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GE177b  I. Introduction II. Methods in GE177b  I. Introduction II. Methods in

GE177b I. Introduction II. Methods in - PowerPoint Presentation

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GE177b I. Introduction II. Methods in - PPT Presentation

Morphotectonics III Determining the time evolution of fault slip 1 Techniques to monitor fault slip 2 EQs phenomenology 3 Slow EQs phenomenology 4 Paleoseismology 5 Paleogeodesy ID: 804412

nord slip crack sud slip nord sud crack fault rupture model eqs seismic stress elastic drop earthquake earthquakes quantification

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Slide1

GE177b

I. Introduction

II. Methods in

Morphotectonics

III.

Determining the time evolution of fault slip

1- Techniques to monitor fault slip

2- EQs phenomenology

3- Slow EQs phenomenology

4-

Paleoseismology

5-

Paleogeodesy

Appendix:

‘Elastic Dislocation’ modeling

Slide2

III.2-Earthquake Phenomenology

Slide3

Hector Mine 1999 earthquake (California), Mw= 7.1

Slide4

Landers 1992 earthquake (California), Mw= 7.3

Slide5

Terminology, components and measurement of a slip vector

Slide6

Yet, these measurements only give a ‘partial’ vision of the slip distribution on the rupture fault, for they only represent the (small?) portion of the slip that has reached the surface.

Besides, such

complete

measurements are quite

rare and really reliable for strike slip faults only.

(

Manighetti

et al, 2007)

Mw=7.3

Mw=7.6

Mw=7.1

Mw=7.3

Mw=6.5

Mw=7.1

Slide7

C

o-seismic

displacement

field due to the 1992, Landers EQ

G. Peltzer

(based on

Massonnet

et al, Nature, 1993)

Slide8

Co-seismic displacement field due to the 1992, Landers EQ

G. Peltzer

Here the measured SAR

interferogram

is compared with a theoretical

interferogram

computed based on the field measurements of co-seismic slip using the elastic dislocation theory

This is a validation that

coseismic

deformation can be

modelled

acurately

based on the elastic dislocation theory

(based on

Massonnet

et al, Nature, 1993)

Slide9

A common approach to investigate earthquake physics consists of producing

kinematic source models

from the inversion of seismic records jointly with geodetic data.

Seth Stein’s web site

Slide10

Kinematic Modeling of Earthquakes

Slide11

Kinematic Modeling of Earthquakes

Parameters to find

out (assuming a propagating slip pulse)

Slip at each

subfault

on the fault

Rise time

(the time that takes for slip to occur at each point on the

fault).

Rupture velocity

(how fast does the rupture propagate)

Slide12

Landers (1992, Mw=7,3)

Hernandez et al., J.

Geophys

.

Res

., 1999

Slide13

Slide14

Sud

Nord

Joined

inversion of

geodetic

,

inSAR

data and

seismic

waveforms

Hernandez

et al., J.

Geophys

.

Res

.,

1999

Slide15

Sud

Nord

Slide16

Sud

Nord

Slide17

Sud

Nord

Slide18

Sud

Nord

Slide19

Sud

Nord

Slide20

Sud

Nord

Slide21

Sud

Nord

Slide22

Sud

Nord

Slide23

Sud

Nord

Slide24

Sud

Nord

Slide25

Sud

Nord

Slide26

Sud

Nord

Slide27

Sud

Nord

Slide28

Sud

Nord

Slide29

Sud

Nord

Slide30

Sud

Nord

Slide31

Sud

Nord

Slide32

Sud

Nord

Slide33

Sud

Nord

Slide34

Sud

Nord

Slide35

Sud

Nord

Slide36

Sud

Nord

Slide37

Sud

Nord

Slide38

Sud

Nord

Hernandez et al., J. Geophys. Res., 1999

Slide39

Observed and predicted waveforms

Strong motion data

Hernandez et al., J. Geophys. Res., 1999

Slide40

(Bouchon et al., 1997)

Slide41

This analysis demonstrates weakening during seismic sliding

Slide42

Some characteristics of the Mw 7.3 Landers EQ:

