Using deformation rates in Northern Cascadia to constrain time-dependent stress- and slip-rate on the megathrust
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1 Using deformation rates in Northern Cascadia to constrain time-dependent stress- and slip-rate on the megathrust Lucile Bruhat Paul Segall Stanford University 1
2 50 Interseismic period for the Cascadia subduction zone 50 o N Vancouver 48 o N Seattle 46 o N Portland 44 o N 42 o N 126 o W o W 2
3 50 Interseismic period for the Cascadia subduction zone 50 o N 48 o N 46 o N 44 o N Juan de Fuca plate 42 o N 126 o W o W 3
4 50 Interseismic period for the Cascadia subduction zone 50 o N 48 o N 46 o N 44 o N Juan de Fuca plate North America plate 42 o N 126 o W o W 4
5 50 Interseismic period for the Cascadia subduction zone 50 o N Vancouver 48 o N Seattle 46 o N Portland 44 o N 42 o N 126 o W o W 5
6 Interseismic period for the Cascadia subduction zone Juan de Fuca plate Trench Locked Region Gap North America plate Slow Slip Event Region 45 Depth (km) 1. What is the physical behavior of this gap? [e.g., Hyndman & Wang (1995), Flück et al. (1997), Dragert et al. (2004), Chapman & Melbourne (2009), Wech & Creager (2011), Hyndman (2013)] 2. How deep can the megathrust rupture go? Can it propagate in the gap? in the ETS region? 6
7 Interseismic period for the Cascadia subduction zone Juan de Fuca plate Trench? Gap North America plate Slow Slip Event Region 45 Depth (km) 1. What is the physical behavior of this gap? [e.g., Hyndman & Wang (1995), Flück et al. (1997), Dragert et al. (2004), Chapman & Melbourne (2009), Wech & Creager (2011), Hyndman (2013)] 2. How deep can the megathrust rupture go? Can it propagate in the gap? in the ETS region? 7
8 Interseismic period for the Cascadia subduction zone Juan de Fuca plate Trench? North America plate Slow Slip Event Region 45 Depth (km) 1. What is the physical behavior of this gap? [e.g., Hyndman & Wang (1995), Flück et al. (1997), Dragert et al. (2004), Chapman & Melbourne (2009), Wech & Creager (2011), Hyndman (2013)] 2. How deep can the megathrust rupture go? Can it propagate in the gap? in the ETS region? 8
9 Looking at long-term deformation Horizontal GPS rates 9
10 Looking at long-term deformation Horizontal GPS rates + tide-gauge & leveling uplift rates 10
11 Forward rate-state friction models of SSE 11
12 Forward rate-state friction models of SSE fit the GPS data Fit to the average GPS horizontal displacements 12
13 Averaged over many ETS cycles, stress within the slow slip zone (30-40km) is nearly constant 13
14 Same rate-state friction models of the interseismic slip rate do not fit the long-term rates 14
15 Physics-based models predict too much locking in the gap, up dip the ETS region. Why? - Bias due to use of homogeneous half-space Green s functions? 15
16 Physics-based models predict too much locking in the gap, up dip the ETS region. Why? - Bias due to use of homogeneous half-space Green s functions? 16
17 Physics-based models predict too much locking in the gap, up dip the ETS region. Why? - Bias due to use of homogeneous half-space Green s functions? - Gap creeping due to velocity-strengthening friction behavior? 17
18 Gap creeping due to velocity-strengthening friction behavior? 18
19 Gap creeping due to velocity-strengthening friction behavior? 19
20 Physics-based models predict too much locking in the gap, up dip the ETS region. Why? - Bias due to use of homogeneous half-space Green s functions? - Gap creeping due to velocity-strengthening friction behavior? 20
21 Physics-based models predict too much locking in the gap, up dip the ETS region. Why? - Bias due to use of homogeneous half-space Green s functions? - Gap creeping due to velocity-strengthening friction behavior? Which slip rate distribution is required by the data? 21
22 Inversion of the residuals from the starting physics-based models 22
23 Physics-based models predict too much locking in the gap, up dip the ETS region. Why? - Bias due to use of homogeneous half-space Green s functions? - Gap creeping due to velocity-strengthening friction behavior? Which slip rate distribution is required by the data? 23
24 Physics-based models predict too much locking in the gap, up dip the ETS region. Why? - Bias due to use of homogeneous half-space Green s functions? - Gap creeping due to velocity-strengthening friction behavior? Which slip rate distribution is required by the data? Larger slip rates are necessary within both the gap and the ETS zone relative to the physics-based model with constant shear stress 24
25 Physics-based models predict too much locking in the gap, up dip the ETS region. Why? - Bias due to use of homogeneous half-space Green s functions? - Gap creeping due to velocity-strengthening friction behavior? Which slip rate distribution is required by the data? Larger slip rates are necessary within both the gap and the ETS zone relative to the physics-based model with constant shear stress 25
26 Inversions for interseismic shear stress rates find negative shear stress rates to explain the large slip rates in the gap and the ETS region [Bruhat & Segall, 2016] Inverted shear stress rates (kpa/yr) Corresponding slip rate profile (mm/yr) 35 Inverted slip rate Depth (km) 5 Constant Δτ crack solution Depth (km) Inversions for solutions as close as possible to constant stress 26
