Reconciling GRACE derived loading deformation with GNSS ... - Chanard.pdf · Reconciling GRACE derived loading deformation with GNSS station position time series MST2, Nepal ... Long

K.Chanard, P. Rebischung, L. Fleitout, L. Métivier, X. Collilieux & Z. Altamimi

IGS WORKSHOP 2017 | PARIS

Reconciling GRACE derived loading deformation with GNSS station position time series

MST2, Nepal

Site positions at continuous GNSS station LHAZ, Tibet

North

East

Vertical

2 IGS WORKSHOP 2017 | PARIS

Irregularities (ex: equipment replacement)(Co-seismic)

• Tectonics • Post-glacial rebound

Quasi-linear displacements

+~2cm/yr

~2cm/yr

~2mm/yr


North

East

Vertical

Measurement discontinuities


• Tectonics • Post-glacial rebound

Quasi-linear displacements

+


ITRF2008

North

East

Vertical• Seasonal loading (continental hydrology,

atmospheric and non-tidal oceanic loads)• (Postseismic deformation)• (Transient deformation)

NON-LINEAR DEFORMATION IN TIME

+

~ 5mm

~ 10mm

Irregularities (ex: equipment replacement)(Co-seismic)

Measurement discontinuities


IGS WORKSHOP 2017 | PARIS

Physical Explanation

3

Surface load Horizontal Vertical

Seasonal displacements

Loading Season Unloading Season

Physical Model 1. Hypothesis: Rheological model for Earth

2. Convolve seasonal load with Green functions associated to Earth model

Modeling Seasonal Deformation

−180˚

−180˚

−120˚

−120˚

−60˚

−60˚

0˚

0˚

60˚

60˚

120˚

120˚

180˚

180˚

−60˚ −60˚

−30˚ −30˚

0˚ 0˚

30˚ 30˚

60˚ 60˚

0 100 200 300 400 500 600 700 800 mm

Datasets - Degree-1 - Earth rheology

GRACE — Seasonal Equivalent Water Height 2002-2012

: Water height variations between Summer and Winter (CNES/GRGS)�h

Continental water, oceanic and atmospheric massLong term trends and earthquake contributions removed

IGS WORKSHOP 2017 | PARIS 4

http://grgs.obs-mip.fr/grace/

−180˚

−180˚

−120˚

−120˚

−60˚

−60˚

0˚

0˚

60˚

60˚

120˚

120˚

180˚

180˚

−60˚ −60˚

−30˚ −30˚

0˚ 0˚

30˚ 30˚

60˚ 60˚

0 100 200 300 400 500 600 700 800 mm

−180˚

−180˚

−120˚

−120˚

−60˚

−60˚

0˚

0˚

60˚

60˚

120˚

120˚

180˚

180˚

−60˚ −60˚

−30˚ −30˚

0˚ 0˚

30˚ 30˚

60˚ 60˚


GNSS - IGS REPRO 2 RESIDUALS

: Water height variations between Summer and Winter (CNES/GRGS)�h


1078 GNSS sites globally distributed Time series corrected for co- and postseismic contributions

(http://acc.igs.org/reprocess2.html)

LHAZGOLD

http://acc.igs.org/reprocess2.html

Numbers of models: difficulty to predict horizontal components

(Fu et al., 2013)

Vertical

GRACE derived model

GPSdata

1cm

Horizontal

GPS dataGRACE derived model

5mm

(Van Dam et al., 2001 ; Davis et al. 2004)

Empirical estimates overlooking spatio-temporal complexity of seasonal signals

(Fu et al., 2013)


Loading models VS GNSS observations

Global seasonal signals in GNSS time series are related to satellite derived hydrology

Elastic spherical and layered Earth model

(PREM)

Seasonal loading (GRACE)

+ GNSS observations

1. Predict seasonal horizontal and vertical displacements

OUTLINE


GRACE-derived model VS GNSS:Degree-1 deformation and reference frame issue

CM

CF

CM

CF

Season 1

Season 2

CN

CN

CM

CF

CM

CF

Season 1

Season 2

CN

CN

Degree-1 loading induces:

- Geocenter Motion (translation CM-CF)- Deformation field of the Earth surface

GRACE does not capture degree-1 spherical harmonics loads, contrary to GNSS

To insure comparison, degree-1 contributions are added using coefficients from Swenson et al. (2008)





−10

−5

0

5

10

Det

. Eas

t (m

m)

2002 2004 2006 2008 2010 2012

LHAZ

−10

−5

0

5

10

Det

. Nor

th (m

m)

