Estimating
Motions at a Site
Attenuation
Relationships
A relationship
between the magnitude of an earthquake and the distance away from the
fault rupture for a particular ground motion parameter is called an attenuation
relationship. These parameters include:
- peak
values of:
- ground acceleration
- velocity
- displacement -
duration of shaking
-
predominant period
-
response spectra
Attenuation
relationships are developed by statistical analyses performed on a large
number of records which were obtained in compatible geomorphic regions.
Most of these relationships are updated as new strong ground motion data
becomes available and many now include additional parameters such as fault
type and site soil conditions.
The relationships are grouped by region, with note to those which are
applicable only to a particular area, such as the Cascadia subduction
zone.It is important to realize that the relationships are only as good
as the data they were generated from, and therefore the relations for
Western North America are the most reliable because the database for that
area is quite rich. The relationships for Eastern and Central North America
should be used with caution because the relationships have been calibrated
with only a few events. In any event, more than one relation should be
used to predict the motions at a site. Links to coefficient tables can
be found in Appendix A.
Relationships
are available for:
A summary of the relationships is provided in the following table (after Abrahamson and Shedlock, 1997):
|
Model
|
What's
Calculated
|
Site
Conditions
|
Parameters
|
Ranges
|
||
|
Tn
(s)
|
r
(km)
|
Mw
|
||||
| Western North America | ||||||
| Abrahamson & Silva |
PHA,
PVA, Sah, Sav
|
Rock,
Deep Soil
|
M,rrup,F,
HW
|
0-5
|
0-100
|
4-8
|
| Boore, Joyner, & Fumal |
PHA,
Sah
|
Vs
in top 30m
|
M
rjb,F
|
0-2
|
0-80
|
5.5-7.5
|
| Campbell |
PHA,
PVA, PHV, PVV, Sah, Sav
|
Hard
rock, soft rock, soil
|
M,rseis,F,D
|
0-4
|
0-100
|
4-9.5
|
| Sadigh et al. 1997 |
PHA,
Sah
|
Rock,
Deep soil
|
M,rrup,F,
HW
|
0-4
|
0-100
|
4-8
|
| Sadigh & Egan 1998 |
PHA,
PHV, PHD
|
Rock,
soil
|
M,rrup
|
N/A
|
0-100
|
4-8
|
| SEA96 - Extensional |
PHA,
Svh
|
Rock,
soil
|
M,rjb
|
0-2
|
0-80
|
5.5-7.5 |
| Central and Eastern North America | ||||||
| Atkinson & Boore |
PHA, Sah
|
Rock
|
M,rhypo
|
0-2
|
10-300
|
4-9.5
|
| Toro et al. |
PHA,
Sah
|
Rock
|
M,rjb
|
0-2
|
1-100
|
5-8
|
| Subduction Zones | ||||||
| Anderson |
PHA
|
Rock
|
Ms
or mb,rrup
|
N/A
|
N/A
|
N/A
|
| Atkinson & Boore |
PHA,
PHV, Sah
|
Rock
|
M,rhypo
|
0-2
|
10-400
|
4-9.5
|
| Youngs et al. |
PHA,
Sah
|
Rock,
soil
|
M,rrup,F,H
|
0-4
|
0-100
|
4-9.5
|
where
PHA = peak horizontal ground acceleration, PVA = peak vertical ground
acceleration, PHV = peak horizontal ground velocity, PVV = peak vertical
ground velocity, Sah = horizontal spectral acceleration, and Sav = vertical
spectral acceleration
Distance
definitions: rrup = closest distance to the rupture surface, rjb = closest
horizontal distance to the vertical projection of the rupture, rhypo =
hypocentral distance, rseis = closest distance to the seismogenic rupture
zone
Attenuate©
Interactive Examples
