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

MODEL FORMULATION
All ground motion models, empirical or theoretical/numerical, attempt to capture three basic
aspects of ground motion estimation, the effect of the amount of energy radiated at the
source, the effect of attenuation of seismic waves along the path due to geometric spreading
and energy absorption, and the effect of local modification of the seismic waves by the nearsurface
materials. The empirical ground motion model developed in this study attempts to
capture these elements using (relatively) simple algebraic expressions to represent the
average behavior observed in the empirical strong motion data. The form of these
expressions was guided by trends in the data, simple seismological models, past experience,
and examination of the results of 1-D and 3-D ground motion simulations conducted as part
of the PEER-NGA project.
Seismic Source Scaling
Effect of Earthquake Size: The simplest and most commonly used measure for correlating
the amount of energy released in an earthquake with the resulting amplitudes of ground
motions is the earthquake magnitude, defined in the PEER-NGA database in terms of
moment magnitude M. Most empirical ground motion models have used a polynomial
function for scaling the log of ground motions y with magnitude of the form
n
ln( y ) ∝ C2
( T ) × M + C3
( T ) × ( mC
− M)
(1)
where coefficients C3 and possibly C2 vary with spectral period T, the exponent n is typically
in the range of 2 to 3, and the value of mC is independent of T.
We have introduced an alternative form for magnitude scaling that reflects the results
obtained using seismological models for the form of the earthquake source spectrum. Figure
7 shows response spectra computed using the stochastic ground motion model (e.g. Boore
2003) with two source spectra models, a Brune (1970, 1971) source with a stress parameter
of 70 bars and the Atkinson and Silva (1997) empirical source spectra model for California
earthquakes. Both forms of source spectra display similar trends in magnitude scaling. For
high frequency motions (> ~ 10 Hz), the magnitude scaling of ln(y) is approximately linear at
a relatively flat slope in the magnitude range of 5 ≤ M ≤ 8.5. The slope of the curves reflects
the scaling of the source spectrum above the corner frequency. For very low frequency
motions (< ~0.3 Hz) the magnitude scaling in the range of 5 ≤ M ≤ 7 is again approximately
linear, but at a much larger slope than for high frequency motions, reflecting scaling of the
source spectrum below the corner frequency.
At intermediate spectral frequencies, there is a transition in the scaling of ln(y) with
magnitude from low-frequency scaling at low magnitudes to high-frequency scaling at large
magnitudes. This transition occurs over the magnitude range where the corner frequency of
the source spectrum is near the spectral frequency of the ground motion. As the spectral
frequency of the ground motions decreases, the magnitude range for this transition shifts to
larger magnitudes, reflecting the decrease in corner frequency with increasing magnitude.
The shape of the magnitude scaling curves shown in Figure 7 is modeled by the expression:
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