2002 2004 2006 2008 2010 2012

−30

−20

−10

0

10

20

30

Det

. Ver

tical

(mm

)

2002 2004 2006 2008 2010 2012

PREM/Deg1-Swenson

Elastic (PREM) & Seasonal Load (GRACE + Deg1-Swenson)

−10

−5

0

5

10

Det

. Eas

t (m

m)

2002 2004 2006 2008 2010 2012

GOLD

−10

−5

0

5

10

Det

. Nor

th (m

m)

2002 2004 2006 2008 2010 2012

−30

−20

−10

0

10

20

30

Det

. Ver

tical

(mm

)

2002 2004 2006 2008 2010 2012

PREM/Deg1-Swenson



Elastic (PREM) & Seasonal Load (GRACE + Deg1-Swenson)



East − PREM/Deg1−Swenson

−180˚

−180˚

−120˚

−120˚

−60˚

−60˚

0˚

0˚

60˚

60˚

120˚

120˚

180˚

180˚

−60˚ −60˚

−30˚ −30˚

0˚ 0˚

30˚ 30˚

60˚ 60˚

−100 −80 −60 −40 −20 0 20 40 60 80 100 WRMS reduction (%)North − PREM/Deg1−Swenson

−180˚

−180˚

−120˚

−120˚

−60˚

−60˚

0˚

0˚

60˚

60˚

120˚

120˚

180˚

180˚

−60˚ −60˚

−30˚ −30˚

0˚ 0˚

30˚ 30˚

60˚ 60˚

−100 −80 −60 −40 −20 0 20 40 60 80 100 WRMS reduction (%)

Vertical − PREM/Deg1−Swenson

−180˚

−180˚

−120˚

−120˚

−60˚

−60˚

0˚

0˚

60˚

60˚

120˚

120˚

180˚

180˚

−60˚ −60˚

−30˚ −30˚

0˚ 0˚

30˚ 30˚

60˚ 60˚

−100 −80 −60 −40 −20 0 20 40 60 80 100 WRMS reduction (%)

WRMS Obs. - Elastic & GRACE + Deg1-Swenson

EAST

NORTH

VERTICAL

WRMS reduction (%)North: 536 sites (mean 1.2% )East: 506 sites (mean 4.1%)Vert.: 864 sites (mean 32%)

GRACE-derived model VS GNSS:Degree-1 deformation and reference frame issue

CM

CF

CM

CF

Season 1

Season 2

CN

CN

CM

CF

CM

CF

Season 1

Season 2

CN

CN

To insure comparison, degree-1 contributions are added using coefficients from Swenson et al. (2008)



derived from comparing GNSS-GRACE derived model with no degree-1

Deformation field

,

Linear combination of:- 1 Translation on horizontal components- 1 Translation on the vertical component

Degree-1

(prevents the deg-1 horizontal deformation to be biasedby unmodelled vertical signals (thermal expansion, etc.))

−10

−5

0

5

10

Det

. Eas

t (m

m)

2002 2004 2006 2008 2010 2012

LHAZ

−10

−5

0

5

10

Det

. Nor

th (m

m)

2002 2004 2006 2008 2010 2012

−30

−20

−10

0

10

20

30

Det

. Ver

tical

(mm

)

2002 2004 2006 2008 2010 2012

PREM/Deg1-Swenson PREM/Deg1-estimated



Elastic (PREM) & Seasonal Load (GRACE + Deg1-Estimated)

−10

−5

0

5

10

Det

. Eas

t (m

m)

2002 2004 2006 2008 2010 2012

GOLD

−10

−5

0

5

10

Det

. Nor

th (m

m)

2002 2004 2006 2008 2010 2012

−30

−20

−10

0

10

20

30

Det

. Ver

tical

(mm

)

2002 2004 2006 2008 2010 2012

PREM/Deg1-Swenson PREM/Deg1-estimated



Elastic (PREM) & Seasonal Load (GRACE + Deg1-Estimated)

Vertical − PREM/Deg1−estimated

−180˚

−180˚

−120˚

−120˚

−60˚

−60˚

0˚

0˚

60˚

60˚

120˚

120˚

180˚

180˚

−60˚ −60˚

−30˚ −30˚

0˚ 0˚

30˚ 30˚

60˚ 60˚

−100 −80 −60 −40 −20 0 20 40 60 80 100 WRMS reduction (%)

