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

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)

Planar strike-slip fault Slip-weakening friction

Gc = fracture

energy

Initial stress 0(x,z)

The “standard” dynamic rupture problem

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

Initial conditions ?

SBIEM simulations by J. Ripperger (ETHZ)

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

Fault constitutive law (“friction law”) ?

Input: Geological field observations Geophysical boreholes Laboratory Strong motion seismology

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

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

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)

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

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

Scale contraction issue

Displacement

Rupture growth

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

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)

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

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

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)