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