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Earthquake dynamics and source inversion

Earthquake dynamics and source inversion. Jean-Paul Ampuero ETH Zurich. Overview. The forward problem: challenges, open questions Dynamic properties inferred from kinematic models Direct inversion for dynamic properties: which parameters can be resolved ? Perspectives.

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Earthquake dynamics and source inversion

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  1. Earthquake dynamics and source inversion Jean-Paul Ampuero ETH Zurich

  2. Overview • The forward problem: challenges, open questions • Dynamic properties inferred from kinematic models • Direct inversion for dynamic properties: which parameters can be resolved ? • Perspectives

  3. The “standard” dynamic rupture problem Planar strike-slip fault Slip-weakening friction Gc= fracture energy Initial stress s0(x,z) Basic ingredients: • linear elastic medium (wave equation) • a pre-existing fault (slip plane) • Friction: a non linear relation between fault stress and slip (a mixed boundary condition) • initial conditions (stress)

  4. The “standard” dynamic rupture problem Planar strike-slip fault Slip-weakening friction Gc= fracture energy Initial stress s0(x,z)

  5. Fault geometry and velocity model ? Boundary element dynamic simulation of Landers earthquake, by Hideo Aochi P-wave tomography and structural interpretation near Parkfield, by Malin et al 2006

  6. Initial conditions ? SBIEM simulations by J. Ripperger (ETHZ)

  7. Fault constitutive law (“friction law”) ? • Input: • Geological field observations • Geophysical boreholes • Laboratory • Strong motion seismology • Candidate ingredients: • Dry friction • Frictional heating • Melting • Fluid thermal pressurization • Off-fault damage • Compaction / porosity evolution

  8. Fault constitutive law (“friction law”) ? Input: • Geological field observations • Geophysical boreholes • Laboratory • Strong motion seismology

  9. Fault constitutive law (“friction law”) ? • Upscaling of fault constitutive law from micro- to macroscopic scales ? • (homogeneization) Candidate ingredients at the micro level: • Dry friction • Frictional heating • Melting • Fluid thermal pressurization • Off-fault damage • Compaction / porosity evolution • Geometrical roughness Rupture propagation on a multi-kinked fault, solved by SEM (Madariaga, Ampuero and Adda-Bedia 2006)

  10. Inferring fault dynamic properties from seismograms Seismograms Slip (x,z,t) Stress (x,z,t) Stress / slip relation Kinematic inversion Elastic wave equation Plot Kobe earthquake Ide and Takeo (1997)

  11. Inferring fault dynamic properties from seismograms Effect of time filtering the initial data at cut-off period Tc (Spudich and Guatteri 2004) Stress / slip relation Space-time resolution problems Interpretation Kobe earthquake Ide and Takeo (1997)

  12. Inferring fault dynamic properties from seismograms One model 19 models with low residuals Non-linear dynamic inversion of the Tottori earthquake, with neighborhood algorithm, by Peyrat and Olsen (2004) Required 60 000 forward simulations

  13. A B Same Gc same strong motion <1Hz Fracture energy Gc controls dynamic rupture Inversion of dynamic friction parameters with frequency band-limited data suffers from strong trade-off Dynamic source inversions of the Tottori earthquake by Peyrat and Olsen 2004

  14. Scale contraction issue Displacement Rupture growth

  15. Scale contraction issue Slip velocity snapshot Energy dissipation and high gradients concentrated within a process zone Problem: The process zone shrinks affecting numerical resolution

  16. The view from classical fracture mechanics Linear elastic fracture mechanics (LEFM) predicts a stress singularity at the tip of an ideal crack. crack Inelastic process zone K-dominant region The stress concentration must be physically accommodated by nonlinear material behavior (damage, plasticity, micro-fractures) Kostrov, Freund, Husseini, Kikuchi, Ida, Andrews (60-70s)

  17. Crack Size = L Gc controls dynamic rupture: theory Classical fracture mechanics +Griffith criterion  local energy balance at the rupture front: Gc = G(vr, L, Dt) • crack tip equation of motion relates rupture speed to Gc Gc = f(vr) Gstatic(L,Dt) Gc = f(vr) K2(L,Dt)/2m where: stress intensity factor = K ≈ Dt √L and f(vr) is a universal decreasing function energy release rate, energy flow towards the crack tip fracture energy

  18. Summary • So far: • The development of dynamic source inversion methodologies is in its infancy • Parameterization issue • Resolution limited by: • Data band-pass filtering • Attenuation • Inaccurate Green’s functions, poor knowledge of the crust • Scarce instrumentation • Coarse parameterization, computational cost • Ideal wish-list: • Reach higher frequencies • Understand the meaning of the inferred macroscopic parameters • Faster, better forward solvers

  19. 2.5D dynamic inversion M7.9 Denali earthquake from inversion of GPS data (Hreinsdottir et al, 2006) Dynamic source inversion = from seismograms +GPS +InSAR to spatial distribution of initial stress and fracture energy along the fault Computationally expensive and low vertical resolution • Reduce the problem dimensionality: solve rupture dynamics averaged over the seismogenic depth (3D wave equation  2D Klein-Gordon equation)

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