Survival in Seattle: Magnitude estimation, survival analysis, and hazard and loss from Puget Lowland paleoearthquakes

Statistical paleoseismology from the Puget Lowland region of western Washington, presented at the Earthquake Science Center, US Geological Survey, Menlo Park, California

Transcript

1. Survival in Seattle: Magnitude estimation, survival analysis, and hazard and loss from Puget Lowland paleoearthquakes Richard Styron Earth Analysis, Seattle, WA Global Earthquake Model Foundation, Pavia, Italy Brian Sherrod, Kate Scharer US Geological Survey Anirudh Rao, Robin Gee, Marco Pagani GEM Foundation BIG THANKS TO DATA COLLECTORS!
2. Introduction • Decades of research by USGS and collaborators gives evidence for ~30 paleoearthquakes in Puget Sound region (WA, USA) • Dataset ‘Reasonably complete’ (B. Sherrod) for late Quaternary (since ~16 ka) surface-breakers • Best way to characterize shallow-crustal seismicity, hazard and loss
3. Motivating questions • Just how big were these earthquakes? • What are the temporal patterns of earthquake occurrence? • If these earthquakes occurred today, how much damage would they do, and how do we prepare?
4. Overview 1. Paleoearthquake magnitude estimation • Incorporation of displacement and length • Reduction in magnitude and uncertainty 2. Earthquake recurrence and survival analysis • Empirical recurrence probability distributions • Time-dependent, conditional EQ hazard • Analysis of clustering behavior 3. Time-dependent Probabilistic Seismic Hazard and Risk Analysis • Simulation of paleoEQs, clusters, aftershocks • Incorporating cumulative damage, rebuilding
5. Cascadia • Oblique subduction at 36 mm/yr (Wang et al., 2003) • E-W shortening at subduction zone • N-S shortening in forearc (Puget Lowland) • 3-7 mm/yr (Mazzotti et al., 2003) Juan de Fuca
6. Cascadia • Oblique subduction at 36 mm/yr (Wang et al., 2003) • E-W shortening at subduction zone • N-S shortening in forearc (Puget Lowland) • 3-7 mm/yr (Mazzotti et al., 2003) Juan de Fuca
7. Puget Lowland • Reverse and strike- slip faults throughout forearc low • Population centers (3 M) conveniently astride faults • ~30 earthquakes inferred from many sites S T O E SFZ
8. Paleoearthquake magnitude estimation • Fault offsets of 0.5-8 m observed in trenches, scarp profiles, uplifted shorelines • Ruptures 1-30 km mapped in LiDAR, may be much longer (full length of mapped faults) • Both data types can constrain paleoearthquake magnitude • We extend methods of Biasi and Weldon 2006: p(M|D) -> p(M|D,L) Styron and Sherrod 2017, vacationing on Brian’s desk
9. Maximum rupture lengths • Full length of mapped/ inferred faults • Faults mostly confined to forearc low S T O E
10. S T O E Minimum rupture lengths • Extent of scarp on LiDAR mapped where possible • Few km surrounding trenches otherwise
11. Magnitude from Displacement: Biasi and Weldon, 2006 Bayesian scheme to estimate magnitude M given displacement observation D [p(M|D)] Incorporates probability of Dave given Dobs
12. Choice of prior p(M) Several options available: • Uniform • Gutenberg- Richter • with, without surface breaks
13. Calculating p(M|D,L) p(M) p(M|D,L) p(L|M) p(D|M) ————- p(D) = * * L = [Lmin, Lmax) p(M(L)) = 5.08±0.1 + 1.06 ±0.07 * log10(L) (Wells and Coppersmith, 1994) Bayesian displacement- magnitude scaling (Biasi and Weldon, 2006) 6.0 7.0 8.0 6.0 7.0 8.0 6.0 7.0 8.0 6.0 7.0 8.0 * * =
14. Results: All earthquakes 6.5-7.5 6.0 6.5 7.0 7.5 8.0 8.5 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Probability p(M | D) 6.0 6.5 7.0 7.5 8.0 8.5 Moment magnitude 2 4 6 8 10 Probability p(M | D,L) n=25
15. Using L decreases M, uncertainty • PNW ruptures have high slip for short length • Accounting for length pushes M estimates lower by M~0.5 • Uncertainty is reduced substantially (esp. long high-M tails) 6.0 6.5 7.0 7.5 8.0 8.5 p(M | D) 6.0 6.5 7.0 7.5 8.0 8.5 p(M | D,L)
16. Magnitude estimation takeaways • New methods incorporating rupture length into magnitude estimation • All earthquakes between Mw 6.4 and 7.5 • Using length reduces magnitude and uncertainty for Puget Lowland events
17. Earthquake timing and recurrence • Ages for all dated events re-calculated in OxCal for internal consistency • Empirical recurrence (inter-event time) probability distributions calculated • Time-dependent recurrence using survival analysis • Characterization of earthquake clustering Styron, Scharer, Sherrod, in prep.
