- Ground-motion model is:
_{1}= 1.81, c_{2}= -1.18, c_{7}= 8.647, c_{8}= -0.028, c_{9}= -0.176, c_{10}= -0.266, c_{11}= -0.476, c_{12}= 0.52, c_{13}= -0.32, c_{14}= 0.4, c_{15}= -0.36, c_{17}= 0, c_{18}= 0, c_{19}= 0, c_{20}= 0.496, c_{21}= 0.427, K_{1}= 2.260, K_{2}= 1.04, V_{lin}= 760, σ = c_{20}(T)+[c_{21}(T)-c_{20}(T)]M_{w}for 5.0 ≤ M_{w}< 7.0 and σ = c_{21}(T) for M_{w}≥ 7.0. - Use V
_{s,30}to characterize site conditions. - Characterize basin by depth to V
_{s}= 1500m∕s, Z_{1.5}, since more likely to be obtained for engineering projects. - Use three mechanism classes:
- 1.
- Normal. 34 records. FN = 1, FS = FR = 0.
- 2.
- Strike-slip. 184 records. FS = 1, FN = FR = 0.
- 3.
- Reverse. Originally classify as thrust, reverse and reverse oblique but combine. 423 records. FR = 1, FN = FS = 0.

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. M
_{w}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 c
_{7}(T) to be monotonically varying with period because otherwise can have large changes in spectral shape at very short distances. - Note that for M
_{w}< 5.8 magnitude dependence may be due to depth-to-top (Z_{FR}and Z_{FS}) 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 f_{5}(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 a
_{1}= 0.04g, a_{2}= 0.1g and PGA_{min}= 0.06g. PGA_{non-lin}is expected PGA on rock (V_{s,30}= 760m∕s). c_{15}(T), c_{16}(T) and V_{lin}taken from Choi and Stewart (2005) and are not determined in regression. - 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. M
_{w}and distance (shown). Find no bias nor trends. Also plot against mechanism, site and other parameters and find no bias nor trends (not shown).