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

GPS and seismic data showing the occurrence of episodic tremor and slip (ETS) at Victoria, British Columbia. The blue circles show daily changes in the east component of position of the continuous GPS site ALBH relative to Penticton which is considered fixed on the North America plate. The green line represents long-term eastward motion due to steady deformation caused by the locked portion of the plate interface on the Cascadia subduction zone. The red line segments show distinct periods of 14 to 15 months with elevated eastward trends, each punctuated by a 1 to 2-week reversal of motion that has been modelled by slow slip on the deeper plate interface. The black graph at the bottom shows the number of hours within a sliding 10-day window that show distinct, low-frequency, non-impulsive seismic activity that has been called "tremor". The correlation of the periods of slow slip with periods of extended tremor prompted the naming of this phenomena as Episodic Tremor and Slip. Periodic aseismic slip events on the Cascadia subduction interface (Herb Dragert and Coll.)

First Slow Eqs Doumented Linde, A., M. Gladwin, M. Johnson, R. Gwyther and R. Bilham, (1996), A slow earthquake sequence on the San Andreas fault, 383,

from Toda & Stein (JGR, 2003)

“Slow earthquakes” Phenomenology

7 The Guerrero subduction zone Perez-Campos et al., 2009 Radiguet et al ‣ Guerrero seismic gap ‣ Flat subduction geometry ‣ GPS stations located above the interface ‣ Guerrero seismic gap ‣ Flat subduction geometry ‣ GPS stations located above the interface

8 Slow slip events ‣ Duration 6 months - 1 year ‣ Recurrence ~ 4 years ‣ Surface displacements ~5 cm

Fault is locked in Interseismic Stable aseismic slip Northward ‘elastic’ displacement of the whole region North If slip is stick-slip due to reccuring Eqs we expect : D North Time EQ (courtesy I. Manighetti) Slow EQs along the Mexican subduction zone

10 ‘Static’ Inversion ‣ Linear inversion (least-square) Controls the weighting of each data in the inversion Correlation between parameters (smoothing) ‣ Direct problem ‣ Interface geometry Tarantola 2005

11 Static displacements for three SSEs Radiguet et al., JGR

12 Slip distributions for three SSEs ‣ Important shallow slip (15-25 km) Radiguet et al., JGR

13 Spatio-temporal evolution of surface displacements ‣ Variations in the direction of surface displacements with time Vergnolle et al JGR

14 Inversion of GPS time series fault plane Slip evolution in each subfault ‣ Source parameterization ‣ Simple description of the source ‣ Analysis similar to regular eaqrthquakes with: ‣ longer time constant ‣ quasi-static problem ‣ Linearized least-square inversion Tarantola & Valette 1982 Liu et Archuleta 2006

15 Constraint on the propagation velocity Time - direct model - constant Vr Horizontal GPS displacement with time

16 5 km/j Constraint on the propagation velocity Time - direct model - constant Vr Horizontal GPS displacement with time Constraint on the propagation velocity

17 1 km/j Constraint on the propagation velocity Time - direct model - constant Vr Horizontal GPS displacement with time Constraint on the propagation velocity

18 ‣ Propagation velocity around 1km/day 0.5 km/j Constraint on the propagation velocity Time - direct model - constant Vr Horizontal GPS displacement with time Radiguet et al GJI Constraint on the propagation velocity

19 Spatio-temporal evolution of the 2006 SSE Time Horizontal displacements: data (black) and model (red) model data Radiguet et al GJI Snapshot of the slip propagation (50 days)

20 Inter-SSE displacements and short-term coupling séismes lentsséismes inter-SSE displacement velocity (mm/yr) Coupling coefficient on the interface ‣ Short-term coupling quasi- homogeneous along-strike ‣ SSEs occur in a region of high short term coupling ‣ Short-term coupling quasi- homogeneous along-strike ‣ SSEs occur in a region of high short term coupling Radiguet et al., JGR

“Slow earthquakes” Phenomenology (Ide et al, nature, 2007)

References on ‘Slow earthquakes’ Dragert, H., K. Wang and T.S. James (2001), A silent slip event on the deeper Cascadia subduction interface, Science, 292, Hirose, H., K. Hirahara, F. Kimata, N. Fujii, and S. Miyazaki (1999), A slow thrust slip event following the two 1996 Hyuganada earthquakes beneath the Bungo Channel, southwest Japan, Geophysical Research Letters, 26(21), Ide, S., G. C. Beroza, D. R. Shelly, and T. Uchide (2007), A scaling law for slow earthquakes, Nature, 447(7140), Miller, M., T. Melbourne, D.J. Johnson, W. Q. Summer (2002), Periodic slow earthquakes from the Cascadia subduction zone, Science, 295, Rogers, G., and H. Dragert (2003), Episodic tremor and slip on the Cascadia subduction zone: The chatter of silent slip, Science, 300(5627), Wallace, L. M., and J. Beavan (2006), A large slow slip event on the central Hikurangi subduction interface beneath the Manawatu region, North Island, New Zealand, Geophysical Research Letters, 33(11). Yoshioka, S., T. Mikumo, V. Kostoglodov, K. M. Larson, A. R. Lowry, and S. K. Singh (2004), Interplate coupling and a recent aseismic slow slip event in the Guerrero seismic gap of the Mexican subduction zone, as deduced from GPS data inversion using a Bayesian information criterion, Physics of the Earth and Planetary Interiors, 146(3-4), Radiguet, M., F. Cotton, M. Vergnolle, M. Campillo, A. Walpersdorf, N. Cotte, and V. Kostoglodov (2012), Slow slip events and strain accumulation in the Guerrero gap, Mexico, Journal of Geophysical Research-Solid Earth, Radiguet, M., F. Cotton, M. Vergnolle, M. Campillo, B. Valette, V. Kostoglodov, and N. Cotte (2011), Spatial and temporal evolution of a long term slow slip event: the 2006 Guerrero Slow Slip Event, Geophysical Journal International, 184(2),