On the earthquake predictability of fault interaction models

On the earthquake predictability of fault interaction models Warner Marzocchi, and Daniele Melini Istituto Nazionale di Geofisica e Vulcanologia, Rome, Italy StatSei 9 meeting, Potsdam, June 15-17, 2015

Outline q The motivation: to get new insights on the predictability of the earthquake occurrence process using Coulomb Failure Function (CFF). q The simulated reality where the physics is perfectly known q Analyzing the seismic catalog of the simulated reality. What can we say about earthquake predictability? q Point to take home

The motivation q Earthquake space-time earthquake clustering is the most clear departure from pure randomness q This space-time clustering has been modeled through the Coulomb Failure Function (CFF) that has received a wide consensus from seismological community q The largest part of CFF applications is focused on a posteriori analysis. The few forward applications are focused on investigating the spatial distribution of aftershocks. q We analyze seismic catalog obtained by a simulated reality where the CFF is the real physics to get new insights on the earthquake predictability of this system.

The simulated reality The simulated reality is based on a simple deterministic model (simplicity is imposed to study the effects of the most relevant physical components) Defining a realistic tectonic setting (we choose central Italy) Modeling the earthquake generation on each single fault ( characteristic model) Modeling the interaction among faults (co- and postseismic stress perturbations) - Building a synthetic seismic catalog - Analyzing the earthquake predictability of the synthetic catalog

The simulated reality: the tectonic setting 44 00' Map of the major seismogenic faults in Central Italy [Basili et al., 2008; Marzocchi et al., 2009], named C-ITALY fault network. The red boxes represent the set of faults that mimics a strongly coupled simplified network geometry (LINE fault network). The two target faults are marked by the abbreviations OPF and FF. 43 20' 42 40' OPF 42 00' FF 41 20' 50 km 11 20' 12 00' 12 40' 13 20' 14 00' 14 40' 15 20'

The simulated reality: the earthquake occurrence process Characteristic earthquake: (about) same recurrence time and magnitude α=0.2 We take the aperiodicity α parameter equal to 0.3 that has been suggested to characterize isolated faults (e.g. Alpine fault in New Zealand; Berryman et al., 2012)

The simulated reality: the earthquake occurrence process Characteristic earthquake: (about) same recurrence time and magnitude α=0.2 Inter-event times We take the aperiodicity α parameter equal to 0.3 that has been suggested to characterize isolated faults (e.g. Alpine fault in New Zealand; Berryman et al., 2012)

The simulated reality: fault interaction Each earthquake produces on the other faults co- and post-seismic stress perturbations due to elastic and visco-elastic effects Co-seismic part Post-seismic part σ(t) = Mo i (Δ CO (x i )H(t t i ) + Δ POST (x i )Ω(t t i )) Δ POST (x) = Δ CO (x)(0.012δ +1) Ω(t * ) =1 exp( t * /τ) σ Δ CO (x) M 0i H(y) τ δ t i Stress perturbation induced on a fault Co-seismic Coulomb Failure Function (CFF) calculated through Okada s model Seismic moment of the i-th earthquake Heaviside function Relaxation time of the viscous layers (30 years in this application) Dimensionless value which corresponds numerically to the distance in km Time of occurrence of the i-th earthquake

The simulated reality: fault interaction 50 Cumulative distribution 40 30 20 10 0 6 5 4 3 2 1 0 1 2 3 4 5 6 Sign( CFF) Log( CFF/1Pa ) Empirical cumulative distribution of the stress changes induced by the C-ITALY fault network on OP-fault. The red dot is the F-fault contribution.

The simulated reality: fault interaction MF 0.20 OPF OPF 0.15 0.10 0.05 0.00 MPa 0.05 FF 0.10 (a) Stress changes on the Ovindoli Pezza fault (OPF) caused by an earthquake on the Fucino fault (FF; left panel), and by the Montereale fault (MF; right panel). (b) 0.15 0.20

The results: analyzing the catalog of simulated reality Quantifying earthquake predictability (1) Probability Gain, G Pr(E OPF Δt OPF ) Pr(E OPF Δt OPF,E FF ) Earthquake probability on OP-fault given the time elapsed since the last earthquake As above but also given an earthquake on F-fault in the last 10 years G = Pr(E OPF Δt OPF,E FF ) / Pr(E OPF Δt OPF )

