Analysis of the deformation of the Earth’s surface
Overarching goal is to find out what is going on at depth - motions,
forces, rheology
Observations largely confined to near Earth’s surface - we make
numerous assumptions about what goes on below
Approaches:
Curve-fitting - estimate strain rates directly from data, no geologic
model
Continuum - surface deformation mirrors deformation in a continuum
substrate (lower crust, mantle)
Blocks - deformation can be discontinuous at surface, i.e, faults
Viscoelastic - deformation continues longer than initial forces
1
Deformation analysis
Velocity field V(x,y) = [ Vx(x,y), Vy(x,y) ]
Solve for deformation gradient tensor:
dVx/dx dVx/dy
dVy/dx dVy/dy
Where:
Vx = x dVx/dx + y dVx/dy + Cx
Vy = x dVy/dx + y dVy/dy + Cy
2
The strain rate tensor is:
dVx/dx
½ (dVx/dy + dVy/dx)
½ (dVx/dy + dVy/dx)
dVy/dy
The vertical axis rotation rate is:
½ ( dVx/dy – dVy/dx )
This is done here in Cartesian coordinates (x,y) but can be
done in spherical coordinates as well. TDEFNODE uses
shperical coordinates (Savage).
3
Large-scale rotation with subduction locking superimposed
Field through mid 2009
4
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Rotation rates
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Strain rates
Not computed with TDEFNODE; but
a program is available.
5
TDEFNODE
Modeling block motions, fault locking, strain rates, transients
Use GPS velocities, displacements, time series, earthquake
slip vectors, fault slip rates, InSAR
6
Acknowledgments
Funding: NSF, NASA, USGS, GNS Science
Routines: Chuck DeMets, Charles Williams, Steve Roecker, Bob
King, W. Randolph Franklin, Dave Hollinger, Numerical Recipes
Debuggers: Dave Hollinger, Larry Baker
Guinea pigs (beta testers): Suzette Payne, Linette Prawirodirdjo,
Laura Wallace, Zhang Zhuqi, and others
7
• Defnode - modeling steady motions
only, use linear velocities
• Tdefnode - includes time-dependent
motions and uses time series; data are
time-sensitive
8
Motivation
• Velocity fields are superposition
of multiple signals; rotations,
strain rates, noise
• Time series showing strong nonlinear (transient) effects
9
Not as scary as GAMIT
10
-0.15 deg/Myr
Calculate
uniform strain
and rotation
rates in regions
Figure has block
rotations
removed from
vectors
-0.39 deg/Myr
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-0.25 deg/Myr
-0.06 deg/Myr
Courtesy of S. Payne
11
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Non-linearity of time series is a major challenge.
2004 quake
millimeters
Steady velocity
Afterslip
2005 quake
Afterslip from both events
East component of continuous GPS site SAMP
The Sumatra quakes of 2004 and 2005, with afterslip
13
Data from PANGA
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Block model can be used in non-steady state settings
to separate kinemtics from transients.
In some cases the
inter-event velocities
are clear - short
transients separated
by long inter-event
times.
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From McCaffrey 2009 GRL
Data from GNS Science
In other cases, it is
difficult to see the
steady site velocity
through the
transients.
Block models help by
taking advantage of
the spatial correlation
among nearby sites
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Long-term velocity?
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Data from GNS Science
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Parkfield quake
TBLP
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P566
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Inter-event velocities
are not independent
Data from PBO
16
Modeling estimated co-seismic offsets
2002
2009
17
Papua time series
Occurrence of earthquakes
results in non-linear GPS
time series.
We model the time series as
a combination of the linear
trend (kinematics) plus the
steps from quakes.
18
Block model from inversion of GPS time series
Mountain building
comprises only ~10%
of the action
Strike-slip
~10 mm/yr
Oblique
~11 mm/yr
Thrusting
~17 mm/yr
19
Yellowstone
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InSAR (M. Aly)
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Time series with sinusoidal term
InSAR data may overlap or have gaps in time
22
Multiple sill-like sources each with own time history
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Complex GPS time series
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Invert simultaneously with InSAR
24
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Blocks
• Closed polygons on surface of Earth
• Each characterized by angular velocity,
uniform strain rate
• Bounded by faults, or pseudo-faults
26
Faults
• Surfaces dipping into the Earth described by
nodes
• Separate blocks in three dimensions
• Coincide with block boundaries at surface
• Slip according to relative velocities of blocks
• Have locking or not
• Can have transients
27
Transients
• Spatial and time dependence types are
specified
• Many types can be modeled - quakes,
after-slip, slow-slip, volcanic
• Superimposed on long-term linear
velocities
28
Data
•
•
•
•
•
•
•
GPS velocities (East, North, Up)
GPS displacements (E, N, U)
GPS time series (E, N, U)
InSAR interferograms (LOS changes)
Fault slip rates or directions
Earthquake slip vectors
Uplift rates or displacements (tidegauge, coral, etc.)
