Version 1.0 6/19/06
In practice there are limitations to the explicit directivity approach of Somerville97. First, the
assumption of a single linear fault segment is typically violated by large earthquakes, including
the 1992 Landers, California (M7.3) and 2002 Denali, Alaska (M7.9) events, where total fault
curvature, or change in strike reached 25-30 degrees. These relations require the angle with
respect to the rupture direction, and the latter changes significantly during the rupture. Secondly,
it has not yet been ascertained (mostly due to limited data) whether these recommended
directivity functions adequately represent directivity from such large events. For example, using
these functions, both ends of a 200 km bilateral rupture experience no directivity, yet intuitively,
both points experience directivity due to a 100 km fetch of rupture coming toward each station.
Finally, for rapidly determined ShakeMaps, directivity cannot be applied without a reasonable
constraint on the rupture location and dimensions, which is not available in near-real time.
It is hoped that directivity for a large earthquake will be sample observational and hence will be
locally constrained upon interpolation. Further improvement to the empirically-based predictive
aspects of ShakeMap might include a azimuthally-dependent term to the bias correction, capable
of adding directivity in real-time based on direct event-specific observations.
Youngs and others 1997 (Youngs97)
This attenuation model is used for the Washington and Alaska ShakeMap regions and for other
subduction zones. Event depth is required for this regression, as well as event type (interface or
intraslab). Because this regression normally used for deep earthquakes, either hypocentral
distance of distance to a 3D fault model can be used. This model is specified by sets of planar
segments (quadrilaterals), each planar segment joined at a common side. Each quadrilateral
segment is defined in the fault file by four (coplanar, noncollinear) corner points. One or two
planar segments should be sufficient for most cases.
The relation has the form:
log (Y) = 0.2418 + 1.414 M + C1 + C2 (10 – M)3
+ C3 log (Rrup + 1.7818 e(0.554 M)) + 0.00607 H
+ 0.3846 Zt
Y is PGA or PSA\ in g
M is the magnitude
Rrup is the hypocentral distance or distance to fault, described above
H is the hypocentral depth
Zt = 1 for intraslab events, 0 otherwise
Values for c1-c5 are given below. PGV is derived from PSA (1.00) using the NH82 relation.
PSA (0.3 s)
APPENDIX A. Regression Relationships