge faults at T-junction
range of seismic moments allowed for a fault
model experiment name, used for output filenames
++ merge two time series
move block/fault surface points
number of iterations
node parameter index numbers (same as old NF:)
node values (same as old NO:)
indices of fixed nodes
** output poles relative to a block
scaling factors for penalty functions
parameter and model I/O file
initialize pole of rotation for GPS vector file
block poles to be adjusted
parameter min and max values allowed
node z-profile parameter index numbers
block pole of rotation values
surface profile line
** file of lon,lat points to compute displacements
node z-profile parameter values
fix node z-profile parameters
remove sites within a specified circular area (e.g., volcanic region)
reference block for vectors
rotate reference frame for vector output
remove named GPS sites or blocks from data
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: Green’s 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
SR: fault slip rate data
SR: saf_rate.dat NOAM PACI 1 0 0
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C20040207E
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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 (1=SA, 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 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 20 500
GS: 30 1.0 5 2 3
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Iteration controls
SA: 0.0 20 500
Simulated Annealing control:
1. Temperature
2. Number of iterations
3. 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 value
2. Nominal size of step (in parameter’s units)
3. Number of times to run through each parameter
4. Grid search type
5. Decrease in step size for each run through
IC: 1 2 1 2
Iteration Control:
1. Run simulated annealing
2. Run grid search
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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
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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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