Dynamic source inversion for physical parameters controlling the 2017 Lesvos earthquake F. Kostka 1, E. Sokos 2, J. Zahradník 1, F. Gallovič 1 1 Charles University in Prague, Faculty of Mathematics and Physics, Dept. of Geophysics, Czech Republic 2 University of Patras, Department of Geology, Laboratory of Seismology, Greece
The 12 th June, 2017 Lesvos earthquake Aegean sea, south of Lesvos Normal faulting mechanism, Mw 6.3 Hypocentral depth (GI NOA): (12.0 ± 1.7) km Centroidal depth: 8 km (3D Grid search, ISOLA, regional data) SW-dipping fault (40 ) consisent with hypocenter and centroid Multiple point source inversion dominated by a single subevent. The closest village to the epicenter was Plomari, but the most struck was Vrisa (1 casualty, heavy structural damage). USGS Red diamond: hypocenter Beachball at the centroid Blue stars: major aftershocks (M>3.9)
Kinematic inversion of the Lesvos earthquake (Kiratzi, 2018) Broad band and strong motion data, 0.05-0.08 Hz Slip confined in a shallow patch, 20 km 10 km along strike and dip, respectively. Mainly unilateral propagation towards WNW Rupture speed: 3.1 km/s Rupture duration: ~6.5 s. M 0 : 4.2 10 18 Nm (MW 6.35) Stress drop: 3.6 MPa Kiratzi, 2018
Method dynamic inversion
Dynamic source inversion Slip Slip rate Green s functions Hypocenter Fault plane Distribution of prestress frictional parameters Compare with observed data and generate new models (Monte Carlo) Dynamic rupture simulation Friction law E.g. Peyrat and Olsen (2004), Ruiz and Madariaga (2011), Twardzik et al. (2014) Evolution of slip
Linear slip-weakening friction (Ida, 1972) 1. Zero slip as long as traction T is smaller than the strength, T u (rupture criterion) 2. When the traction reaches T u, it starts evolving according to: T D = T u 1 D D c for 0 < D < D C T D = 0 otherwise. where D Slip T- Friction T u - Upper yield stress (strength) D C critical slip distance G C = T 0 D C /2 fracture energy density
Linear slip-weakening friction (Ida, 1972) 1. Zero slip as long as traction T is smaller than the strength, T u (rupture criterion) 2. When the traction reaches T u, it starts evolving according to: T D = T u 1 D D c for 0 < D < D C T D = 0 otherwise. where D Slip T- Friction T u - Upper yield stress (strength) D C critical slip distance G C = T 0 D C /2 fracture energy density
Linear slip-weakening friction (Ida, 1972) 1. Zero slip as long as traction T is smaller than the (strength), T u (rupture criterion) 2. When the traction reaches T u, it starts evolving according to: T D = T u 1 D D c for 0 < D < D C T D = 0 otherwise. where D Slip T- Friction T u - Upper yield stress (strength) D C critical slip distance G C = T 0 D C /2 fracture energy density
Linear slip-weakening friction (Ida, 1972) 1. Zero slip as long as traction T is smaller than the strenght, T u (rupture criterion) 2. When the traction reaches T u, it starts evolving according to: T D = T u 1 D D c for 0 < D < D C T D = 0 otherwise. where D Slip T- Friction T u - Upper yield stress (strength) D C critical slip distance G C = T 0 D C /2 fracture energy density
Forward solver (need for speed) Dynamic rupture by FD3D code (Madariaga et al., 1998): Finite differences (4 th order) on a Cartesian box 200m grid Vertical fault reaching a free surface Boundary conditions Initial conditions: displacement and traction zero everywhere, except for the fault (which has nonzero prestress and a nucleation zone with T=T nucl >T u ). Symmetry conditions permit to solve the problem on half of the domain Box covers only the fault only slip rates are saved Wave propagation by Axitra (Bouchon, 1981; Coutant, 1989) 1D layered velocity model Pre-calculated Green s functions on a coarser grid, respecting the true fault geometry Representation theorem is used to obtain station waveforms