18. Paleoearthquake Ages • Radiocarbon data taken from published sources • Remodeled in OxCal with limited constraints to yield PDFs for all ages -14 -10 -6 -2 0 2 Thousand Year (C.E.)
19. Paleoearthquake Ages -14 -10 -6 -2 0 2 Thousand Year (C.E.) Earthquakes may be clustered: • Debatable clumps of old events • Major group of earthquakes ~1000 C.E. • 8-9 separate fault zones • Poisson probability: ~7 E -9
20. Paleoearthquake Ages Earthquakes may be clustered: • Debatable clumps of old events • Major group of earthquakes ~1000 C.E. • 8-9 separate fault zones • Poisson probability: ~7 E -9 -14 -10 -6 -2 0 2 Thousand Year (C.E.)
21. Earthquake Recurrence: methods 600 700 800 900 1000 1100 1200 1300 1400 Calendar Years B.P. −0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 probability 0 100 200 300 400 500 600 Recurrence Interval (years) 0 200 400 600 800 1000 1200 1400 count PDF CDF
22. Recurrence results: SFZ 0 2000 4000 6000 8000 10000 12000 14000 16000 Earthquake time, calendar years BP 0.000 0.001 0.002 0.003 0.004 0.005 Seattle Fault EQ times (8 EQs) 0 1000 2000 3000 4000 5000 6000 7000 8000 Earthquake recurrence interval (years) 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 mean = 1690 yrs median = 752 yrs mode = 236 yrs Seattle Fault recurrence PDF 0 100 200 300 400 (detail) total PDF total CDF 0.0 0.2 0.3 0.5 0.7 0.8 1.0 cumulative probability
23. Recurrence results: All Puget EQs 0 2000 4000 6000 8000 10000 12000 14000 16000 Earthquake time, calendar years BP 0.000 0.001 0.002 0.003 0.004 0.005 Puget Lowland EQ times (31 EQs) 0 1000 2000 3000 4000 5000 6000 Earthquake recurrence interval (years) 0.000 0.001 0.002 0.003 0.004 0.005 0.006 mean = 409 yrs median = 166 yrs mode = 19 yrs Puget Lowland recurrence PDF 0 100 200 300 400 (detail) total PDF total CDF 0.0 0.2 0.3 0.5 0.7 0.8 1.0 cumulative probability
24. Recurrence results: SAF
25. Recurrence interval takeaways • Regional fault recurrence PDF shows very short mode (earthquake clusters), long tail • Very short modal recurrence may result from earthquake triggering
26. The age-old question:
27. Survival Analysis • Statistics of timing of or between events • sociology, epidemiology, engineering applications • Hazard (instantaneous probability of occurrence): λ(t) = pdf(t) / 1 - cdf(t) • Expected time until next event, probability in time interval, etc. • Incorporation of open intervals (censoring): WIP
28. Survival Analysis • Name comes from mortality studies, particularly conditional mortality/survival: • A child at birth will live on average for 60 years (life expectancy at birth) • If child lives to age 5, will live on average to 75 (conditional life expectancy) • Extends well to earthquake recurrence
29. Hazard curves https://en.wikipedia.org/wiki/Bathtub_curve#/media/ File:Bathtub_curve.svg
30. Matthews et al. 2002 BPT Lognormal Gamma Poisson/exponential Weibull
31. Matthews et al. 2002 BPT Lognormal Gamma Poisson/exponential Weibull
32. Empirical earthquake hazard • Empirical PDFs for earthquake recurrence used • No assumption of analytical recurrence model (with associated geophysical implications) • Can easily accommodate multiple faults or multiple rupture modes (whatever they may be) • Subject to small n sampling problems
33. Earthquake hazard (rate) 0 1000 2000 3000 4000 5000 6000 0.000 0.001 0.002 0.003 0.004 0.005 0.006 instantaneous earthquake probability 0 200 600 1000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0 1000 2000 3000 4000 5000 6000 years since last earthquake 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0 100 300 500 0.000 0.001 0.002 0.003 0.004 0.005 0.006 Seattle Fault Zone Puget Lowland
34. Earthquake hazard (rate) 2000 3000 4000 5000 6000 7000 0.000 0.001 0.002 0.003 0.004 0.005 0.006 1200 1600 2000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 2000 3000 4000 5000 6000 7000 calendar year C.E. 0.000 0.001 0.002 0.003 0.004 0.005 0.006 1800 2000 calendar year C.E. 0.000 0.001 0.002 0.003 0.004 0.005 0.006 instantaneous earthquake probability Seattle Fault Zone Puget Lowland
