SHORT-TERM EARTHQUAKE PROBABILITIES BASED ON LONG-TERM PROBABILITY MODELS Andrew J. Michael

SHORT-TERM EARTHQUAKE PROBABILITIESBASED ON

LONG-TERM PROBABILITY MODELSAndrew J. Michael

Edward H. Field

M4.8 Event At Bombay Beach On March 24, 2009Could It Be A Foreshock To A Larger Earthquake In The Next 3 Days?

Mainshock:SAF, Coachella Seg.UCERF2:Length = 69 kmM 75-yr Prob. = 5%



Karen Felzer:ETAS ModelProbabilityof M4.8 beinga foreshock toan M 7 event:PF = 0.05%



Karen Felzer:ETAS ModelPF = 0.05%

Lucy Jones:Agnew &Jones ModelPF = 5%


What is the Agnew and Jones (JGR, 1991) Model?

After discarding aftershocks,earthquakes are divided into three categories for statistical purposes:

Mainshocks: which we want to forecastForeshocks: which are always followed by mainshocksBackground Events: which are never followed by mainshocks

When a candidate event occurs we can’t tell if it isa foreshock or a background event.

We can calculate the probability that the candidate eventis a foreshock (PF) if we know:

1. The rate of background events (estimated from the seismicity)2. The rate of mainshocks (estimated by models such as UCERF2)3. The rate at which mainshocks are preceded by foreshocks.

Need these rates over the area of interest.

Implementation of Agnew and Jones Model

1991 Implementation: Characteristic Mainshocks on Segments

Mainshock Fault

Candidate Event

Area of Integration

Updated Implementation:Utilize current probability modelssuch as UCERF2.Add Gutenberg-Richter mainshocks.Area of integration is foreshock-centric.Allows for multiple faults & area sources.

Mainshock Fault

Candidate Event

Area of Integration

Details on Estimating the Three Input Rates1. The rate at which mainshocks are preceded by foreshocks:

50% of San Andreas physiographic province mainshockshave a foreshock within 3 days, 3 units of magnitude, &10 km (Jones, 1984; Michael & Jones, 1998).

2. The rate of mainshocks (estimated by models such as UCERF2).For linear sources we use a rate of nucleation which isuniformly distributed along the fault (McGuire et al., 2002).

3. The rate of background events (estimated from the seismicity).Declustered to remove events with a larger event in theprevious 3 days.

Mainshock source:50 km long withrate of0.1/year.

A candidate event could be aforeshock to mainshocks thatnucleate within a 10 km radius.

Mainshock nucleation ratewithin 10 km of candidate:0.1*(20km/50km) = 0.04/yr

Agnew and Jones in a Gutenberg-Richter World

Candidate EventM = 5 ± 0.1

Mainshock 5.1 ≤ M ≤ 8

b=1, a=2PF = 5%




b=1, a=2PF = 5%

b=1, a=3PF = 5%




b=0.7, a=?PF = 7%

b=1, a=?PF = 5%

Agnew and Jones ModelGives Spatial VariationsIf Gutenberg-RichterBehavior Is Not UniversalWith Constant b-value.

Violating Gutenberg-Richter with Variable Maximum Magnitude


b=1, a=2Mainshock 5.1 ≤ M ≤ 8PF = 5%


b=1, a=2Mainshock 5.1 ≤ M ≤ 8PF = 5%

Maximum magnitudehas a small effect on probabilitiesbut may have a larger effecton hazard and risk.

b=1, a=2Mainshock 5.1 ≤ M ≤ 6

PF = 4%

Violating Gutenberg-Richter with Variable Maximum Magnitude

Mainshock:SAF, Coachella Seg.UCERF2:Length = 69 kmM 75-yr Prob. = 5%1-yr Poisson Rate = 0.011Nucleation uniformlydistributedalong segment


Background Seismicity:M≥ 31981 – 2008

Declustered byremoving eventswith a larger eventin the previous3 days.











Within 10 km:25 Background Events14 After Declustering8 km of Fault Segment11% of Fault SegmentPF = 0.4%






Within 10 km:17 Background Events13 After Declustering20 km of Fault Seg.29% of Fault SegmentPF = 1%



Within 10 km:0 Background Events0 After Declustering0.9 Assumed Max20 km of Fault Seg.29% of Fault SegmentPF ≥ 14%

Within 10 km:17 Background Events13 After Declustering20 km of Fault Seg.29% of Fault SegmentPF = 1%




Summary

Agnew and Jones reduces to standard clustering models (e.g. ETAS, Reasenberg & Jones)if the world is Gutenberg-Richter with constant b-value.

Gutenberg-Richter holds for an entire region and for the entire southern San Andreas fault(Page et al., this meeting) but may not hold for individual rupture sources withbackground seismicity integrated over 10 km radius circles.

Variations in maximum magnitude make only small changes in probabilities but largerchanges in hazard and risk. Maximum magnitude variations could also be accomplishedin simpler clustering models.

Applicability of the Agnew and Jones model depends on our conclusions aboutGutenberg-Richter behavior over small scales.

Conclusions

Agnew and Jones Model has been updated to compute probabilities in a way that canbe consistent with current probability models including:

Gutenberg-Richter Behavior of MainshocksForeshock-Centric Calculations That Allow For Multiple Faults

Key Factors Are:If Gutenberg-Richter behavior is universal with constant b-value thenAgnew and Jones reduces to standard clustering models (e.g. ETAS).

Utility of Agnew and Jones depends on deciding that Gutenberg-Richterbehavior is violated due to:

characteristic behavior ordifferences in the behavior of small and large earthquakes such ascreeping versus locked sections.

However changes in maximum magnitude from one region to anothermake only small differences in the resulting probabilities.

What is the Agnew and Jones (JGR, 1991) Model?After discarding aftershocks,earthquakes are divided into three categories for statistical purposes:

Mainshocks: which we want to forecastForeshocks: which are always followed by mainshocksBackground Events: which are never followed by mainshocks

When a moderate event occurs we can’t tell if it isa foreshock or a background event.

We calculate the probability that it is a foreshock by

PF = Rate of Foreshocks Rate of Foreshocks + Rate of Background Events

Rate of Foreshocks = Rate of Mainshocks * Rate of Foreshocks Before Mainshocks

50% of mainshocks have a foreshock within 3 days, 3 M, & 10 km.

Seemingly Good Behavior of this Model

Then resulting probability goes• up with higher mainshock rate and• down with higher background rate.

PF = Rate of Mainshocks * Rate of Foreshocks (Rate of Mainshocks * Rate of Foreshocks + Rate of Background Events)

InitialImplementationof Agnew & Jones

A candidate event is analyzedwith respect to a fault segment.

Mainshock Rate andBackground Rate arecalculated for aCharacteristic Eventon that segment.

But, what if wedon’t know whichmainshock we are working on?

Different faults have• Different background rates• Different mainshock

probabilities• Different resulting probabilities.

Problem: Mainshock Centric Calculation!

Integrate background eventrate and mainshocknucleation ratearound the foreshock.

Solution: Foreshock Centric Calculation!

Also add Gutenberg-Richterdistribution of mainshocks to matchcurrent probability models suchas UCERF2.

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SHORT-TERM EARTHQUAKE PROBABILITIES BASED ON LONG-TERM PROBABILITY MODELS Andrew J. Michael