Foreshocks Aftershocks and Characteristic Earthquakes or Reconciling the

Foreshocks, Aftershocks, and Characteristic Earthquakes or Reconciling the Agnew & Jones Model with the Reasenberg and Jones Model Andrew J. Michael

Model 1: Reasenberg and Jones, Science, 1989 Modified-Omori Law Probability of earthquakes during an aftershock sequence as a function of time and magnitude. Initial estimates are based on parameters for a “generic” California earthquake sequence. Gutenberg-Richter Distribution Results start the same for all sequences. Sequence specific parameters are used once they can be determined. Extend aftershocks to foreshocks.

Should we say the same thing after every event? Agnew and Jones, JGR, 1991: “But it ought to be possible to do better: the probability of a very large earthquake should be higher if the candidate foreshock were to occur near a fault capable of producing that mainshock than if it were located in an area where we believe such a mainshock to be unlikely. Moreover, the chance of a candidate earthquake actually being a foreshock should be higher if the rate of background (nonforeshock) activity were low. ”

Model 2: Agnew and Jones, JGR, 1991 After discarding aftershocks, earthquakes are divided into three categories for statistical purposes: Mainshocks: which we want to forecast Foreshocks: which are always followed by mainshocks Background Events: which are never followed by mainshocks When a moderate event occurs we can’t tell if it is a foreshock or a background event. We calculate the probability that it is a foreshock by PF = Rate of Foreshocks + Rate of Background Events Rate of Foreshocks = Rate of Mainshocks * Probability of Foreshocks Before Mainshocks

M 4. 8 Event At Bombay Beach On March 24, 2009 Could It Be A Foreshock To A Larger Earthquake In The Next 3 Days?

M 4. 8 Event At Bombay Beach On March 24, 2009 Could It Be A Foreshock To A Larger Earthquake In The Next 3 Days? Mainshock: SAF, Coachella Seg. UCERF 2: Length = 69 km M 7 5 -yr Prob. = 5% 3 -day Prob. = 0. 009%

M 4. 8 Event At Bombay Beach On March 24, 2009 Could It Be A Foreshock To A Larger Earthquake In The Next 3 Days? Mainshock: SAF, Coachella Seg. UCERF 2: Length = 69 km M 7 5 -yr Prob. = 5% 3 -day Prob. = 0. 009% Reasenberg & Jones, 1989: Probability of M 4. 8 being followed by an M≥ 7 event PF = 0. 05%

M 4. 8 Event At Bombay Beach On March 24, 2009 Could It Be A Foreshock To A Larger Earthquake In The Next 3 Days? Mainshock: SAF, Coachella Seg. UCERF 2: Length = 69 km M 7 5 -yr Prob. = 5% 3 -day Prob. = 0. 009% Reasenberg & Jones, 1989: Probability of M 4. 8 being followed by an M≥ 7 event PF = 0. 05% Agnew and Jones, 1991: PF = 4%

Reasenberg & Jones with Gutenberg-Richter Rate Overall Productivity vs. Initiating Event Magnitude modified-Omori Decay Probability of m≥M given an Earthquake P(m≥M|E) (Mmin=0) Can we modify this to include characteristic behavior?

Gutenberg-Richter + Characteristic Earthquake Relationships Rate of Characteristic Earthquake Heaviside Function Magnitude of Characteristic Earthquake

Gutenberg-Richter versus Characteristic Clustering Models Rate Overall Productivity vs. Initiating Event Magnitude modified-Omori Decay Probability of m≥M given an Earthquake P(m≥M|E) (Mmin=0)

Approximate the Probability of an M≥Mc event following an M=Mi event assuming: rate of M=0 events 10 a >> D the rate of Mc events rate of Mi events 10 a-b. Mi >> D the rate of Mc events D >> 10 a-b. Mc the Gutenberg-Richter rate of M≥Mc small probabilities so P≈λ

Characteristic Reasenberg & Jones Approximate Model Agnew & Jones Approximate Model Both models are proportional to the rate of characteristic events inversely proportional to the rate of initiating events

Reasenberg & Jones w/ Characteristic Clustering

Summary The behavior of the Agnew and Jones model can be captured by the characteristic clustering version of the Reasenberg and Jones model. The characteristic clustering model covers a wider range of conditions: magnitudes above and below the initiating event times longer than 3 days post-initiating event The characteristic clustering model is therefore more useful. Implications Uncertainty in characteristic earthquake rates is high -> uncertainty in clustering probabilities is high for magnitudes close to the characteristic magnitude. Even if testing guides us to the best clustering model for M < MC the uncertainties for M≥MC will be high For foreshock probabilities of large earthquakes the key question is “do characteristic earthquakes exist and can we determine their long-term probabilities. ”