Earthquake dynamics and source inversion
description
Transcript of Earthquake dynamics and source inversion
![Page 1: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/1.jpg)
Earthquake dynamics and source inversion
Jean-Paul Ampuero
ETH Zurich
![Page 2: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/2.jpg)
Overview
The forward problem: challenges, open questions Dynamic properties inferred from kinematic models Direct inversion for dynamic properties: which
parameters can be resolved ? Perspectives
![Page 3: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/3.jpg)
The “standard” dynamic rupture problem
Planar strike-slip fault Slip-weakening friction
Gc = fracture
energy
Initial stress 0(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)
![Page 4: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/4.jpg)
Planar strike-slip fault Slip-weakening friction
Gc = fracture
energy
Initial stress 0(x,z)
The “standard” dynamic rupture problem
![Page 5: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/5.jpg)
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
![Page 6: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/6.jpg)
Initial conditions ?
SBIEM simulations by J. Ripperger (ETHZ)
![Page 7: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/7.jpg)
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
![Page 8: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/8.jpg)
Fault constitutive law (“friction law”) ?
Input: Geological field observations Geophysical boreholes Laboratory Strong motion seismology
![Page 9: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/9.jpg)
Fault constitutive law (“friction law”) ?
Rupture propagation on a multi-kinked fault, solved by SEM (Madariaga, Ampuero and Adda-Bedia 2006)
Upscaling of fault constitutive law from micro- to macroscopic scales ?
(homogeneization)
Candidate ingredients at the micro level:Dry frictionFrictional heatingMeltingFluid thermal pressurizationOff-fault damageCompaction / porosity evolutionGeometrical roughness
![Page 10: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/10.jpg)
Inferring fault dynamic properties from
seismograms
Kobe earthquake Ide and Takeo (1997)
Kinematic inversion
Elastic wave equation
Seismograms
Slip (x,z,t)
Stress (x,z,t)
Stress / slip relation
Plot
![Page 11: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/11.jpg)
Interpretation
Inferring fault dynamic properties from
seismograms
Kobe earthquake Ide and Takeo (1997)
Stress / slip relation
Space-time resolution problems
Effect of time filtering the initial data at cut-off period Tc
(Spudich and Guatteri 2004)
![Page 12: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/12.jpg)
Inferring fault dynamic properties from
seismograms
Non-linear dynamic inversion of the Tottori earthquake, with neighborhood algorithm, by Peyrat and Olsen (2004)
Required 60 000 forward simulations
One model 19 models with low residuals
![Page 13: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/13.jpg)
Fracture energy Gc controls dynamic rupture
Inversion of dynamic friction parameters with frequency band-limited data suffers from strong trade-off
Same Gc same strong motion <1Hz
A B
Dynamic source inversions of the Tottori earthquake by Peyrat and Olsen 2004
![Page 14: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/14.jpg)
Scale contraction issue
Displacement
Rupture growth
![Page 15: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/15.jpg)
Scale contraction issue
Slip velocity snapshot
Problem: The process zone shrinks affecting numerical
resolution
Energy dissipation and high gradients concentrated within a process process zonezone
![Page 16: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/16.jpg)
Linear elastic fracture mechanics (LEFM) predicts a stress singularity at the tip of an ideal crack.
crack
K-dominant
regionThe stress concentration must be physically accommodated by nonlinear material behavior (damage, plasticity, micro-fractures)
Inelastic process zone
The view from classical fracture mechanics
Kostrov, Freund, Husseini, Kikuchi, Ida, Andrews (60-70s)
![Page 17: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/17.jpg)
Gc controls dynamic rupture: theory
Classical fracture mechanics +Griffith criterion local energy balance at the rupture front:
Gc = G(vr, L, )
crack tip equation of motion relates rupture speed to Gc
Gc = f(vr) Gstatic(L,)
Gc = f(vr) K2(L,)/2
where: stress intensity factor = K ≈ √Land f(vr) is a universal decreasing function
fracture energy
energy release rate, energy flow towards the crack tip
Crack
Size =
L
![Page 18: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/18.jpg)
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
![Page 19: Earthquake dynamics and source inversion](https://reader036.fdocuments.in/reader036/viewer/2022081520/56814cc4550346895db9d0ea/html5/thumbnails/19.jpg)
2.5D dynamic inversion
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)
M7.9 Denali earthquake from inversion of GPS data (Hreinsdottir et al, 2006)