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

Calculate ground motion parameters with any of the above attenuation relationships. Attenuate© Interactive Examples