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

data truncated at a maximum distance of RRUP = 70 km. In addition, the magnitude scaling
parameters c2 and c3 were fixed at 1.06 and 3.45 for all analyses and in the final model. As
discussed in the model development section, c3 = 3.45 represents scaling of low-frequency
amplitudes proportional to seismic moment. Parameter c2 was fixed at 1.06, the value
derived from the Atkinson and Silva (2006) seismic source model. All previous applications
of the general function form used by Ross Sadigh have yielded far-source high-frequency
magnitude scaling coefficients that are consistent with this value. Preliminary analysis of the
PEER-NGA data also produced values near 1.06. Parameter c4 was examined by analyses of
PEER-NGA data and TriNet data. It was concluded that a range of values for c4 would
provide satisfactory fits to the data with adjustments to the rate of attenuation occurring
through changes of parameters c5 and c6. The change in attenuation rate with distance was
set to occur at cRB = 50 km. A value near 50 km was consistently found in all preliminary
analyses.
After extensive exploratory analysis of the data, we concluded that the PEER-NGA dataset
does not sample a sufficiently wide range of motion and Vs30 to allow the simultaneous
estimation of all 3 nonlinear soil parameters (φ2, φ3,, and φ4) We thus decided to fix φ4
through other supporting information. Both our preliminary analysis of the PEER-NGA data
and our analysis of the simulated soil amplification factors from Silva (2004) suggested that
φ4 is about 0.1g in the case of pga. The empirical study of Choi and Stewart (2005) also
indicate 0.1g is a viable value for φ4. We thus fix pga’s φ4 at 0.1g. To fix φ4 of other periods,
we anchor the rock spectral shape of M6.5 at 10 km (Silva et a. Add referrecne) at 0.1g pga.
The remaining two nonlinear parameters will adjust to the fixed value of φ4 and they are
more than sufficient to capture the nonlinear soil behavior existing in the PEER-NGA
dataset.
In the preliminary analyses it was found that the data exhibited a statistically significant
dependence on source depth parameterized as the depth to top of rupture, ZTOR and that
aftershocks showed a stronger dependence on depths than main shocks. Also, the data
indicated that the style of faulting effects were weaker for aftershocks than for main shocks.
Therefore, the analyses were performed with separate depth dependence and style of faulting
effects for main shocks and aftershocks.
First Phase:
Step 1: The first phase of the analysis used only data from neutral sites. Sites with the
hanging wall/foot wall flags set to ‘fw’ or ‘hw’ in the PEER-NGA database were removed.
This simplification was performed to examine other portions of the model without interaction
with the hanging wall function fHW. In particular, regression with the full model showed high
correlation between estimates of the hanging wall parameters and the parameters for style of
faulting and soil nonlinearity. Using a simple model for the reference motion (without style
of faulting, depth of rupture, and variable magnitude scaling) the parameters of the non-linear
soil model (φ2 and φ3) were obtained from fits to the NGA data. At longer periods when the
soil response becomes nearly linear, estimates of the nonlinear soil parameter φ3 fluctuated
wildly and had very large errors of estimation. Therefore parameter φ3 for periods longer
than 1.0 seconds were fixed to produce a smooth transition to linear behavior at spectral
periods near 1.0 sec and greater.
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