GE177b

I. IntroductionII. Methods in MorphotectonicsIII. Determining the time evolution of fault slip

1- Techniques to monitor fault slip2- EQs phenomenology3- Slow EQs phenomenology4- Paleoseismology 5- Paleogeodesy

Appendix: ‘Elastic Dislocation’ modeling

III.2-Earthquake Phenomenology

Landers 1992 earthquake (California), Mw= 7.3

Terminology, components and measurement of a slip vector

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=6.5Mw=7.1

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

G. Peltzer(based on Massonnet et al, Nature, 1993)

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)

• 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

Kinematic Modeling of Earthquakes

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)

Landers (1992, Mw=7,3)

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

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Joined inversion of geodetic, inSAR data and seismic waveforms

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

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

Observed and predicted waveforms

Strong motion data

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

(Bouchon et al., 1997)

This analysis demonstrates weakening during seismic sliding

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

• Kinematic inversion of earthquake sources show that– Seismic 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.

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

Quantification of EQs- Moment

Slip Potency (in m3):

Seismic Moment tensor ( in N.m):

Scalar seismic Moment (N.m): M0= .D.S where D is average slip, S is surface area and m is elastic shear modulus (30 to 50 GPa)

Mw = 2/3 * log10Mo - 6.0

Moment Magnitude:

(where M0 in N.m)

0 ( )t tM d n n d S

Quantification 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

i. The predicted slip distribution is ellipticalii. Dmean and Dmax increase linearly with fault

length (if stress drop is constant).

Slip on the crack

Stress on the crack

2 24 (1 )

(2 )u a x

8 (1 )

3 (2 )meanD u a

max max

4 (1 )

(2 )D u a

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)

2 22u a z

i. The predicted slip distribution is elliptical with depth

ii. Maximum slip should occur at the surface iii. Dmean and Dmax should increase linearly with

fault width (if stress drop is constant) and be idependent of fault length.

Quantification of EQs: The Elastic crack model

Coseismic surface displacements due to the Mw 7.1 Hectore Mine EQ measured from correlation of optical images(Leprince et al, 2007)

Quantification of EQs: The Elastic crack model

Quantification of EQs: The Elastic crack model

Ds of the order of 5 MPa

Quantification of EQs: The Elastic crack model

• 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

mean meanD DC C

a S

Quantification of EQs- Stress drop

Average static stress drop:

0 meanM D S

3 3/20 0C M a C M S

- 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= 7p/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 M0

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

Ck

S

But S not always well-known; and all type of faults mixed together

Modified from Kanamori & Brodsky, 2004

M0 scales indeed with S3/2 as expected from the simple crack model.Ds of the order of 3 MPa on average

Bigger Faults Make Bigger EarthquakesBigger Faults Make Bigger Earthquakes

3 3/20 0C M a C M S

3Mpa

0.3Mpa

0

2log log log log

3S M C

30Mpa

Stress drop is generally in the range 0.1-10 MPa

Quantification of EQs- Scaling Laws

Bigger Earthquakes Last a Longer TimeBigger Earthquakes Last a Longer TimeFrom Kanamori & Brodsky, 2004

M0 scales approximately with (duration)3

M0= .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

(Wesnousky, BSSA, 2008)

Bigger Earthquakes produce larger average slipBigger Earthquakes produce larger average slip

8 (1 )

3 (2 )meanD L

The mean slip, Dmean, 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

(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 Dmean is highly model dependent. Also the circular crack model should not apply to large magnitude earthquakes (Mw>7, Dmax>3-5m).

max max

2 (1 )

(2 )D u L

Seismogenic depths

typically 0-15km within continent probably primarily thermally controlled (T<350°C)

(from Marone & Scholz, 1988)

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

From Scholz, 1989

log N(Mw)= - bMw + log a where b is generally of the order of 1

N(M0)=aM0-2b/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 (Mw) be number of EQs per year with magnitude ≥ Mw

This relation can be rewritten

From Kanamori & Brodsky, 2004

The Gutenberg-Richter lawThe Gutenberg-Richter law

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 10000Time (days)

0.001

0.01

10

1000n (t)

Time (days)

n (t)

(0)( )

(1 / ) p

nn t

t

where p ~ 1

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.