Attenuation
Relationships for Shallow
Crustal Earthquakes - Western North America |
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Several types of relationships are available: General
relations: Abrahamson & Silva, Boore,
Joyner & Fumal, Campbell, Sadigh et al.
This
relationship is used to calculate horizontal and vertical spectral accelerations
(including the peak ground acceleration) and is valid for moment magnitudes
4 to 8 and distances 0 to 100 km. The distance Spectral accelertation is given as a function of moment magnitude, distance to the rupture plane, fault type, soil conditions, and whether the site is on the hanging wall: lnPHA = Ff_{3}(M) + HWf_{4}(M,
r) + _{rup}Sf_{5}(PGA_{rock})where
Basic rock attenuation model: The basic rock attenuation model
is given by: a_{1} +
a_{2}(M-c_{1}) + a_{12}(8.5-M)^{n}
+ [a_{3} + a_{13}(M-c_{1})]lnR for
a_{1} +
a_{4}(M-c_{1}) + a_{12}(8.5-M)^{n}
+ [a_{3} + a_{13}(M-c_{1})]lnR
where ^{2}
+ c_{4}^{2}]^{1/2}Style-of-faulting factor: The style-of-faulting factor accounts for the differences between ground motions generated by strike-slip and reverse faults. The dummy variable F, the multiplier for the style-of-faulting factor, is 1 for reverse, 0.5 for reverse/oblique, and 0 otherwise. The style-of-faulting factor is given by:
Hanging wall effect: The hanging wall effect factor accounts
for the differences between ground motions on the hanging wall and the
foot wall of dipping faults. The dummy variable HW, the multiplier for
the hanging wall effects factor, is 1 for sites over the hanging wall,
and 0 otherwise. The hanging wall effect factor is given by: f_{HW}(M)f_{HW}(r)
_{rup}
and
Soil conditions: The
effects of nonlinear soil response are accounted for by the inclusion
of the site effects term. _{5}(PGA_{rock}) = a_{10}
+ a_{11ln}(PGA_{rock}+c_{5}) where
PGA
Links to coefficient tables can be found in Appendix A.
Peak horizontal acceleration is given as a function of magnitude, soil conditions and surface distance between the site and the fault: lnPHA or Sa = V_{S}/V_{A}
^{2}
+ h^{2}]^{1/2}Here d is the closest surface projection of the fault to the site in km. This relationship is only valid for magnitudes 5.5 < Mw < 7.5 and distances up to 80 km. Links to coefficient tables can be found in Appendix A. Recommended values of average shear-wave velocity Vs:
The
recommended Vs values shown above are used in the interactive example.
If you wish to use a different value of V
- Campbell Interactive Example
- Sadigh et al. - California Interactive Example
- Spudich et al. (SEA96) - Extensional regimes Interactive Example
Somerville et al. have developed attenuation relationships to add the effects of fault rupture directivity to ground motion parameters developed using other relationships, particularly the Abrahamson and Silva relationship. A response spectrum and/or PGA value can be converted into the spectrum or PGA value for either the fault normal or the fault parallel component. Use the following interactive example to see the effect of fault rupture directivity on spectra. See also the notes on this topic in Elastic Response. |