- Ground-motion model is: The model for the standard deviation is: where Sa is in g, is median peak acceleration for V S30 = 1100m∕s, σB and τB (= τ0(M,T))
are intra-event and inter-event standard deviations, σ0 and τ0 are intra-event and inter-event standard
deviations of the observed ground motions for low levels of outcrop rock motions (directly from regression),
σamp is intra-event variability of the site amplification factors (assumed equal to 0.3 for all periods based
on 1D site response results), c1 = 6.75, c4 = 4.5, a3 = 0.265, a4 = -0.231, a5 = -0.398, N = 1.18,
c = 1.88, c2 = 50, V LIN = 865.1, b = -1.186, a1 = 0.804, a2 = -0.9679, a8 = -0.0372 ,a10 = 0.9445,
a12 = 0.0000, a13 = -0.0600, a14 = 1.0800, a15 = -0.3500, a16 = 0.9000, a18 = -0.0067, s1 = 0.590 and
s2 = 0.470 for V S30 estimated, s1 = 0.576 and s2 = 0.453 for V S30 measured, s3 = 0.470, s4 = 0.300 and
ρ(T,PGA) = 1.000.
- Characterise sites using V S30 and depth to engineering rock (V s = 1000m∕s), Z1.0. Prefer V s,30 to generic
soil/rock categories because it is consistent with site classification in current building codes. Note that this
does not imply that 30m is key depth range for site response but rather that V s,30 is correlated with entire
- Classify events in three fault mechanism categories:
- FRV = 1, FNM = 0. Earthquakes defined by rake angles between 30 and 150∘.
- FRV = 0, FNM = 1. Earthquakes defined by rake angles between -60 and -120∘.
- FRV = 0, FNM = 0. All other earthquakes.
- Believe that model applicable for 5 ≤ Mw ≤ 8.5 (strike-slip) and 5 ≤ Mw ≤ 8.0 (dip-slip) and
0 ≤ dr ≤ 200km.
- Use simulations for hard-rock from 1D finite-fault kinematic source models for 6.5 ≤ Mw ≤ 8.25, 3D
basin response simulations for sites in southern California and equivalent-linear site response simulations
to constrain extrapolations beyond the limits of the empirical data.
- Select data from the Next Generation Attenuation (NGA) database (flat-file version 7.2). Include data from
all earthquakes, including aftershocks, from shallow crustal earthquakes in active tectonic regions under
assumption that median ground motions from shallow crustal earthquakes at dr < 100km are similar. This
assumes that median stress-drops are similar between shallow crustal events in: California, Alaska, Taiwan,
Japan, Turkey, Italy, Greece, New Zealand and NW China. Test assumption by comparing inter-event
residuals from different regions to those from events in California. Since aim is for model for California and
since difference in crustal structure and attenuation can affect ground motions at long distances exclude
data from dr > 100km from outside western USA.
- Also exclude these data: events not representative of shallow crustal tectonics, events missing key source
metadata, records not representative of free-field motion, records without a V s,30 estimate, duplicate
records from co-located stations, records with missing horizontal components or poor quality accelerograms
and records from western USA from dr > 200km.
- Classify earthquakes by event class: AS (aftershock) (FAS = 1); MS (mainshock), FS (foreshock) and
swarm (FAS = 0). Note that classifications not all unambiguous.
- Use depth-to-top of rupture, ZTOR, fault dip in degrees, δ and down-dip rupture width, W.
- Use rjb and Rx (horizontal distance from top edge of rupture measured perpendicular to fault strike) to
model hanging wall effects. For hanging wall sites, defined by vertical projection of the top of the rupture,
FHW = 1. T1, T2 and T3 constrained by 1D rock simulations and the Chi-Chi data. T4 and T5 constrained
by well-recorded hanging wall events. Only a14 was estimated by regression. State that hanging-wall scaling
is one of the more poorly-constrained parts of model.
- Records well distributed w.r.t. Mw and rrup.
- For four Chi-Chi events show steep distance decay than other earthquakes so include a separate coefficient
for the ln(R) term for these events so they do not have a large impact on the distance scaling. Retain
these events since important for constraining other aspects of the model, e.g. site response and intra-event
- Only used records from 5 ≤ M ≤ 6 to derive depth-to-top of rupture (ZTOR) dependence to limit the
effect on the relation of the positive correlation between ZTOR and M.
- Constrain (outside the main regression) the large distance (Rrup > 100km) attenuation for small and
moderate earthquakes (4 ≤ M ≤ 5) using broadband records of 3 small (M4) Californian earthquakes
because limited data for this magnitude-distance range in NGA data set.
- Note difficult in developing model for distinguishing between shallow and deep soil sites due to significant
inconsistencies between V S30 and depth of soil (Z1.0), which believe to be unreliable in NGA Flat-File.
Therefore, develop soil-depth dependence based on 1D (for Z1.0 < 200m) and 3D (for Z1.0 > 200m) site
response simulations. Motion for shallow soil sites do not fall below motion for V S30 = 1000m∕s.
- TD denotes period at which rock (V S30 = 1100m∕s) spectrum reaches constant displacement. Using
point-source stochastic model and 1D rock simulations evaluate magnitude dependence of TD as
log 10(TD) = -1.25 + 0.3M. For T > TD compute rock spectral acceleration at TD and then scale this
acceleration at TD by (TD∕T)2 for constant spectral displacements. The site response and soil depth
scaling is applied to this rock spectral acceleration, i.e. Sa(TD,V S30 = 1100) +f5(,V S30,T)+
- Reduce standard deviations to account for contribution of uncertainty in independent parameters M, Rrup,
ZTOR and V S30.
- Note that regression method used prevents well-recorded earthquakes from dominating regression.
- Examine inter-event residuals and find that there is no systemic trend in residuals for different regions.
Find that residuals for M > 7.5 are biased to negative values because of full-saturation constraint. Examine
intra-event residuals and find no significant trend in residuals.
- Although derive hanging-wall factor only from reverse-faulting data suggest that it is applied to
normal-faulting events as well.
- State that should use median PGA1100 for nonlinear site amplification even if conducting a seismic hazard
analysis for above median ground motions.
- State that if using standard deviations for estimated V S30 and V S30 is accurate to within 30% do not need
to use a range of V S30 but if using measured-V S30 standard deviations then uncertainty in measurement
of V S30 should be estimated by using a range of V S30 values.
- State that if do not know Z1.0 then use median Z1.0 estimated from equations given and do not adjust