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

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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