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*

Seismic wavespropagation

Static permanent deformation

Earthquake occurrence

epicentre

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

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.

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

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

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

Ship models used for deformation modeling

Hayes et al.

USGS

Shao et al.

UCSB

Wei et al.

ARIA Seismic waveformSeismic waveformSeismic waveform

+GPS

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%.

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

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

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.

Thank you