characteristic recurrence model for individual faults
Further discussion of earthquake recurrence models,
with the exponential model for distributed source
including real-time models, is contained in Navy
areas (Youngs et al., 1987, 1988; Youngs et al.,
publication TR-2016-SHR (Ferritto, 1994).
1993); such a comparison is illustrated in the
f.
Characterizing Ground Motion Attenuation.
example in Appendix E for the San Francisco Bay
region (Paragraph E-5b).
(1)
Attenuation relationships describe the
(c) A Poisson probability model is usually
variation of the amplitude of a ground motion
assumed for probabilistic ground motion analyses.
parameter as a function of earthquake magnitude
In the Poisson model, earthquake occurrence in time
and source-to-site distance. A number of attenuation
is assumed to be random and memoryless.
The
relationships have been developed for PGA and also
probability of an earthquake in a given time period is
for response spectral accelerations or velocities for
thus determined by the average frequency of
different structural periods of vibration. Figure 3-10
earthquakes, and is independent of when the last
illustrates typical attenuation relationships for PGA
earthquake occurred. This model has been shown to
and response spectral accelerations for three periods
be consistent with earthquake occurrence on a
of vibration.
These relationships are in terms of
regional basis; however, it does not conform to the
earthquake moment magnitude, and the distance is
process believed to result in earthquakes on an
the closest distance to the ruptured fault. The curves
individual fault -- one of a gradual accumulation of
in Figure 3-10 are median (50th percentile)
strain followed by a sudden release. More realistic
relationships.
In a probabilistic ground-motion
"real time" earthquake recurrence models have been
analysis, it is important to include the uncertainty in
developed that predict the probability of an
the ground motion estimates, which reflects the
earthquake in the next time period, rather than any
scatter in ground motion data.
An example of
time period, taking into account the past history (and
ground motion data scatter for a single earthquake is
paleo-history) of large earthquakes on a fault.
illustrated in Figure 3-11. To model this source of
Usually, there are insufficient geologic and seismic
uncertainty
in
ground
motion
estimation,
a
data on the timing of past earthquakes to justify the
probabilistic distribution about the median-curves is
use of these models; however, real-time recurrence
assigned, as schematically illustrated in diagram b of
models have been used, for example, in the study of
Figures 3-3 and 3-4, and as illustrated by the plus-
the probabilities of large earthquakes on the San
and-minus-one standard deviation curves in Figure
Andreas fault system in Northern California by the
3-11. A log-normal distribution is typically used,
Working
Group
on
California
Earthquake
and the standard deviation of the distribution is
Probabilities (1990).
These models can be
usually provided by the developer of the particular
considered for site-specific applications when there
attenuation relationship.
are sufficient data on the time-dependent occurrence
of earthquakes on specific earthquake sources.
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