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

III.2-Earthquake Phenomenology

Hector Mine 1999 earthquake (California), Mw= 7.1

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

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

Sud Nord Joined inversion of geodetic, inSAR data and seismic waveforms Hernandez et al., J. Geophys. Res., 1999

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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 ( 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 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  is elastic shear modulus (30 to 50 GPa) M w = 2/3 * log 10 M o Moment Magnitude: (where M 0 in N.m)

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, , in a perfectly elastic body (Eshelbee, 1957) NB: This model produces un realistic infinite stress at crack tips i.The predicted slip distribution is elliptical ii. D mean and D max increase linearly with fault length (if stress drop is constant). Slip on the crack Stress on the crack

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) i.The predicted slip distribution is elliptical with depth ii.Maximum slip should occur at the surface iii.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

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

 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

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  /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).

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 MPa

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.  of the order of 3 MPa on average Bigger Faults Make Bigger Earthquakes Stress drop is generally in the range MPa Quantification of EQs- Scaling Laws

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

(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

(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).

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

(Wesnousky, 2006)

log N(M w )= - bM w + log a where 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 ≥ M w This relation can be rewritten From Kanamori & Brodsky, 2004 The 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 Time (days) n (t) Time (days) n (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), 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, 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), 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, 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), 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),