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Paul Denys and Chris Pearson
School of Surveying
University of Otago
Modelling Time Dependent Transient Deformation
in New ZealandPresente
d at the FIG
Working W
eek 2016,
May 2-6, 2
016 in Christchurch, N
ew Zealand
• Motivation– Surveying positioning applications are
transferred to the national datum at a
specific reference epoch
• e.g. NZGD2000, epoch 2000.0
• Positioning Applications– Long baselines – PositionNZ-PP
– Current epoch positioning – ITRF2008
• PPP, PositioNZ-PP
– Network RTK
• Deformation– Time dependent and transient
Christc
hurc
h C
BD
post 2010-1
1
Earthquake Events
• 12 major events since 2003• many cGNSS sites affected
Tectonic Setting
Source: GNS Science
Centimetre Positioning ApplicationsComplex deformation affects
centimetre positioning applications :
GNSS Positioning Engines• Satellites in terms of ITRF2008
• User/Rover transformed to user’s
local datum
Network RTK• Reference station coordinates in
terms of ITRF2008
• Secular velocity only :
• User/Rover transformed to user’s
local datum
165 170 175 180-48
-46
-44
-42
-40
-38
-36
-34
50 mm/yr
Longitude (degrees)
Lati
tud
e (
de
gre
es)
165 170 175 180-48
-46
-44
-42
-40
-38
-36
-34
Longitude (degrees)
Lati
tud
e (
de
gre
es)
20
25
30
35
40
45
TimeC
oord
inate
t0Reference
Epoch
tCurrent
Epoch
How are geophysical processes with
non-linear signatures such as seismic
events dealt with?
• Coseismic offsets• Easy
TimeC
oord
inate
t0Reference
Epoch
tCurrent
EpochteEvent Epoch
How are geophysical processes with
non-linear signatures such as seismic
events dealt with?
• Coseismic offsets• Easy
• Post-seismic relaxation• Harder
• Requires measurements to
determine amplitude of decay
TimeC
oord
inate
t0Reference
Epoch
tCurrent
EpochteEvent Epoch
How are geophysical processes with
non-linear signatures such as seismic
events dealt with?
• Coseismic offsets• Easy
• Post-seismic relaxation• Harder
• Requires time to determine
amplitude of decay
• Transient velocities• Harder
• Requires time to determine change
in velocity
TimeC
oord
inate
t0Reference
Epoch
tCurrent
EpochteEvent Epoch
How are geophysical processes with
non-linear signatures such as seismic
events dealt with?
• Coseismic offsets• Easy
• Post-seismic relaxation• Harder
• Requires time to determine
amplitude of decay
• Transient velocities• Harder
• Requires time to determine change
in velocity
• Slow slip events• Difficult
• Events occur over days – weeks –
months – years
TimeC
oord
inate
t0Reference
Epoch
tCurrent
Epocht
Event Epoch
2010-11 Christchurch Earthquake Events: MQZG
Coseismic deformation is
easily modelled
2000 2005 2010 2015
-150
-100
-50
0
Eas
t (m
m)
2000 2005 2010 2015
-20
0
20
40
60
80
No
rth
(m
m)
2000 2005 2010 2015
-20
0
20
40
Heig
ht
(mm
)
Years
-800 -600 -400 -200 0 200
0
100
200
300
400
500
No
rth
ing
s (
mm
)
Eastings (mm)
Source: GNS Science
Coseismic deformation2009 Mw 7.8 Dusky Sound earthquake
167 168 169 170 171-48
-47
-46
-45
-44
-43
-42
Longitude (degrees)
Lati
tud
e (
de
gre
es)
5
10
20
50
100
200
500
167 168 169 170 171-48
-47
-46
-45
-44
-43
-42
100 mm
Longitude (degrees)
Lati
tud
e (
de
gre
es)
Post-seismic relaxation2009 Dusky Sound
earthquake
Post-seismic decay function
• logarithmic
• exponential
• power law
-600 -500 -400 -300 -200 -100 0
0
50
100
150
PYGR
No
rth
ing
s (
mm
)
Eastings (mm)
-450 -400 -350 -300 -250 -200 -150 -100 -50 0 50
-50
0
50
100
150
200
250
300
350
400
MAVL
No
rth
ing
s (
mm
)
Eastings (mm)
Post-seismic Relaxation - 2009 Dusky Sound• Log decay function (5yrs): E: -60 mm N: -80 mm H: +70 mm
• Transient velocity (5yrs): E: -16 mm N: -1 mm H: 0 mm
2008 2009 2010 2011 2012 2013 2014
-20
-10
0
10
20PYGR
East
(mm
)
2008 2009 2010 2011 2012 2013 2014
-20
-10
0
10
20
No
rth
(m
m)
2008 2009 2010 2011 2012 2013 2014
-30
-20
-10
0
10
20
