A1. Rate-and-State Equations
We use the expression for seismicity rate R as a function of state variable
under
secular tectonic shear stressing rate . Under constant shear stressing rate at each location
reaches a steady state, and is expressed as
𝛾𝑜 =
1
(1)
𝜏̇
At steady state, the seismicity rate R equals the background rate r since R is given by the
following equation
𝑅=
𝑟
(2)
𝛾𝜏̇
If there is no stress perturbation, then seismicity rate is constant but in the opposite case
the state variable of the system g n-1 before the event evolves co-seismically to a new
value g n ,
𝛾𝑛 = 𝛾𝑛−1 𝑒𝑥𝑝 (
−Δ𝐶𝐹𝐹
) (3)
Α𝜎
where As is a constitutive parameter times the effective normal stress, which varies
between 0.1 and 2 bars. The seismicity rate within the time period Dt is transient and
given sufficient time recovers, providing a new state variable for the system given by
equation
1
−Δ𝑡𝜏̇
1
𝛾𝑛+1 = [𝛾𝑛 − ] 𝑒𝑥𝑝 [
]+
(4)
𝜏̇
Α𝜎
𝜏̇
In our implementation the time period Δ𝑡 is taken as the interevent time between
successive events within a specific cluster (Table A2). The duration of the transient
effects has an inverse proportional relation with the tectonic loading rate [Parsons, 2002]
implying that if we give sufficient time, even in cases of slow stressing rates, the transient
seismicity will eventually disappear.
A2. Definition of log-likelihood metrics
The modified N test evaluates the consistency between the forecast and observed
number of events within a test area. Zechar et al. [2010] improved the original N test
metric by introducing the following equations,
𝛿1 = 1 − 𝐹(𝑁𝑂𝑏𝑠 − 1|𝑁𝐹 ) (1)
𝛿2 = 𝐹(𝑁𝑂𝑏𝑠 |𝑁𝐹 ) (2)
where 𝐹(𝑥|𝜇) is the right-continuous Poisson cumulative distribution function with
expectation
model.
evaluated at
.and NF is the forecast number of events determined by the