29
GPS velocity vectors and uplift rates
Vk(X) = [ RG  X ]k + [ RB  X ]k + ekk DXk + ekl DXl +
j=1,2 i=1,N [- HF  Qi ]j i Gjk (X, Xi)
X is the position of the surface observation point,
k represents the velocity component (x, y, or z),
RB is the angular velocity of the block containing the observation point relative to
the
reference frame,
RG is the angular velocity of the GPS velocity solution containing the observation
point
relative to the reference frame,
e is the horizontal strain rate tensor (DX is the offset from strain rate origin)
HF is the Euler pole of the footwall block of fault relative to the hangingwall block,
N is the number of nodes along the fault,
Qi is the position of node i,
i is the coupling fraction at node i,
Gjk (X, Qi) is the kth component of the response function giving the velocity at X due
to a
unit velocity along fault at Qi in the jth direction on fault plane (downdip or
along
strike)
30
Other data types
Tilt rates:
T(X) = [ Vz(X+DX) - Vz(X - DX) ] / (2 DX )
(X is at the mid-point of the leveling line and DX is the offset from the mid-point to the ends)
Slip vector and transform fault azimuths:
A(X) = arctan{[( HR - FR )  X]x / [( HR - FR )  X]y }
Geologically estimated fault slip rates or spreading rates:
R(X) = | ( HR - FR )  X |
31
Compiling
• TDEFNODE is written in fortran and has one C
program to link
• Edit tdefcom1.h - set dimensions of arrays
• Edit tdefiles.h - set filenames for earthquakes
and volcanoes to be included in profile lines
• Edit Makefile provided, put in your compiler
names and flags
• gcc and gfortran work fine
• Put the executable file ‘tdefnode’ in your
path.
32
Control file
• All input information (except data files) are put in a
file that the program reads at startup
• Each line has a 2-character key that signifies its
purpose
• Key characters are in first two columns, followed
by a colon :
• Order of lines does not matter except for repeated
lines it uses the last instance
33
Models
• Model names are specified by MO:
option and are 4-characters long
• The Control file can have multiple
models using the MO: - EM: structure
• The model to run is selected in the
command line:
% defnode control_file model
34
Building the Blocks
Two options
1. Define all block outlines and faults
separately
2. Program builds blocks from faults
35
Method 1. Define Blocks and Faults
Fault
Block
Use BL: to outline block;
FA: to describe fault
36
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Block boundaries are determined by seismicity, faulting, strain
rates, … (reviewers and co-authors always ask for justification
of block boundaries).
37
Fault segment
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Block outline
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• The block outline has the surface nodes
and must coincide exactly with the fault
surface nodes.
• Not every edge of block has to be a defined
fault.
• But every fault must fall on a block edge.
38
Faults - defined by nodes
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Nodes are in an irregular grid.
Confined to depth contours.
Designated by (longitude, latitude, depth).
Subsurface nodes can be generated by program.
39
Representation of fault slip
•
•
•
•
Pyramidical
Bilinear
Nodes are specified along depth contours of
fault
Slip at each node is jV, where j ranges from
0 to 1 and V is taken from poles
Area between nodes is broken into small
patches
Surface deformation for each patch is
determined and summed
Response (Green’s)
functions are
determined by
putting unit velocity
at one node and
zero at all other
nodes, then
calculating the
surface velocities
by integration. 40
Half-space dislocation model (HSDM) to calculate surface
deformation due to fault locking and slip events
41
Velocities from elastic strain rates arising from fault locking
Use back-slip method to
compute elastic deformation
around locked fault.