East − PREM/Deg1−estimated

−180˚

−180˚

−120˚

−120˚

−60˚

−60˚

0˚

0˚

60˚

60˚

120˚

120˚

180˚

180˚

−60˚ −60˚

−30˚ −30˚

0˚ 0˚

30˚ 30˚

60˚ 60˚

−100 −80 −60 −40 −20 0 20 40 60 80 100 WRMS reduction (%)

North − PREM/Deg1−estimated

−180˚

−180˚

−120˚

−120˚

−60˚

−60˚

0˚

0˚

60˚

60˚

120˚

120˚

180˚

180˚

−60˚ −60˚

−30˚ −30˚

0˚ 0˚

30˚ 30˚

60˚ 60˚

−100 −80 −60 −40 −20 0 20 40 60 80 100 WRMS reduction (%)



WRMS Obs. - Elastic & GRACE + Deg1-EstimatedEAST

NORTH

VERTICAL

WRMS reduction (%)North: 1048 sites (mean 43% )East: 1010 sites (mean 31%)Vert.: 902 sites (mean 34%)

Derived Geocenter motion compatible with other techniques (annual amplitude: Tx=2.3mm,Ty=2.6mm,Tz=4.5mm)

2. Use seasonal deformation to infer Earth rheological properties

OUTLINE

Rheology of the Earth at an annual time scale?

Seasonal loading (GRACE)

+ GNSS Observations


Viscoelasticity in the asthenosphere (70-270km)?

Surface displacements & Seismic cycleEa

st d

ispl

acem

ent n

orm

aliz

ed b

y co

seis

mic

Time since earthquake (yr) (Trubienko et al., 2014)

Earthquake

Postseimic deformation

East

dis

plac

emen

t nor

mal

ized

by

cose

ism

ic

Time since earthquake (yr)

Rapid deformationAfterslip?Transient viscosity?Poroelastic rebound?


Constraints on the asthenosphere transient viscosity

Burger rheology in the asthenosphere derived from postseismic studies

Compatible with seasonal deformation?

η

ηT

µT

µ

Burgers material

Elastic material

Elastic material

H

He

, κ

µ, κ

µ, κ

η

Burger material

η1

η2

µ2

µ1

⌘Tµ ⌘

µTTransient viscosity

Long-term viscosity

Maxwell




−10

−5

0

5

10

2002 2004 2006 2008 2010 2012

−10

−5

0

5

10

2002 2004 2006 2008 2010 2012

SAGA (Brazil)

−30

−20

−10

0

10

20

30

2002 2004 2006 2008 2010 2012

Det

. Nor

th (m

m)

Det

. Eas

t (m

m)

Det

. Ver

tical

(mm

)

Time (years)

Burger 1 Elastic Burger 2= µ/10µT1.1017 Pa.sηT = ,( ) = µ/10µT1.1018 Pa.sηT = ,( ) = µµT1.1017 Pa.sηT = ,( )

Burger 3

(Values from published postseismic studies)




0.2

0.4

0.6

0.8

1µ/ 10

µ/ 5

µ1.1017 5.1017 1.1018

µ T

ηT (Pa.s)

(frac

tion

of

) µ

a) Effect of transient viscosity and shear modulus (H=200km, He=70km)

Horizontal Adm

ittance

b) Effect asthenospheric thickness and transient viscosity (He=70km, = µ/5)µT

0.2

0.4

0.6

0.8

Horizontal Adm

ittance

1

1.1017 5.1017 1.1018ηT (Pa.s)

200

150

100

Asth

enos

pher

ic th

ickn

ess (

km)

c) Effect asthenospheric thickness and transient shear modulus (He=70km, = )ηT 1 10 17. Pa.s

0.4

0.6

0.8

Horizontal Adm

ittance 1200

150

100

Asth

enos

pher

ic th

ickn

ess (

km)

µ µ/ 10µ/ 50.2

µT (fraction of )µ

0.2

0.4

0.6

0.8

1µ/ 10

µ/ 5

µ1.1017 5.1017 1.1018

µ T

ηT (Pa.s)

(frac

tion

of

) µ


Horizontal Adm

ittance


0.2

0.4

0.6

0.8

Horizontal Adm

ittance

1

1.1017 5.1017 1.1018ηT (Pa.s)

200

150

100

Asth

enos

pher

ic th

ickn

ess (

km)


0.4

0.6

0.8

Horizontal Adm

ittance

1200

150

100

Asth

enos

pher

ic th

ickn

ess (

km)

