John B RundleDistinguished Professor, University of California, Davis (www.ucdavis.edu)
Chairman, Open Hazards Group (www.openhazards.com)
Market StreetSan FranciscoApril 14, 1906
YouTube Video
Role of the World Wide WebIn Disaster Forecasting, Planning, Management and Response:
Challenges and Promise
Major Contributors
Open Hazards Group:
James Holliday (and University of California)William Graves Steven Ward (and University of California)Paul RundleDaniel Rundle
QuakeSim (NASA and Jet Propulsion Laboratory):
Andrea Donnellan
On Forecasting
• Why forecast? (A vocal minority of our community says we shouldn’t or can’t)– Insurance rates
– Safety
– Building codes
• Fact: Every country in the world has an earthquake forecast (it may be an assumption of zero events, but they all have one)
• Premise: Any forecast made by the seismology community is bound to be at least as good as, and probably better than, any forecast made by:– Politicians
– Lawyers
– Agency bureaucrats
Forecasting vs. Prediction
Context Characteristic
Prediction A statement that can be validated or falsified with 1 observation
ForecastA statement for which multiple
observations are required to determine a confidence level
Challenges in Web-Based Forecasting
Data & Models Information
Delivery Meaning
Acquiring & validating data Automation What is probability?
Model building Web-based integration Visual presentation
Efficient algorithms UI GIS
Validating/verifying models Tools Correlations
Error reporting, correction, model
steering
Collaboration/social networks
Expert guidance/blogs
California ForecastFeatures
~5 years in production
250,000 possible rupture rates37,000 data
1440 branches on logic treeWeights set by expert opinion
Constrained to stay close to UCERF2 model, which was constrained by the National Seismic Hazard Map
Removes overprediction of M6.7-7 earthquake rates
Comprised of 2 fault models;Every additional model requires another 720 logic tree branche
A self-consistent global forecast
Displays elastic rebound-type behavior Gradual increase in probability prior to a large earthquake Sudden decrease in probability just after a large earthquake
Only about a half dozen parameters (assumptions) in the model whose values are determined from global data
Based on global seismic catalogs
Probabilities are highly time dependent and can change rapidly
Probabilities represent perturbations on the time average probability
Web site displays an ensemble forecast consisting of 20% BASS (ETAS) and 80% NTW forecasts
A Different Kind of Forecast: Natural Time WeibullFeatures
JBR et al., Physical Review E, 86, 021106 (2012)J.R. Holliday et al., in review, PAGEOPH, (2014)
“If a model isn’t simple, its probably wrong” – Hiroo Kanamori (ca. 1980)
Data from ANSS catalog + other real time feeds
Based on “filling in” the Gutenberg-Richter magnitude-frequency relation
Example: for every ~1000 M>3 earthquakes there is 1 M>6 earthquake
Weibull statistics are used to convert large-earthquake deficit to a probability
Fully automated
Backtested and self-consistent
Updated in real time (at least nightly)
Accounts for statistical correlations of earthquake interactions
NTW MethodJBR et al., Physical Review E, 86, 021106 (2012)
NTW-BASS is an Ensemble ForecastJBR et al., Physical Review E, 86, 021106 (2012)J.R. Holliday et al., in review, PAGEOPH, (2014)
+
NTW x 80%
BASS x 20%
=
Mainshock
Time
Prob
abili
tyPr
obab
ility
Prob
abili
ty
Time
“Probability of the earthquake for ETAS is greatest the instant after the earthquake happens” – Ned Field (USGS)
Mainshock
Example: Vancouver Island EarthquakesLatest Significant Event was M6.6 on 4/24 /2014
JR Holliday et al, in review (2014)
Chance of M>6 earthquake in circular regionof radius 200 km for next 1 year.