Rupture length:

~

75 km

Maximum slip:

~

6m

Rupture duration:

~

25 seconds

Rise time: 3-6 seconds

Slip rate: 1-2 m/s

Rupture velocity:

~

3 km/s

Slide43

Kinematic inversion of earthquake sources show thatSeismic ruptures are “pulse like” for large earthquakes (Mw>7) with rise times of the order of 3-10s typically

(

e.g

, Heaton, 1990)

the rupture velocity is variable during the rupture but generally close to Rayleigh waves velocity (2.5-3.5

kms

) and sometimes ‘

supershear

’ (>3.5-4km/s)

Seismic sliding rate is generally of the order of 1m/s

Large earthquakes typically ruptures faults down to 15km within continent and down to 30-40km along

subduction

Zones.

Slide44

P = D.S (Integral of slip over rupture area)

Quantification of

EQs- Moment

Slip Potency (in m

3

):

Seismic

Moment tensor

( in

N.m

):

Scalar seismic Moment (

N.m

):

M

0

=

.D.S

where D is average slip, S is surface area

and

m

is elastic shear modulus (30 to 50

GPa

)

M

w

= 2/3 * log

10

M

o

- 6.0

Moment Magnitude:

(where M0 in N.m)

Slide45

Quantificatio

n of EQs:

The

Elastic

crack

model

See Pollard et

Segall

, 1987 or

Scholz

, 1990 for more details

A

planar

circular crack of radius a with

uniform

stress drop,

Ds

,

in a perfectly elastic body (Eshelbee, 1957)

NB: This model produces

un realistic infinite stress at crack tips

The predicted

slip

distribution is

elliptical

D

mean

and

D

max

increase linearly with fault length (if stress drop is constant).

Slip

on the crackStress on the crack

Slide46

See Pollard et

Segall

, 1987 or

Segall

, 2010 for

more details

A rectangular fault extending from the surface to a depth h, with uniform stress drop (‘infinite Strike-Slip fault)

The predicted

slip

distribution is

elliptical with depth

Maximum slip should occur at the surface

D

mean

and

D

max

should increase linearly with fault width (if stress drop is constant) and be

idependent

of fault length.

Quantification of EQs: The Elastic crack model

Slide47

Coseismic surface displacements due to the Mw 7.1 Hectore

Mine EQ measured from correlation of optical images

(

L

eprince

et al, 2007)

Quantification of EQs: The Elastic crack model

Slide48

Quantification of EQs: The Elastic crack model

Slide49

Ds

of the order of 5

MPa

Quantification of EQs: The Elastic crack model

Slide50

The crack model works approximately in this example, In general the slip distribution is more complex than perdicted from this theory either due to the combined effects of non uniform prestress, non uniform stress drop and fault geometry.

The theory of elastic dislocations can always be used to model surface deformation predicted for any slip distribution at depth,

Quantification of EQs: The Elastic crack model

Slide51

Quantification of

EQs- Stress drop

Average

static stress drop

:

S

is rupture area;

a

is characteristic fault length (fault radius in the case of a circular crack, width of

inifinite

rectangular crack).

C

is a geometric factor, of order 1, C= 7

p

/8 for a circular crack, C=½ for a infinite SS fault.

is equivalent to an elastic stiffness (1-D spring and slider model).

Given that

The stress drop can be estimated from the seismological determination of M

0

and from the determination of the surface ruptured area (geodesy, aftershocks).

Slide52

M

0

~

Δσ

S

3/2

M

0

linked to stress drop

Es ~ ½

Δσ

D

mean

Seismic

Energy

M

0

= μ

DS

Es/M

0

~

Δσ

/2μ

Stress

Drop

Stress

drop is generally in the range 0.1-10

MPa

Slide53

But S not always well-known; and all

type of faults

mixed

together

Modified from

Kanamori

& Brodsky, 2004

M

0

scales indeed with S

3/2

as expected from the simple crack model.