27 Inversions for interseismic shear stress rates find negative shear stress rates to explain the large slip rates in the gap and the ETS region [Bruhat & Segall, 2016] Latitude Longitude Vertical rates (Variance Reduction = 95.9%) mm/yr observed predicted Corresponding slip rate profile (mm/yr) 35 Inverted slip rate km Longitude 5 Constant Δτ crack solution Depth (km) Inversions for solutions as close as possible to constant stress 27
28 Rate & State friction numerical models Fit the average ETS displacements No change in shear stress in the ETS region Inversions for shear stress rates Fit the long-term rates Require negative shear stress rates within the gap & ETS region Change with time in effective stress? Fault strength? 28
29 Implicit assumption 29
30 Implicit assumption Can the interseismic transition depth change with time? slip Locking depth length a Along fault distance 30
31 Implicit assumption Can the interseismic transition depth change with time? 1 Slip s(z,t) =f(z,t)v 1 t slip Slip rate ds dt = f(z,t)v 1 Locking depth length a Along fault distance 31
32 Implicit assumption Can the interseismic transition depth change with time? 1 Slip s(z,t) =f(z,t)v 1 t slip Migrating up dip length a Slip rate ds dt = f(z,t)v 1 + v Locking depth Along fault distance 32
33 Implicit assumption Can the interseismic transition depth change with time? 1 Slip s(z,t) =f(z,t)v 1 t slip Migrating up dip Locking depth length a Along fault distance Slip rate ds dt = f(z,t)v 1 + v = f(z,t)v 1 + v Propagation rate 33
34 Temporal evolution of the locking depth Numerical simulations from Jiang & Lapusta (2016) Locking depth The locking depth migrates up dip à the size of the locked region reduces w/ time 34
35 Crack model for the interseismic slip profile Spatial variable Expand stress drop in Chebyshev polynomials: = 1X c i (t)t i ( (t)) i=0 1 X 1 35
36 Crack model for the interseismic slip profile Spatial variable X X For a crack with finite stress at the Xcrack tip and driven by steady displacement: X 1X Slip s = tg( (t)) + a(t) c i (t)f i ( (t)) i=2 X 1X X = µ v1 t a(t) (t)+µ 1 X i=2 1X c i (t)t i ( (t)) Slip rate ds dt = g( (t)) + a(t) 1 1X i=2 i (t) f i ( (t)) t a(t) + # 1X c i (t)v( (t)) i=2 Propagation effect 36
37 Effect of the propagation time 37
38 Crack model for the interseismic slip profile New method to derive expressions for stress drop, slip and slip rate Ø Allows for the up dip propagation of the creeping region Ø Massively underdetermined (as most geodetic inversions) Ø Can be used to invert deformation rates using MCMC methods under specific assumptions (c i = 0, stress characteristics in the ETS region, etc.) to look for extremal models (e.g., bounds on propagation speed) Ø Examples for Cascadia 38
39 Application to Cascadia Non propagating crack, invert for c i (N=6) Best fitting model (MCMC inversion) Locking depth: 20.5km Slip rate (mm/yr) 30 Vertical rates (VR = 98.1%) 50 3 mm/yr observed predicted 49 Horizontal rates (VR = 92%) mm/yr observed predicted Latitude 48 Latitude Gap ETS Depth (km) km Longitude km Longitude 39
40 Application to Cascadia Propagating crack Best fitting model (MCMC inversion) Locking depth: 21km Up-dip propagation velocity: 33.4m/year 40
41 Application to Cascadia Posterior distributions 41
42 X Application to Cascadia Models w/ no change in shear stress in the ETS region Minimizing 1/2 (d ˆd) ( = ETS) = 0 Stress rates do take into account the free surface effects Assuming c i / t = 0 42
43 Application to Cascadia Models w/ no change in shear stress in the ETS region Best fitting model (MCMC inversion) Locking depth: 21.9km Up-dip propagation velocity: 41m/year 43
44 Rate & State friction numerical models Fit the average ETS displacements No change in shear stress in the ETS region Inversions for shear stress rates Fit the long-term rates Require negative shear stress rates within the gap & ETS region Change with time in effective stress? Fault strength? 44
45 Rate & State friction numerical models Fit the average ETS displacements No change in shear stress in the ETS region Inversions for shear stress rates Fit the long-term rates Require negative shear stress rates within the gap & ETS region Change with time in effective stress? Fault strength? Propagating crack Fit the long-term rates Allows for models that with negative shear stress rate within the gap but no change in the ETS region Gap acts as a region of fault weakening. 45
46 Rate & State friction numerical models Fit the average ETS displacements No change in shear stress in the ETS region Inversions for shear stress rates Fit the long-term rates Require negative shear stress rates within the gap & ETS region Change with time in effective stress? Fault strength? Propagating crack Fit the long-term rates Allows for models that with negative shear stress rate within the gap but no change in the ETS region Gap acts as a region of fault weakening. Bruhat & Segall, JGR, 2016 Bruhat & Segall, in review 46
47 Conclusions: u New method to estimate interseismic slip rates u Include the possibility for the creeping zone to propagate up dip u Between purely kinematic inversions and fully physics-based models u Possible mechanical explanations u Gap locked after deep rupture propagation, interseismic transition propagating up due to reloading by deep creep [Jiang & Lapusta, 2016]? u For Cascadia: current (?) locking depth (20-22km), steep slip rate gradient at bottom of the locked region, and important slip deficit in gap & ETS region Questions? lbruhat@stanford.edu Funding from: Thanks! 47
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