Publication Date:
2004

Description:
One of the major challenges in engineering seismology is the reliable
prediction of site-specific ground motion for particular earthquakes, observed at
specific distances. For larger events, a special problem arises, at short distances,
with the source-to-site distance measure, because distance metrics based on a
point-source model are no longer appropriate. As a consequence, different attenuation
relations differ in the distance metric that they use. In addition to being a source of
confusion, this causes problems to quantitatively compare or combine different
ground-motion models; for example, in the context of Probabilistic Seismic Hazard
Assessment, in cases where ground-motion models with different distance metrics occupy
neighboring branches of a logic tree. In such a situation, very crude assumptions about
source sizes and orientations often have to be used to be able to derive an estimate of
the particular metric required. Even if this solves the problem of providing a number to
put into the attenuation relation, a serious problem remains. When converting distance
measures, the corresponding uncertainties map onto the estimated ground motions
according to the laws of error propagation. To make matters worse, conversion of
distance metrics can cause the uncertainties of the adapted ground-motion model to
become magnitude and distance dependent, even if they are not in the original relation.
To be able to treat this problem quantitatively, the variability increase caused by the
distance metric conversion has to be quantified. For this purpose, we have used well
established scaling laws to determine explicit distance conversion relations using
regression analysis on simulated data. We demonstrate that, for all practical purposes,
most popular distance metrics can be related to the Joyner-Boore distance using models
based on gamma distributions to express the shape of some "residual function." The
functional forms are magnitude and distance dependent and are expressed as polynomials.
We compare the performance of these relations with manually derived individual distance
estimates for the Landers, the Imperial Valley, and the Chi-Chi earthquakes. [Online
material available at the SSA Web site: Distance conversion coefficients for the
simulation scenarios used in this study.]

Keywords:
Earthquake hazard
;
PSHA
;
Attenuation
;
relations
;
Error analysis
;
BSSA

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