30
Heig
ht
(mm
)
Years
2008 2009 2010 2011 2012 2013 2014
-400
-300
-200
-100
0
East
(mm
)
2008 2009 2010 2011 2012 2013 2014
-150
-100
-50
0
No
rth
(m
m)
2008 2009 2010 2011 2012 2013 2014
-20
0
20
40
60
80
Heig
ht
(mm
)
Years
2008 2009 2010 2011 2012 2013 2014
-400
-300
-200
-100
0
East
(mm
)
2008 2009 2010 2011 2012 2013 2014
-150
-100
-50
0
No
rth
(m
m)
2008 2009 2010 2011 2012 2013 2014
-20
0
20
40
60
80
Heig
ht
(mm
)
Years
Post-seismic deformation
2009 Dusky Sound earthquake
167 168 169 170 171-48
-47
-46
-45
-44
-43
-42
Longitude (degrees)
Lati
tud
e (
de
gre
es)
0.5
1
2
5
10 mm/yr
Post-seismic horizontal
displacement after 5 years:
• epicentre: 100 mm
• 250-300km 20 mm
250-300 km
East Coast Slow Slip Events
-80 -60 -40 -20 0 20
-50
0
50
100
150
200
250
300
350
400
No
rth
ing
s (m
m)
Eastings (mm)-10 0 10 20 30
-50
0
50
100
150
200
250
300
No
rth
ing
s (m
m)
Eastings (mm)
Gisborne (GISB)Hastings (HAST)
Slow Slip Events
-150 -100 -50 0 50-50
0
50
100
150
200
250
300
350
400KAPT
No
rth
ing
s (
mm
)
Eastings (mm)
-300 -200 -100 0 100-100
0
100
200
300
400
500
600PAEK
No
rth
ing
s (
mm
)
Eastings (mm)
-150 -100 -50 0 50-50
0
50
100
150
200
250
300
350
400
450TORY
No
rth
ing
s (
mm
)
Eastings (mm)-100 0 100
-100
0
100
200
300
400
500
600NLSN
Nort
hin
gs (
mm
)
Eastings (mm)
-100 -50 0 50-100
0
100
200
300
400
500DURV
Nort
hin
gs (
mm
)
Eastings (mm)
-100 -50 0 50-50
0
50
100
150
200
250TRWH
Nort
hin
gs (
mm
)
Eastings (mm)
Paekakariki Hill – Slow Slip Events
-400 -200 0 200-100
0
100
200
300
400
500
600PAEK
Nort
hin
gs (
mm
)
Eastings (mm)
2002 2004 2006 2008 2010 2012 2014
0
20
40
60
80
Eas
t (m
m)
2002 2004 2006 2008 2010 2012 2014
-20
-10
0
10
20
30
No
rth
(m
m)
2002 2004 2006 2008 2010 2012 2014
-20
0
20
40
60
80
Heig
ht
(mm
)
Years
Offsets : 10mm 8mm 22mm 36mm
Total Offsets (over 15 years) E : +76 mm N : 13 mm H : 47 mm
Kapiti Coast – Slow Slip Events
2000 2005 2010 20150
20
40
60
80
100
120
140
160
180
200
220
WGTN
Eas
t T
ren
d [
mm
]
Time [years]
WGTT
TRWH
MTQN
CLIM
PAEK
KAPT
2000 2005 2010 2015
0
20
40
60
80
100
120
140
160
180
WGTN
No
rth
Tre
nd
[m
m]
Time [years]
WGTT
TRWH
MTQN
CLIM
PAEK
KAPTEasting Northing
2013 Kapiti Coast Slow Slip Event
173 174 175 176-43.5
-43
-42.5
-42
-41.5
-41
-40.5
-40
-39.5
-39
-38.5
25 mm
Kapiti Coast 2013 Slow Slip Event
Longitude (degrees)
Lati
tud
e (
de
gre
es)
173 174 175 176-43.5
-43
-42.5
-42
-41.5
-41
-40.5
-40
-39.5
-39
-38.5
Longitude (degrees)
Lati
tud
e (
de
gre
es)
20
30
40
50
mm
Reference Station CoordinatesNetwork RTK reference stations require current epoch coordinates:
• Based on linear (uniform) velocities:• Coordinate error up to 50 mm • Majority of reference sites may be affected by deformation• Non-linear trends are difficult to predict (Data from 2011–2015)
-40 -20 0 20 40 60
-200
-150
-100
-50
0
East (mm)
No
rth
(m
m)
Observed
Modelled
Computed
2015.2 2015.3 2015.4 2015.5 2015.6 2015.7 2015.872.22
72.24
72.26
No
rth
(m
)
2015.2 2015.3 2015.4 2015.5 2015.6 2015.7 2015.846.84
46.86
46.88
Heig
ht
(m)
Years
Long term linear trend
-50 0 50 100
-200
-150
-100
-50
0
No
rth
(m
m)
Observed
Modelled
Computed
What Positioning Applications are Affected?
Long baseline applications
– Connections to PositioNZ
Current epoch coordinates applications• i.e. ITRF2008
– PPP
– GNSS Positioning Engines
• e.g. PositioNZ-PP, AUSPos
– Network RTK
How?
– Reference stations: Compute coordinates
– User/Rover: Transform current epoch coordinates to the user’s datum
• i.e. ITRF2008 NZGD2000
Summary
• Active deformation in New Zealand is widespread• Non-linear deformation can affect surveying
applications
• Especially GNSS positioning• Positioning over long distances
Challenges
• Monitor/Prediction of non-linear deformation• Accurate modelling of deformation with a sparse cGNSS
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