surface
Locked fault
Free slipping
Integrate over fault using small patches,
can represent non-planar fault and nonuniform locking
42
Angular velocities - AV (Euler poles)
• Each block has an AV assigned
• Multiple blocks can have same AV, in which case there is no slip
between them
• Long-term linear velocity V of each point in block is V =  x r
• AVs can be fixed or adjusted in inversion
• Entered as Cartesian or Spherical coords, always units of
‘degrees per Million years’ and right-hand rule
• PO: option to input AV
• BP:, BC: options assign AV to blocks
• PI: option to adjust AV in inversion
43
Strain Rate Tensors (SRT)
• Each block may have uniform SRT assigned (optional)
• May arise due to small faults within block (anelastic, permanent
deformation)
• Multiple blocks can have same SRT (use common origin)
• Long-term linear velocity V of each point in block is relative to
specified origin
• SRTs can be fixed or adjusted in inversion
• Entered as nanostrain per year (10-9 / year)
• Described by 3 components Exx, Eyy, Exy
• ST: option to input SRT and origin
• BP: or BC: option to assign SRT to blocks
• SI: option to adjust SRT in inversion
44
Strain Rate Velocities
Point (j, )
Origin (jo, o)
Block
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Assign AV and SRT to Blocks
Block
Blk1
Blk3
Blk2
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Method 2. Define Faults, Build blocks
Fault (extends to
depth, can be
locked)
Pseudo-fault
(surface boundary,
free-slip)
Block
Set flag +mkb
FA: to describe faults
BC: to identify blocks
47
Region is divided into
‘blocks’, contiguous areas
that are thought to rotate
rigidly.
The relative long-term
slip vectors on the faults
are determined from
rotation poles.
Each block rotates
about a pole.
Back-slip is applied at
each fault to get surface
velocities due to locking.
Velocities due to fault locking are
added to rotations to get full
velocity field.
The rotating blocks are
separated by dipping faults.
48
The strain rate tensor near a locked fault represents a spatial transition from the velocity of one
block to the velocity of the other. In other words, a locked fault allows one block to
communicate information about its motion into an adjacent block.
49
Rotate velocity fields (or time series) into
common reference frame.
Specify reference frame block with RE: option
Velocity fields are rotated to minimize velocities of sites on that
block.
GI: option - list fields to be rotated
Does not require all velocity fields to have sites on reference
block, since all velocity fields must agree on all blocks.
50
Total long-term (linear) velocities
are the sum of the 4 terms:
• Velocity field rotation
• Block rotation
• Anelastic strain rate within block
• Elastic strain rates from fault
locking
51
Sample control file:
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Run 1 - get poles and strain rates
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Run 2: use PBO field,
rotate into PNW field
reference frame
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Run 3: Multiple fields;
strain rates, rotation
rates and reference
frames.
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Reference
frame
adjustments for
PNW1 and
PBO.
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Models - a particular set of input parameters, designated by 4-char
name. Multiple models can be in a single control file.
--- Model input
These lines pertain for mod1, mod2, and mod3
--- First mo signals start of MO: - EM: structure
mo: mod1 mod2
These line pertain to mod1 and mod2
mo: mod1
These lines pertain to mod1 only
mo: mod2
These lines pertain to mod2 only
mo: mod3
These lines pertain to mod3 only
em:
end of models
These lines pertain to mod1, mod2, and mod3
en: end of input
57
-- Fault input, blocks from faults
-- If making blocks from faults,
(+mkb flag) make pseudo-faults
from remaining borders. They
will be free-slip boundaries.
FA: for fault segments
-- For Fault1, it dips to east so
start in south
Fa: Blk1_bndry 2
4 1 Blk1 Blk1 1 0 0
0.0
-90.0 30.0
-80.0 30.0
-80.0 40.0
-90.0 40.0
Fa: Fault1 1
2 3 Blk2 Blk1 1 0 0
0.0
-90.0 30.0
-90.0 40.0
Zd: 5 89
Zd: 10 89
-100, 40
-90, 40
-80, 40
-- Give interior point of block
to identify it, and specify pole
and strain tensor for each
Blk2
Blk1
BC: Blk1 -95.0 35.0 1 0
BC: Blk2 -85.0 35.0 2 0
Fault1
-100, 30
-90, 30
Fa: Blk2_bndry 3
4 1 Blk2 Blk2 1 0 0
0.0
-90.0 30.0
-100.0 30.0
-100.0 40.0
-90.0 40.0
-80, 30
All segments must end
at another segment or
58
an error occurs.