35. Very fast re-rupture? • Mt. Vettore fault slipped 20 cm in Amatrice EQ, >1 m in Norcia EQ two months later https://twitter.com/bruno_pace/status/796724732854992896
36. Earthquake hazard (rate) Instantaneous earthquake probability
37. Earthquake hazard (rate) Instantaneous earthquake probability
38. Survival analysis: EQ expectations • 2.5% chance of M 6.5+ earthquake on Seattle Fault Zone in next 50 years, given 750 years since last event • 12% chance of M 6.5+ earthquake in Puget Lowland in next 50 years, given 312 years since last event 10 20 30 40 50 0.005 0.010 0.015 0.020 0.025 probability EQ Probabilities in next T years 0 10 20 30 40 50 0.00 0.02 0.04 0.06 0.08 0.10 0.12 probability SFZ Puget Lowland
39. Survival analysis: takeaways • Significant time-dependent earthquake hazards on SFZ, Puget Lowland faults • Earthquake hazard is highest in decades following an earthquake • Previously-damaged infrastructure may be very risky • Mitigation plans need to account for repeated events
40. The age-old question: No.
41. Earthquake time dependence • Clustering and periodicity commonly inferred or invoked, linked to physics (triggering, elastic rebound) • Distribution of inter-event times matters • Ordering of inter-event times probably does as well
42. ‘Burstiness’ and ‘memory’ • Burstiness (coeff. of variation) • Probability distribution of inter- event times • b: high B (clustered) • c: low B (periodic) • Memory (autocorrelation) • Ordering of inter-event times • d: high M (long->long) • e: low M (short -> long) Goh and Barabasi, 2008
43. Periodic Clustered (short->long) (long->long, short->short)
44. Burstiness and memory: but what to they mean? Periodic vs. bursty: • Elastic rebound, stable system, fault independence • Stress storage, unstable system, fault interdependence Memory: • Very little work done on inter-event autocorrelation • Crustal stress budget? Crustal ‘failure state’?
45. Earthquake timing and recurrence takeaways • Empirical recurrence PDFs offer data-first alternative to popular statistical models • Maybe more appropriate for aggregate data • p(EQ) > 0 at t=0 • Survival analysis of empirical PDFs shows ‘bathtub’ behavior • triggering -> stress accumulation ->elastic rebound? • ‘Burstiness’ (COV) and ‘memory’ (autocorrelation) may be better characterization of clustering behavior • Physical/geological implications of memory under- explored
46. Time-dependent PSHRA: A path forward • Simulate earthquake sequences based on paleoseismic data (Mw, recurrence, clustering) with aftershocks • Model damage and rebuilding • Cumulative fragility functions • Probabilistic rebuilding • Identify areas of major concerns
47. Cumulative building damage Iervolino et al., 2015
48. Capacity rebuilding • Probabilistic rebuilding models are being constructed • Building-level models account for state of components (frame, electric, etc.) • Community-level models use societal indicators Burton et al., 2015
49. Work in Progress: Simulate paleoseismic history • [X] Calculate ground motions from all paleoearthquakes, simulated aftershocks • [X] Place in (relative) time according to age observations, uncertainties • [/] Calculate damage, loss and rebuilding in each Puget Lowland census tract • [ ] Analysis: • How much higher are losses in clusters vs. Poisson assumption? • Where is infrastructure most vulnerable?
50. Mainshock and aftershock epicenters
51. SFZ Mw7.5 PGA
52. Conclusions 1. Magnitudes: • Large (Mw 6.5-7.5), surface-breaking earthquakes under Puget Sound metro area 2. Time dependence: • Survival analysis of empirical recurrence PDFs show ‘bathtub’-like hazard (high, then low, then high again) •Puget Lowland paleoseismicity is more clustered than Poisson assumption 3. Hazard and risk: • Simulated past earthquakes characterize present risk • Innovations in EQ occurrence, engineering and societal resilience models needed [and in progress]
53. Questions?