The results: analyzing the catalog of simulated reality Quantifying earthquake predictability (2) Synchronization X i =t (OPF) i -t (FF) k, where t (OPF) i >t (FF) k If D close to zero, no significant synchronization If D close to 1, there is a significant synchronization

The results: analyzing the catalog of simulated reality Probability gain 5 4 3 2 1 (a) (b) C ITALY, =0.3, =3MPa 10 0 10 1 10 2 10 3 PDF (yr 1 ) 0 1000 2000 3000 4000 0 1000 2000 3000 4000 10 4 Elapsed time t (yr) Inter event time between OPF and FF (yr) Results of the model using C-ITALY and α = 0.3. (a) Probability gain G; the horizontal dotted line marks the case G = 1 of no probability gain. The vertical bar shows the onesigma uncertainty. (b) Probability density function (PDF) of the interevent times between events on OP-fault and F-fault; the red line shows the distribution when the earthquakes occur randomly on OP-fault and F-fault, and the black line shows the distribution observed in the synthetic catalogs. The vertical dashed lines show the average of these distributions.

The results: analyzing the catalog of simulated reality Quantifying earthquake predictability (3): the influence parameter (Assuming that the variability of the process and the contributions of faults are independent) Ψ* without the F-fault contribution

The results: analyzing the catalog of simulated reality Quantifying earthquake predictability: the influence parameter

The results: analyzing the catalog of simulated reality Quantifying earthquake predictability: the influence parameter

The results: analyzing the catalog of simulated reality As for Figure 3 but relative to some different parametrizations of the model. The results for other parametrizations of the model are reported in the supporting information. Probability gain Probability gain 5 4 3 2 1 0 5 4 3 2 1 (a) (c) (b) CITALY, =0.15, =2MPa (d) C ITALY, =0, =3MPa 10 0 10 1 10 2 10 3 10 4 10 0 10 1 10 2 10 3 PDF (yr 1 ) PDF (yr 1 ) 0 10 4 Probability gain 5 4 3 2 1 (e) (f) LINE, =0, =3MPa 10 0 10 1 10 2 10 3 PDF (yr 1 ) 0 1000 2000 3000 4000 0 1000 2000 3000 4000 10 4 Elapsed time t (yr) Inter event time between OPF and FF (yr)

Points to take home In our simulated reality.. CFF-modeling can increase the earthquake predictability on one fault only when the CFF stress change from a specific source fault is largely predominant over the stress changes caused by the other remaining faults, and over the intrinsic variability of the earthquake occurrence process. This result may pose some limits to the expected predictability of CFF in real Earth (that is certainly more complicated that our simulated reality)

Thank you

The results: analyzing the catalog of simulated reality Probability gain 5 4 3 2 1 (a) (b) C ITALY, =0.3, =2MPa 10 0 10 1 10 2 10 3 PDF (yr 1 ) 0 10 4 Probability gain 5 4 3 2 1 (c) (d) C ITALY, =0.15, =3MPa 10 0 10 1 10 2 10 3 PDF (yr 1 ) 0 1000 2000 3000 4000 0 1000 2000 3000 4000 10 4 Elapsed time t (yr) Inter event time between OPF and FF (yr)

5 The results: analyzing the catalog of (a) simulated reality 4 Probability gain 3 2 1 (b) LINE, =0.3, =3MPa 10 0 10 1 10 2 10 3 PDF (yr 1 ) 0 10 4 Probability gain 5 4 3 2 1 (c) (d) LINE, =0.15, =3MPa 10 0 10 1 10 2 10 3 PDF (yr 1 ) 0 10 4 Probability gain 5 4 3 2 1 (e) (f) LINE, =0.3, =2MPa 10 0 10 1 10 2 10 3 PDF (yr 1 ) 0 10 4 Probability gain 5 4 3 2 1 (g) (h) LINE, =0.15, =2MPa 10 0 10 1 10 2 10 3 PDF (yr 1 ) 0 1000 2000 3000 4000 0 1000 2000 3000 4000 10 4 Elapsed time t (yr) Inter event time between OPF and FF (yr)

The simulated reality: fault interaction