Estimating Motions at a Site
Attenuation Relationships for Subduction Zones

Youngs, Chiou, Silva, and Humphrey

This relationship is used to calculate peak ground acceleration and horizontal spectral accelerations and is valid for moment magnitudes 4 to 9.5, distances 1 to 100 km, and depths 1 to 150 km. The distance rrup is defined as the closest distance from the site to the rupture surface.
Spectral accelertation is given as a function of moment magnitude,
distance between the site and the fault rupture, source type, and depth:

For rock:
lnPHA or Sa = 0.2418 + 1.414M + C1 + C2(10-M)3 + C3ln(rrup + 1.7818 e0.554M) + 0.00607 + 0.3846ZT

For soil:
lnPHA or Sa = -0.6687 + 1.438M + C1 + C2(10-M)3 + C3ln(rrup + 1.097 e0.617M) + 0.00648 + 0.3643ZT

where ZT = depth in km

Links to coefficient tables can be found in Appendix A.

Interactive Example

Other Relationships for Subduction Zones