µ µ/ 10µ/ 50.2


0.2

0.4

0.6

0.8

1µ/ 10

µ/ 5

µ1.1017 5.1017 1.1018

µ T

ηT (Pa.s)

(frac

tion

of

) µ


Horizontal Adm

ittance


0.2

0.4

0.6

0.8

Horizontal Adm

ittance

1

1.1017 5.1017 1.1018ηT (Pa.s)

200

150

100

Asth

enos

pher

ic th

ickn

ess (

km)


0.4

0.6

0.8

Horizontal Adm

ittance

1200

150

100

Asth

enos

pher

ic th

ickn

ess (

km)

µ µ/ 10µ/ 50.2


0.2

0.4

0.6

0.8

1µ/ 10

µ/ 5

µ1.1017 5.1017 1.1018

µ T

ηT (Pa.s)

(frac

tion

of

) µ


Horizontal Adm

ittance


0.2

0.4

0.6

0.8

Horizontal Adm

ittance

1

1.1017 5.1017 1.1018ηT (Pa.s)

200

150

100

Asth

enos

pher

ic th

ickn

ess (

km)


0.4

0.6

0.8

Horizontal Adm

ittance

1200

150

100

Asth

enos

pher

ic th

ickn

ess (

km)

µ µ/ 10µ/ 50.2


0.2

0.4

0.6

0.8

1µ/ 10

µ/ 5

µ1.1017 5.1017 1.1018

µ T

ηT (Pa.s)

(frac

tion

of

) µ


Horizontal Adm

ittance


0.2

0.4

0.6

0.8

Horizontal Adm

ittance

1

1.1017 5.1017 1.1018ηT (Pa.s)

200

150

100

Asth

enos

pher

ic th

ickn

ess (

km)


0.4

0.6

0.8

Horizontal Adm

ittance

1200

150

100

Asth

enos

pher

ic th

ickn

ess (

km)

µ µ/ 10µ/ 50.2


0.2

0.4

0.6

0.8

1µ/ 10

µ/ 5

µ1.1017 5.1017 1.1018

µ T

ηT (Pa.s)

(frac

tion

of

) µ


Horizontal Adm

ittance


0.2

0.4

0.6

0.8

Horizontal Adm

ittance

1

1.1017 5.1017 1.1018ηT (Pa.s)

200

150

100

Asth

enos

pher

ic th

ickn

ess (

km)


0.4

0.6

0.8

Horizontal Adm

ittance

1200

150

100

Asth

enos

pher

ic th

ickn

ess (

km)

µ µ/ 10µ/ 50.2


Global Admittance (195 cGPS stations)

Transient Viscosities lower than

0.2

0.4

0.6

0.8

1µ/ 10

µ/ 5

µ1.1017 5.1017 1.1018

µ T

ηT (Pa.s)

(frac

tion

of

) µ


Horizontal Adm

ittance


0.2

0.4

0.6

0.8

Horizontal Adm

ittance

1

1.1017 5.1017 1.1018ηT (Pa.s)

200

150

100

Asth

enos

pher

ic th

ickn

ess (

km)


0.4

0.6

0.8

Horizontal Adm

ittance

1200

150

100

Asth

enos

pher

ic th

ickn

ess (

km)

µ µ/ 10µ/ 50.2


Pa.s

0.2

0.4

0.6

0.8

1µ/ 10

µ/ 5

µ1.1017 5.1017 1.1018

µ T

ηT (Pa.s)

(frac

tion

of

) µ


Horizontal Adm

ittance


0.2

0.4

0.6

0.8

Horizontal Adm

ittance

1

1.1017 5.1017 1.1018ηT (Pa.s)

200

150

100As

then

osph

eric

thic

knes

s (km

)


0.4

0.6

0.8

Horizontal Adm

ittance

1200

150

100

Asth

enos

pher

ic th

ickn

ess (

km)

µ µ/ 10µ/ 50.2


are not compatible with seasonal observations Shear modulus smaller than

1.2

1

0.8

0.6

0.4

Other mechanisms may play a role when low transient viscosities are required to explain observations

Transposable to longer periods of loading, constraining larger viscosities



Phase transformations in the mantle transition zone (400-660km)

Peak to Peak Pressure at 400km

−180˚

−180˚

−120˚

−120˚

−60˚

−60˚

0˚

0˚

60˚

60˚

120˚

120˚

180˚

180˚

−60˚ −60˚

−30˚ −30˚

0˚ 0˚

30˚ 30˚

60˚ 60˚

0 1 2 3 4 5 6 7 8 9 10kPa

Influence of seasonal surface loading in the Earth mantle:

