where y is in g, c1= 1.81, c2= -1.18, c7= 8.647, c8= -0.028, c9= -0.176, c10= -0.266, c11= -0.476,
c12= 0.52, c13= -0.32, c14= 0.4, c15= -0.36, c17= 0, c18= 0, c19= 0, c20= 0.496, c21= 0.427,
K1= 2.260, K2= 1.04, Vlin= 760, σ = c20(T)+[c21(T)-c20(T)]Mw for 5.0 ≤ Mw< 7.0 and σ = c21(T)
for Mw≥ 7.0.
Use Vs,30 to characterize site conditions.
Characterize basin by depth to Vs= 1500m∕s, Z1.5, since more likely to be obtained for engineering
Use three mechanism classes:
Normal. 34 records. FN= 1, FS=FR= 0.
Strike-slip. 184 records. FS= 1, FN=FR= 0.
Reverse. Originally classify as thrust, reverse and reverse oblique but combine. 423 records. FR= 1,
Note lack of records from normal earthquakes.
Use data from earthquakes with focal depths ≤ 15km.
Only use data from instrument shelters, non-embedded buildings with < 3 stories (< 7 if located on firm
rock) and dam abutments (to enhance database even though could be some interaction with dam).
Not sufficient data to investigate effect of tectonic environment. Exclude data from subduction zones
because that is different tectonic regime than for shallow crustal earthquakes.
Data well distributed in magnitude-distance space so do not use special statistical procedures to decouple
source and path effects. Do not use weights due to uniform distribution w.r.t. Mw and distance.
Exclude data from > 60km to avoid records with multiple reflections from lower crust.
Vast majority of data from western USA. Some from Alaska, Canada, Greece, Iran, Italy, Japan, Mexico,
New Zealand and Turkey.
Constrain c7(T) to be monotonically varying with period because otherwise can have large changes in
spectral shape at very short distances.
Note that for Mw< 5.8 magnitude dependence may be due to depth-to-top (ZFR and ZFS) effects since
small earthquakes have on average larger depth-to-top than larger earthquakes. Inter-event residuals from
preliminary regression are functions of rake and depth-to-top (stronger than rake dependency) particularly
for reverse earthquakes. These observations influence functional form of f5(Z).
Use residuals from 1D simulations to define functional form for hanging wall effect (HW= 1).
Coefficients for nonlinear soil effects determined from analytical results because of correlations between
other parameters and nonlinearity and since analytical results better constrained at high amplitudes than
empirical data. Set a1= 0.04g, a2= 0.1g and PGAmin= 0.06g. PGAnon-lin is expected PGA on rock
(Vs,30= 760m∕s). c15(T), c16(T) and Vlin taken from Choi and Stewart (2005) and are not determined
Applied limited smoothing (using piecewise continuous linear fits on log period axis) to avoid variability in
predicted spectral ordinates for neighbouring periods particularly at large magnitudes and short distances.
Examine normalized inter- and intra-event residuals w.r.t. Mw and distance (shown). Find no bias nor
trends. Also plot against mechanism, site and other parameters and find no bias nor trends (not shown).