Chiou and Youngs PEER-NGA Empirical Ground Motion Model for ...

Appendix B
Estimation of Distance and Geometry Measures for Earthquakes without Finite
Rupture Models
Approach
There are 110 earthquakes in the NGA data set that do not have finite fault models, and
therefore have only epicentral and hypocentral distances listed in the flat file. Rupture
distances and source-site geometry parameters were estimated for the recordings from
these earthquakes by simulating 101 possible rupture planes for each earthquake,
computing the distance measures for each site for each simulation, and then taking the
median of these values for use in completing the metadata in the PEER-NGA data base.
The estimated parameters include RRUP, RJB, RSEIS, RRMS, the source=site angle θSITE, the
hanging wall and foot wall indicators FHW and FFW, and the fault rupture width W and
depth to top of rupture, ZTOR.
Simulation Process
The first step was to simulate the fault rupture dimensions. The rupture area, A, was
simulated using the Wells and Coppersmith (1994) relationship for all fault types:
log( = log( Area)
A) −3.
49 + 0.
91M
σ = 0.
24
(B-1)
Figure B-1 shows the data for rupture area versus M for the finite rupture models in the
PEER-NGA database. The black lines show a linear fit to the data (solid = mean, dashed
= 90% confidence on mean). The blue line is Wells and Coppersmith (1994), which falls
within the 90% confidence interval and provides a closer fit to the data for smaller
magnitude earthquakes of primary interest in the simulation, as those earthquakes without
finite fault models are principally of magnitude < M 6.
The aspect ratio of the rupture was then simulated using the relationship:
log( = NM
RV
log( AR)
3.
097
AR) ( 0.
01752 − 0.
00472F
− 0.
01099F
) * ( M − 4)
σ = 0.
16 (B-2)
where FNM and FRV are (0,1) dummy variables for normal and revere earthquakes,
respectively. This relationship was defined by fitting the aspect ratio data for the PEER-
NGA finite fault model data set (Figure B-2). Correlation in the residuals between
rupture area and aspect ratio was low (