--- Block and Fault input
If inputting blocks, make
polygon of borders of blocks.
They will be free-slip
boundaries.
BL: for closed blocks
FA: for fault segments
For Fault1, it dips to east so start
in south
BL: Blk1 1 0
4
-90.0 30.0
-80.0 30.0
-80.0 40.0
-90.0 40.0
Fa: Fault1 1
2 3 Blk2 Blk1 1 0 0
0.0
-90.0 30.0
-90.0 40.0
Zd: 5 89
Zd: 10 89
-100, 40
-90, 40
-80, 40
BL: Blk2 2 0
4
-90.0 30.0
-100.0 30.0
-100.0 40.0
-90.0 40.0
-- BP: is alternative way to
specify poles and strain tensors
BP: Blk1 1 0
BP: Blk2 2 0
Blk2
Blk1
Fault1
-100, 30
-90, 30
-80, 30
All block and fault
points must coincide or
an error occurs.
59
Nodes - slip or locking on nodes can be represented in several ways
Locking parameter is (x,z) or (x,w)
Independent nodes with or
without smoothing;
 decreases down-dip; or
 is specified function of z
-Boxcar
-Gaussian
-Exponential
V
 is specified function of x,z
- 2D Gaussian
- Uniform Polygon
x
z, w
60
The fault below has 6 surface nodes and 5 downdip for a total of 30.
For independent nodes (fault type FT: 0 or 1) we specify the interdependence of the nodes (NN:) and their starting values (NV:).
z
V
FT: 1 0
NNg: 1 6
1 1 2 2
1 1 2 2
4 4 5 5
4 4 5 5
0 0 0 0
NV: 1
5
3
3
6
6
0
3
3
6
6
0
x
1.0 1.0 1.0 0.8 0.8 0.8
x
z, w
61
The fault below has 6 surface nodes, so 6 downdip ‘profiles’. For each
one the function (z) can have different parameters. For example the
function may be:
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V
# DD Prof 1 2 3 4 5 6
FT: 1 2 1 1 1
PN: 1
1 1 2 2 3 3
PV: 1 3

5.0 5.0 5.0
5.0 5.0 5.0
zu
15.0 15.0 15.0
x
zl
z, w
62
Approximating ‘locking depth’; using downdip
boxcar fixing upper depth (0 km) and locking
amplitude (1); solve for lower depth
x
Locked nodes
z, w
Unlocked nodes
63
Variable locking depths
along San Andreas
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Types of downdip (1D) functions:
Exponential (Type 2)
Boxcar (Type 3)
Gaussian (Type 4)
Boxcar with cosine taper (Type 5)
Types of 2D functions:
Gaussian (Type 6)
Boxcar (Type 7)
Irregular polygon (Type 8)
Types of off-fault functions (not on block
boundary)
Planar shear slip (Type 9)
Mogi (Type 10)
Planar expansion crack (Type 11)
65
Interseismic; I
recommend locking the
updip edge and forcing
monotonic decrease in
locking downdip
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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
• Viscoelastic relaxation can be included by generating Green’s
functions with VISCO-1D (Pollitz)
67
From block model,
due to block motion,
elastic and anelastic
strain rates
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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
70
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)
71
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:
1
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)
72
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)
73
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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
77
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
15
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
85
Examples
• Costa Rica block model
• Cascadia SSE
• Taupo volcanic source
86
Example:
Costa Rica
block model
GPS velocities from 2
separate studies (rotate
into common frame),
uplift rates, solve for
block motions and fault
locking.
QuickTime™ and a
decompressor
are needed to see this picture.
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.
87
QuickTime™ and a
decompressor
are needed to see this picture.
88
Cascadia 2010 slow-slip event
Select continuous GPS sites in region
Solve for block motions, interseismic locking on
subduction zone, slip distribution in SSE, Gaussian
time history of SSE
1. 2D Gaussian slip distribution
2. 1D Gaussian downdip slip distribution
89
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
90
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
91
QuickTime™ and a
decompressor
are needed to see this picture.
92
QuickTime™ and a
decompressor
are needed to see this picture.
93
Taupo 2007 volcanic event
GPS time series, select time around
event
Use a small block around event to
remove steady velocity
Assume a Mogi source with Gaussian
time history
Solve for source amplitude, depth,
location, duration
QuickTime™ and a
decompressor
are needed to see this picture.
94
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
95
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
96