Ds

of the order of 3

MPa

on average

Bigger Faults Make Bigger Earthquakes

Stress

drop is generally in the range 0.1-10

MPa

Quantification of

EQs- Scaling Laws

Slide54

Bigger Earthquakes Last a Longer Time

From

Kanamori

& Brodsky, 2004

M

0

scales

approximately with

(duration)

3

M

0

=

.D.S

2004, Mw 9.15 Sumatra Earthquake (600s)

Quantification of

EQs- Scaling Laws

Rupture velocity during seismic ruptures varies by less than 1 order of magnitude

Slide55

(

Wesnousky

, BSSA, 2008)

Bigger Earthquakes produce larger average slip

The mean slip,

D

mean

, is generally larger for larger earthquakes, but not as linear as expected from the crack model. Recall:

where here L is fault Length (2a for a circular crack)

We expect the circular crack model not to apply any more as the rupture start ‘saturating’ the depth extent of the

seismogenic

zone (M>7).

Quantification of

EQs- Scaling Laws

Slide56

(

Manighetti

et al, 2007)

The maximum slip,

Dmax

, is generally larger for larger earthquakes, but not as linear as expected from the crack model. Recall:

where here L is fault Length (2a for a circular crack)

The

pb

might be that the estimate of

D

mean

is highly model dependent. Also the circular crack model should not apply to large magnitude earthquakes (Mw>7,

Dmax

>3-5m).

Slide57

Seismogenic

depths

typically

0-15km

within continent

probably primarily thermally controlled (

T<350°C)

(from Marone & Scholz, 1988)

Slide58

In oceans, the lower friction stability transition corresponds approximately with the onset of ductility in olivine, at about 600°C.

From Scholz, 1989

Slide59

(

Wesnousky

, 2006)

Slide60

(

Wesnousky

, 2006)

Slide61

(

Wesnousky

, 2006)

Slide62

log N(M

w

)=

-

bM

w

+

log

a

w

here b is generally of the order of 1

N(M

0

)=aM

0

-2b/3

Here the seismicity catalogue encompassing the entire

planet. It shows that every year we have about 1 M≥8 event, 10 M>7 events …

Let N (M

w) be number of EQs per year with magnitude ≥ Mw

This relation can be rewritten

From

Kanamori

& Brodsky, 2004

The Gutenberg-Richter law

Slide63

The Omori law (aftershocks)

The

decay of aftershock activity follows a

power law

.

Many different mechanisms have been proposed to explain such decay: post-seismic creep, fluid diffusion, rate- and state-dependent friction, stress corrosion, etc… but in fact, we don’t know…

Aftershock decay since the 1891, M=8

Nobi

EQ: the Omori law holds over a very long time!

Same for 1995 Kobe EQ

1

100

10000

Time (days)

0.001

0.01

10

1000

n (t)

Time (days)

n (t)

where p

~

1

Slide64

References on EQ phenomenology and scaling laws

Kanamori

, H., and E. E. Brodsky (2004), The physics of earthquakes,

Reports on Progress in Physics, 67(8), 1429-1496.

Heaton, T. H. (1990), Evidence for and implications of self-healing pulses of slip in earthquake rupture,

Physics of the Earth and Planetary Interiors, 64, 1-20.

Wells, D. L., and K. J. Coppersmith (1994), New Empirical Relationships Among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement,

Bulletin of the Seismological Society of America

,

84

(4), 974-1002.

Hernandez, B., F. Cotton, M.

Campillo

, and D.

Massonnet

(1997), A comparison between short term (co-seismic) and long term (one year) slip for the Landers earthquake: measurements from strong motion and SAR

interferometry, Geophys

. Res. Lett., 24, 1579-1582.Manighetti, I., M. Campillo, S.

Bouley, and F. Cotton (2007), Earthquake scaling, fault segmentation, and structural maturity, Earth and Planetary Science Letters, 253(3-4), 429-438.Wesnousky, S. G. (2008), Displacement and geometrical characteristics of earthquake surface ruptures: Issues and implications for seismic-hazard analysis and the process of earthquake rupture,

Bulletin of the Seismological Society of America, 98(4), 1609-1632.