Data accessed 4/26/2014
m6.6 11/17/2009
m6.0,6.1 9/3,4/2013
Probability Time Series
Sendai, Japan100 km Radius
Accessed 2014/06/25
M>7
M8.3 5/24/2013
M8.3
NTW-BASS is an Ensemble ForecastJBR et al., Physical Review E, 86, 021106 (2012)J.R. Holliday et al., in review, PAGEOPH, (2014)
+
NTW x 80%
BASS x 20%
=
Mainshock
Time
Prob
abili
tyPr
obab
ility
Prob
abili
ty
Time
“Probability of the earthquake is greatest the instant after it happens” – Ned Field (USGS)
Probability Time Series
Tokyo, Japan100 km Radius
Accessed 2014/06/25
M>7
M8.3 5/24/2013
M8.3
Probability Time Series
Miyazaki, Japan100 km Radius
Accessed 2014/06/25
M>6
M8.3 5/24/2013
M8.3
QuakeWorks Mobile App (iOS)
Verification and Validationhttp://www.cawcr.gov.au/projects/verification/
• Australian site for weather and more general validation and verification of forecasts
• Common methods are Reliability/Attributes diagrams, ROC diagrams, Briar Scores, etc.
Scatter Plot1980-present
Observed Frequency vs. Computed Probability
Verification: Example
Japan NTW ForecastAssumes Infinite Correlation Length
Optimized 48 month Japan forecast:Probabilities (%) vs. Time for Magnitude ≥ 7.25 & Depth < 40 KM
Temporal Receiver Operating Characteristic
1980-present
Optimal forecasts via backtesting, with
most commonly used verification testing
procedures.
Forecast Date: 2013/04/10
Challenges in Web-Based Forecasting
Data & Models Information
Delivery Meaning
Acquiring & validating data Automation What is probability?
Model building Web-based integration Visual presentation
Efficient algorithms UI GIS
Validating/verifying models Tools Correlations
Error reporting, correction, model
steering
Collaboration/social networks
Expert guidance/blogs
MathematicsJBR et al., Physical Review E, 86, 021106 (2012)JR Holliday et al, in review (2014)
Use small earthquakes (m ≥ 3.5) to forecast large earthquakes (M ≥ 6).
N = # small earthquakes per 1 large earthquake
t = time since last large earthquake
€
N = 10 b (M − m)
€
P(t,Δn) =1− exp{− f [n
N+
Δn
N]β + f [
n
N]β }
Conditional Weibull probability in natural time of next M event, where n = # of m events since last M event.
Δn = number of future m events
€
Δn ≈ ν Δtν = Time average rate of m events
€
P(t,Δt) =1− exp{− f [n
N+
νΔt
N]β + f [
n
N]β }
f = factor defined later
“Elastic Rebound” in NTWJBR et al., Physical Review E, 86, 021106 (2012)
JR Holliday et al, in review (2014)
€
P(t,Δt) =1− exp{−[n
N+
νΔt
N]β +[
n
N]β } ⇒ P(0,Δt) =1− exp{−[
νΔt
N]β }
Probability generally increases with time after the last large earthquake.
However, finite correlation length allows large distant earthquakes to partially reduce the count n(t) thereby decreasing P(t,Δt)
Probability just after the last large earthquake nearby is suddenly decreased because the count of small earthquakes
n(t) = 0 at t = 0+
Before After
€
P(t,Δt) ≥ P(0,Δt)Thus:
Probabilities are Perturbations on Time AverageJBR et al., Physical Review E, 86, 021106 (2012)JR Holliday et al, in review (2014)
€
P(t,Δt) =1− exp{− f [n
N+
νΔt
N]β + f [
n
N]β }
f = factor defined so that:
€
f = νΔt
[n
N+
νΔt
N]β − f [
n
N]β
All events prior to M9.1 on 3/11/2011 (“Normal” statistics)
All events after M7.7 on 3/11/2011 (Deficit of large events)
Filling in the Gutenberg-Richter RelationStatistics Before and After 3/11/2011Radius of 1000 km Around Tokyob=1.01 +/- 0.01
