I. Introduction II. Methods in Morphotectonics III. Methods in Geodesy an Remote sensing IV. Relating strain, surface displacement and stress, based on elasticity V. Fault slip vs time VI. Learnings from Rock Mechanics VII. Case studies

V. Fault slip vs time Earthquakes Paleoearthquakes Aseismic creep

We have seen techniques which can be used to estimate the long term slip rate on faults (over many ‘earthquake cycles’, or to document recent slip events of interseismic strain build up. We are now going to see how the time history of slip on a fault over several seismic cycle can be revealed.

Sudden slip events generally leave a geological signature. Aseismic creep is more challenging to document from geology or morphotectonic

Earthquakes REFERENCE Avouac, J. P., F. Ayoub, S. J. Wei, J. P. Ampuero, L. S. Meng, S. Leprince, R. Jolivet, Z. Duputel, and D. Helmberger (2014), The 2013, Mw 7.7 Balochistan earthquake, energetic strike-slip reactivation of a thrust fault, Earth and Planetary Science Letters, 391, Ji, C., D. Wald, and D. V. Helmberger (2002), Source Description of the 1999 Hector Mine, California Earthquake, Part I: Wavelet Domain Inversion Theory and Resolution Analysis, Bull. Seismol. Soc. Am., 92(4), Hernandez, B., F. Cotton, and M. Campillo (1999), Contribution of radar interferometry to a two-step inversion of the kinematic process of the 1992 Landers earthquake, Journal of Geophysical Research-Solid Earth, 104(B6), Bouchon, M., M. Campillo, and F. Cotton, Stress field associated with the rupture of the 1992 Landers, California, earthquake and its implications concerning the fault strength at the onset of the earthquake, Journal of Geophysical Research-Solid Earth, 103, , Kanamori, H., and E. E. Brodsky (2004), The physics of earthquakes, Reports on Progress in Physics, 67(8),

Landsat-8 images: -USGS website -Pre-earthquake images September, 10, 2013 (14 days before) -Post-earthquake images September, 26, 2013 (2 days after) The 2013, Mw7.7 Balochistan Earthquake (Avouac et al., EPSL, 2014)

Strike-parallel Strike-perpendicular The 2013, Mw7.7 Balochistan Earthquake (Avouac et al., EPSL, 2014)

(Zinke, Hollingsworth and Dolan, 2015) The 2013, Mw7.7 Balochistan Earthquake

Rupture follows a preexisting thrust fault within the Makran accretionnary prism (Lawrence, Kahn,Dejong, Farah and Yeats, 1981) Kech Band (Ellouz-Zimmermann et al, 2007)

Comparison with interseismic strain, GPS velocities from Szeliga et al (JGR, 2012) PANG BEDI PANG-BEDI -Interseismic strain is not representative of pre-seismic stress -Or dynamic stresses are dominant and are not parallel to pre-seismic stress LAKC PANG/LAKC

Rupture kinematics from backprojection of teleseismic waveforms -Data: Japanese Hi-net seismic network -Multitaper-MUSIC array processing technique (Meng et al, 2011) -Frequency band: 0.5-2Hz -HF source duration: 50s The 2013, Mw7.7 Balochistan Earthquake

Backprojection of teleseismic waveforms (Hi-NET), 0.5-2Hz The 2013, Mw7.7 Balochistan Earthquake

Finite Source Modeling Parametrisation: – 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) (Ji, C., D. J. Wald and D. V. Helmberger, 2002a.b, BSSA) Inversion: simulated annealing

The 2013, Mw7.7 Balochistan Earthquake -No shallow slip deficit -Rupture velocity ≈3 km/s -Short rise times <8s

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

A common approach to investigate earthquake physics consists of producing kinematic source models from the inversion of seismic records jointly with geodetic data.

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.

Quantification of EQs- Moment Slip Potency (in m 3 ): Seismic Moment tensor ( in N.m, G is shear modulus): Scalar seismic Moment (N.m): where D is average slip, S is surface area  is elastic shear modulus (30 to 50 GPa) Moment Magnitude: (where M 0 in N.m)

 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 infinite rectangular crack). - C is a geometric factor, of order 1, C= 7π/8 for a circular crack, C=½ for a infinite SS fault. Given that and 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 = G 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

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). (Wesnousky, BSSA, 2008) Bigger Earthquakes produce larger average slip 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).

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),