Motions at a Site
Several types of relationships are available:
relations: Abrahamson & Silva, Boore,
Joyner & Fumal, Campbell, Sadigh et al.
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 rrup
as the closest distance from the site to the rupture plane.
lnPHA = f1(M, rrup) + Ff3(M) + HWf4(M, rrup) + Sf5(PGArock)
where f1(M, rrup) is the basic attenuation form for rock sites, and the other three terms are modifications for fault type, hanging wall effects, and soil conditions, respectively.
Basic rock attenuation model:
The basic rock attenuation model
is given by:
where R = [rrup2 + c42]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:
effects of nonlinear soil response are accounted for by the inclusion
of the site effects term.
The dummy variable S, the multiplier for the site effects term, is 1 for
deep soil, and 0 for rock or shallow soil. The site effects factor is
where PGArock is the expected peak ground acceleration on rock (ie. the attenuation relationship for PGA with the S term set to zero).Standard Deviation:
Links to coefficient tables can be found in Appendix A.
lnPHA or Sa = b1 + b2(M-6) + b3(M-6)2 + b5lnr + bVlnVS/VA
r = [rjb2 + h2]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 VS, a Custom option is provided in the 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.