Unconstrained reactions kinetics between seismic waves and postglacial rebound



Induced pressure variations at 400km depth Pressure variations in the mantle from seasonal surface

loading

Mineral transformations

Volume variations at 400-660km(effect on compressibility)

Charge saisonnière

400k

m66

0km

Zone de Transition du

ManteauEquilibre

1 2Seasonal load

➡➡

Mineral Equilibrium



Bulk modulus rheology

ηκ

κ0

κ∞


ηκ

κ0

κ∞


ηκ

κ0

κ∞


ηκ

κ0

κ∞, ~transformation kinetics

, elastic incompressibility, relaxed incompressibility

Incompressibility is frequency dependent

Phase transformations in the mantle are divariantAt thermodynamic equilibrium:

Modeling phase transformations:

0 = ⇢�P

�⇢

0 10 20 30 40 50 600

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Spherical harmonic order

Am

plitu

de

of

Ve

rtic

al d

isp

./E

WH

Elastic

Phase transition

Constraints on Phase transformations in the mantle transition zone

0 10 20 30 40 50 600

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Am

plitu

de o

f H

orizonta

l dis

p./E

WH

Spherical harmonic order

Elastic

Phase transition

+ phase shift < 10days



−10

−5

0

5

10

Det

. Eas

t (m

m)

2002 2004 2006 2008 2010 2012

LHAZ

−10

−5

0

5

10

Det

. Nor

th (m

m)

2002 2004 2006 2008 2010 2012

−30

−20

−10

0

10

20

30

Det

. Ver

tical

(mm

)

2002 2004 2006 2008 2010 2012

PREM/Deg1-Swenson PREM/Deg1-estimated Phase transtions

Best fitting model for completion of 22% of total reaction, kinetics ~ 250 days

−10

−5

0

5

10

Det

. Eas

t (m

m)

2002 2004 2006 2008 2010 2012

GOLD

−10

−5

0

5

10

Det

. Nor

th (m

m)

2002 2004 2006 2008 2010 2012

−30

−20

−10

0

10

20

30

Det

. Ver

tical

(mm

)

2002 2004 2006 2008 2010 2012

PREM/Deg1-Swenson PREM/Deg1-estimated Phase transtions



Best fitting model for completion of 22% of total reaction, kinetics ~ 250 days

North − Mantle Phase Transitions

−180˚

−180˚

−120˚

−120˚

−60˚

−60˚

0˚

0˚

60˚

60˚

120˚

120˚

180˚

180˚

−60˚ −60˚

−30˚ −30˚

0˚ 0˚

30˚ 30˚

60˚ 60˚

−100 −80 −60 −40 −20 0 20 40 60 80 100 WRMS reduction (%)

East − Mantle Phase Transitions

−180˚

−180˚

−120˚

−120˚

−60˚

−60˚

0˚

0˚

60˚

60˚

120˚

120˚

180˚

180˚

−60˚ −60˚

−30˚ −30˚

0˚ 0˚

30˚ 30˚

60˚ 60˚

−100 −80 −60 −40 −20 0 20 40 60 80 100 WRMS reduction (%)

Vertical − PREM/Deg1−estimated

−180˚

−180˚

−120˚

−120˚

−60˚

−60˚

0˚

0˚

60˚

60˚

120˚

120˚

180˚

180˚

−60˚ −60˚

−30˚ −30˚

0˚ 0˚

30˚ 30˚

60˚ 60˚

−100 −80 −60 −40 −20 0 20 40 60 80 100 WRMS reduction (%)


WRMS Obs. - Phase transitions

EAST

NORTH

VERTICAL

WRMS reduction (%)

North: 1054 sites (mean 56% )East: 1015 sites (mean 41%)Vert.: 943 sites (mean 39%)



Conclusions

Seasonal horizontal and vertical displacements are indeed related to surface hydrology

GRACE can be used to accurately model seasonal deformation providing that degree-1 loads coefficients are re-estimated

Seasonal deformation may provide insights on the Earth rheology:

- lower bound on asthenospheric transient viscosities,

- partial occurrence of mantle phase transitions at an annual time scale

Summer

Winter

Pattern of Mw>7 deep earthquakes (>70km) from 1900 to present

(Zhan & Shearer, 2015)

Documents

Reconciling GRACE derived loading deformation with GNSS ... - Chanard.pdf · Reconciling GRACE derived loading deformation with GNSS station position time series MST2, Nepal ... Long