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Forecasting when a large earthquake is likely to happen •! ! earthquakes do not happen at regular time intervals •! ! ! even at Parkfield CA, famous for “regular” earthquakes, the time spacing is not actually regular Three types of forecasts 2004 Conventional forecast Probability remains constant. We assume this when we don’t know standard deviation of the return period, or if the standard deviation is big (i.e. the earthquakes occur at seemingly random time intervals). Renewal forecast (blue line): If stress increases gradually, then the chance of a damaging shock grows as time passes. Requires: • mean recurrence time • standard deviation • time since the last earthquake Renewal forecast with earthquake interaction (red line): Effects of Coulomb stress changes caused by nearby earthquakes may cause probabilities of another shock to rise or fall temporarily. Renewal Forecast in the SF Bay Area Probability of a M 6.7 or larger earthquake in the San Francisco Bay Area between 2003 and 2032 Probability of a large quake in a region includes probabilities on all of the local faults http://pubs.usgs.gov/fs/2003/fs039-03/ Renewal forecast record of earthquakes vs. time time For each fault, requires • mean recurrence time • standard deviation • time since the last earthquake One large quake or lots of small ones? “Probability density function” Assume the recurrence times fit a Gaussian (normal) distribution (x−µ)2 1 − φ = √ e 2σ2 σ 2π 500 years−1σ 500 500 years +1σ (for the red line) years (for the red line) = mean = µ x is recurrence time Cumulative Probability : from 0 to 1 Integrate the Gaussian to get the probability of an earthquake over a time interval Φ= x−µ 1 (1 + erf ( √ )) 2 σ 2 500 years−1σ 500 500 years +1σ (for the red line) years (for the red line) = mean = µ x is recurrence time Cumulative Probability 0 Probability density function (based on recurrence times) Cumulative Probability Probability density function (based on recurrence times) t1 t1 0 t1 t1 t1 is just after the last big quake small σ t2 large σ 500 years 1 0 1 t2 t1 t2 t2 0 t2 500 years 0 0.1 t1 t1 500 years 0.5 t1 t2 t2 time 1 time t2 time 500 years 1 0.5 time Probability density function (based on recurrence times) Predicting the probability for a time interval in the future time Cumulative Probability now 500 years 1 500 years 1 0.5 0.1 0 Probability density function (based on recurrence times) now 0.3 40% chance during ∆T Cumulative Probability 20% chance during ∆T time 0 ∆T ∆T If we know the quake has not happened yet... and we are at time “__” no earthquake occurred no earthquake occurred then only use this part of the PDF now 500 years 1 500 years 1 0.5 .4/.9 = 45% chance during next 30 years 0 0.5 now ∆T = 30 yr 0 0.5 .2/.7 = 30% chance during next 30 years ∆T = 30 yr Probability density (scaled) also # of meetings at each recurrence time Earthquake clustering: non-Gaussian (or lognormal) distribution EOSC 256 meeting times ... ... Probability we meet during this time interval Integrated probability density Time since the last class June - December 2009 probability that EOSC 256 meets during the summer never goes to zero using this approach yet we know that EOSC 256 never meets during the summer or fall ... clustering of seismicity would also complicate probability estimates Time since last class Cascadia Subduction Zone Fault drowned ancient stumps from tress killed by sudden subsidence in a Cascadia earthquake M9 (Sumatra-like) earthquakes every (300 to 1300!) years wood fragments sandwiched between sand layers where land surface dropped suddenly and killed a mature forest photos by Steve Carlson plus catastrophic undersea debris flows (turbidites), and other geological evidence Onur and Seeman, 2004 13th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 1065 PROBABILITIES OF SIGNIFICANT EARTHQUAKE SHAKING IN COMMUNITIES ACROSS BRITISH COLUMBIA: IMPLICATIONS FOR EMERGENCY MANAGEMENT Tuna ONUR, and Mark R. SEEMANN Earthquake forecasting summary We can usually forecast where damaging earthquakes will be (seismic gaps on known faults) but we are still often surprised (e.g., blind faults, intraplate faults) We can usually forecast their effects (e.g., strength and duration of shaking, tsunami genesis) We cannot predict the timing of earthquakes very well (though probabilities over long time periods can sometimes be estimated)