Parametrization : a single elliptic patch (barrier) 13 inverted parameters: 8 geometric parameters (5 for the ellipse, 3 for the nucleation zone) 3 parameters to determine initial stress: T 0, T avg prestress inside the ellipse (gaussian shape) T nucl initial stress inside the nucl. zone 2 parameters governing friction: T u Upper yield stress constant D C critical slip consant The fault plane
Bayesian inversion by Monte Carlo approach Data errors: Gaussian distribution with constant variance Prior information (constraints) on model parameters: Homogeneous prior PDF D c > 0.10m (for numerical reasons) Nucl. zone not fixed Posterior PDF is sampled using Monte Carlo Markov Chain by the Parallel tempering method (Sambridge, 2013)
Application to the Lesvos earthquake
Data, the model fault plane and the velocity model 21 accelerograms from Greek and Turkish national seismic networks. Distance of stations from the centroid: 30 150 km. Integrated to displacements, processed with causal Butterworth s filter of fourth-order in the range of 0.05-0.3 Hz. The velocity model 0 5 Plot of Vp, Vs Karagianni 5 th=4thlayer Vp Vs 10 15 Depth (km) 20 25 30 35 40 45 1 2 3 4 5 6 7 8 Velocity (km/sec) Karagianni et al., 2002
Results: the best found model (out of ~10 6 ) Quantity Value T u 13 Mpa T nucl 17 Mpa R nucl D C Stress drop 1.3 km 0.25 m 6.2 MPa M 0 3 x 10 18 Nm Duration of rupture 8.2 s Avg. rupture velocity 1.1 km/s Variance Reduction 37.2 %
Optimal model: evoluton of slip rate
Comparison with kinematic inversion Slip from optimal dynamic model Kinematic model (Kiratzi, 2018)
Comparison with kinematic inversion Rupture velocity: 1200 m/s vs 3000 m/s Stress drop: 6 MPa vs 3.6 MPa Slip from optimal dynamic model Kinematic model (Kiratzi, 2018)
esults : fits to data Variance reduction: VR 1 i 2 s i o i 2 2 = 37 % o i Frequency range: 0.05-0.3 Hz 2 Observed data Simulated data
Uncertainties: the stress and friction parameters (1-D marginals)
Correlations between dynamic parameters (2-D marginals)
Correlations between dynamic parameters (2-D marginals)
Correlations between dynamic parameters (2-D marginals)
Uncertainties in geometric parameters Fault plane Blue : contours of slip Yellow-orange: Nucleation zones Green star: centroid Red star: hypocenter
Histograms of various rupture properties (1-D marginals)
Histograms of various rupture properties (1-D marginals) M 0 = 3.5 ± 0.9 10 18 N.m Kiratzi: 4.2 10 18 N.m Papadimitriou et. al.: 3.5 10 18 N.m
Histograms of various rupture properties (1-D marginals) V r = 1.1 ± 0.08 km/s Kiratzi: 3.2 km/s Δσ = 5.8 ± 0.8 MPa Kiratzi: 3. 6 MPa
V r = 1.1 ± 0.08 km/s Kiratzi: 3.2 km/s Δσ = 5.8 ± 0.8 MPa Kiratzi: 3. 6 MPa
Conclusion We use Parallel tempering to obtain a dynamic model along with estimates of uncertainties and correlations. Our dynamic model fits data with 37 % variance reduction in the frequency range of 0.05-0.3 Hz M 0 consistent (within infered std) with other researchers Slow (1 km/s) rupture propagation to the northwest High (6 MPa) stress drop Centroid location within nucleation zone uncertainty (unlike the hypocenter) Some parameters are correlated (e.g. T 0 and Dc, R and Dc) and can be varied together to obtain the same fit to data.