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Determining the Dislocation Love Numbers using geodetic data
Key Laboratory of Computational GeodynamicsUniversity of Chinese Academy of Sciences
August 13, 2019
Junyan Yang Wenke Sun*
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Seismic wavespropagation
Static permanent deformation
Earthquake occurrence
epicentre
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Seismic Dislocation TheoryDislocation theory describes the relationship between the earthquake
fault model and the physical field changes on the Earth surface. It providesan essential theoretical basis for studying source mechanisms, invertingfault slip models, interpreting seismic physical field changes and geodeticobservation data.
Half-space earth model
A SNREI earth 9model
3-D heterogeneous earth model
Okada, 1985; Okubo, 1992 et al.
Sun et al., 192-2009
Fu et al.,2007-2010
Fault slip model Coseismic deformationDislocation theory
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GRACE gravity satellite
22 0
( , ) ( 1) ( cos sin ) (cos )N n
GRACE mnm nm n
n m
GMg n C m S m Pa
q j j j q= =
D = - D + Då å
2011 Tohoku-Oki earthquake
CSR trend over 2002-2015 with GIA correction
GRACE can provide an extremely accurate, global, and high-resolution estimate of constant and time-variable components of the earth’s gravity field.
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Dislocations in an SNREI Earth model
,
, , ,( , , ) ( ) ( , )solid i j mlm l
n m i ja k a Yy q j q j= å
,
, , ,( , , ) ( ) ( , )ij i j mr lm n
n m i ju a h a Yq j q j= å
Green's function of gravity change:
Green’s function of vertical displacement
Dislocation model
4 independent seismic sources:
Dislocation Love number
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Observation EquationTheoretically, the theoretical coseismic gravity change should be identical to the
GRACE observed gravity change, that is:
( , , ) ( , , )total GRACEg a g aq j q jD = D
Theoretical coseismicgravity change
GRACE observed gravity change
=12 32 33 222 1 0 01 2 3( , ) ( , ) ( , )( ) 4 ( , )n n n
GRACEo n n nnf f f G H w gk k k kq j q j q j p r q j+ + - D- =
unknownFault parameters( , ) (Fault model)if fq j =ocean waterredistribution
GRACE change
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The Inversion Theory
Observation equation
Constraint conduction
Objective function
Ø ABIC (Yabuki and Matsu’ura,1992)Ø Generalized Cross ValidationØ L-curve (Hansen and O’Leary, 1993)
= +Gm d e
0a a= +m m ε2 2 2
0min{|| || (|| || )}a- + -Gm d m m
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Ship models used for deformation modeling
Hayes et al.
USGS
Shao et al.
UCSB
Wei et al.
ARIA Seismic waveformSeismic waveformSeismic waveform
+GPS
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Results gravity dislocation Love number(k)
Blue PREM model
Red inversion from
GRACE
Before
After
122nK
321nK 33 220 0n nK K-
(a) (c)(b)
(f)(e)(d)
(i)(h)(g)
inversion GRACE residual
theory GRACE residual
The gravity change using the inverted dislocation Love numbers/ Green’s function is more consistent with GRACE observation, and the residual error is
reduced by 80%.
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Vertical displacement observed by cGPS
Inland GPS observationHorizontal displacement
observed by cGPS
There are 1232 continuous GPS stations on the island of Japan, which show aneastward striking horizontal component with a maximum value of greater than 5.2 mand a significant downward vertical component with a maximum value of greaterthan 1.1 m
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Results displacement dislocation Love number(h)
122h n 321h n 33 220 0h hn n-
(a) (c)(b)
(f)(e)(d)
inversion GPS observation residual
The dislocation Love number/Green’s function inverted from geodeticobservation data can better reflect the real local tectonic information of the earthand provide more accurate dislocation theory for seismic research in this region.
after
Blue PREM model
Red inversion from GPS
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Conclusion :
Ø We give a method to show using geodetic data (GRACEand GPS) to invert dislocation Love number / Green’s
function;
Ø All of the results imply that the inverted dislocation Lovenumbers are different from the PREM model.
Ø The inverted results show the difference between the localstructure and a global average structure. The coseismic
change using the inverted dislocation Love number/Green’s
function agrees well with the observation, and can better
interpret the geodetic observation.
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Thank you