- Ground-motion model is: where y is in cm (to obtain PGA in cm∕s2 it is necessary to multiply y by (2π∕0.01)2), c1 = -2.19617,
m1 = 0.52375, m2 = -0.06094, r1 = -3.80190, r2 = 0.35508, r3 = 11.64156, sB = 0.21070, sC = 0.28251,
sD = 0.28288, bV = -0.31007, bV 800 = -0.70244, V A = 2319.18598, fN = -0.02411, fR = 0.07246,
fSS = -0.05632, ϕ = 0.25892 (intra-event), τ = 0.22145 (inter-event) and σ = 0.34071 (total).
- Use three alternative site terms. Mean V s,30 equals 365m∕s. Either use V s,30 to characterise sites or four Eurocode
8 site classes:
- Rocklike, V s,30 ≥ 800m∕s. 7% of data. SB = SC = SD = 0.
- Stiff, 360 ≤ V s,30 < 800m∕s. 43% of data. SB = 1, SC = SD = 0.
- Soft, 180 ≤ V s,30 < 360m∕s. 40% of data. SC = 1, SB = SD = 0.
- Very soft, V s,30 < 180m∕s. 10% of data. SD = 1, SB = SC = 0.
- Use three faulting mechanisms using classification of Boore and Atkinson (2008):
- 20 earthquakes. FN = 1, FR = FSS = 0.
- 43 earthquakes. FSS = 1, FN = FR = 0.
- 26 earthquakes. FR = 1, FN = FSS = 0.
- Focal depths ≤ 20km..
- Update of previous models by Cauzzi and Faccioli (2008), Cauzzi (2008), Cauzzi et al. (2008), Faccioli
et al. (2010) and Cauzzi et al. (2011).
- All data from digital accelerometers.
- Most data from Japan (K-Net) (1448 records, 49 earthquakes) with some data from Europe and Middle East
(Italy, Iceland, Iran, Turkey, Switzerland, Greece) (195 records, 35 earthquakes), western USA (California
and Alaska) (79 records, 7 earthquakes), New Zealand (61 records, 5 earthquakes) and China and Taiwan
(95 records, 2 earthquakes).
- Only use data from earthquakes with known fault geometries (from which rrup can be estimated) except
for Mw ≤ 5.7, where comparison of rrup and rhypo shows that statistically indistinguishable.
- Use procedure of Paolucci et al. (2008) to avoid filtering records with a probability > 0.9 of long-period
disturbance levels being < 15%. High-pass filter remaining records with 20s cut-off.
- Did not check for regional dependency since now largely accepted to merge data from various regions.
- Aim for simple though physically-sound functional form. Prefer a simple magnitude-independent r3 over
one that is magnitude-dependent because of stability in regression results and lack of trade-off with other
coefficients. Also this choice allows use of two-stage regression thereby yielding a smaller σ. Do not include
anelastic term because of negligible impact on predictions for rrup < 150km.
- Derive model in four stages. First, undertake regressions to investigate overall variation of coefficients and
to identify trade-offs. Constrain r2 and r3 from this step in subsequent steps. Second, undertake two-step
maximum-likelihood regression to find r1, sB, sC, sD, c1, m1 and m2. Smooth m2(T) for T < 1s by fitting a
high-order polynomial to the raw coefficients. Next repeat regression holding m2 fixed. This had a positive
effect on stability of c1 and m1. Third, find bV , bV 800 and V A by two-stage weighted maximum-likelihood
regression. Fourth, find fN, fR and fSS by two-step maximum-likelihood regression.
- Examine predicted magnitude-scaling and observations from rrup < 10km adjusted to rock-like conditions.
Find evidence for over-saturation at large magnitudes but note that there is large uncertainty because of
limited data for Mw > 7.2. Model predicts oversaturation for short-periods and large magnitudes, which
is retained. Provide equations to remove oversaturation from model.
- Examine residuals w.r.t. predicted PGA on rock and grouped by EC8 site class to seek nonlinear site
amplification. Fit lines to residuals and find trends, which could interpret as nonlinearity but given scatter
in results believe evidence for soil nonlinearity is weak.
- Find inclusion of faulting mechanism terms slightly reduces σ for T < 0.3s.
- Believe that because model developed independently of other recent models and using an independent
dataset that it can contribute to capturing epistemic uncertainty in ground-motion prediction.
- Note that one limitation of model is the use of V s,30 but cannot add terms to account for 2D or 3D
basin-type effects because of lack of require information for most records.
- Note that there is still a lack of data from rock-like sites.