1. 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

2. From block model

4. 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., )
- 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

5. 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)

6. Transients 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 ln lt 22.1 zh 10.0 xw 20.0 xx 50.0 am 500.0
EX: 1 ln lt
EF: 1 ln lt zh xw xx am
ES: 2 sp 10 ts 2 to ln lt 22.1 zh 5.0 am 500.0
EX: 2 ln lt zh
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

7. 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)

9. 2D Gauss
1D Gauss profiles

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

11. COMMANDS (++ new to TDEFNODE;
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

12. COMMANDS (++ new to TDEFNODE;
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

13. COMMANDS (++ new to TDEFNODE;
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:

14. 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: gf
PF: Parameter file
PF: “mod1/pio” 3
GP: GPS vector files
GP: NORA "nora_2003.vec"
GI: rotate GPS files
GI: 2
SV: slip vector data
SV: cr.svs FORE COCO 5.0
SVd: Tual BHed C E
SR: fault slip rate data
SR: saf_rate.dat NOAM PACI 1 0 0

15. Input
PO: Pole of rotation
PO:
ST: Strain rate tensor
ST:
FL: set flags
FL: +mkb -cov
FF: fault flags (turns on/off elastic strain)
FF:
FB: fault flag (removes fault from blocks)
FB:
SA: simulated annealing controls
SA: 0 80
GS: grid search controls
GS:
IC: iteration control (1=SA, 2-GS)
IC:

16. Input
RM: remove site from velocity field
RM: PNW1 TILL DAYV
MV: move node to new position
MV:
TS: time series data file
TS: PBO1 "PNW.gts ”
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

17. 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:
GS:

18. Iteration controls SA: 0.0 20 500 Simulated Annealing control:
Temperature
Number of iterations
Number of calls to ‘amoeba’ for each iteration
GS:
Grid Search control:
Number of steps away from current value
Nominal size of step (in parameter’s units)
Number of times to run through each parameter
Grid search type
Decrease in step size for each run through
IC:
Iteration Control:
Run simulated annealing
Run grid search

19. 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

20. 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.

21. Strike-slip
Subduction

22. crc0 - solve for block model

30. Planar slip source; using offset picks for 2007 SSE

31. 2D Gaussian slip source; fit picks and time series

33. 1D Gaussian