- Ground-motion model is:
_{S30}= 1100m∕s, σ_{B}and τ_{B}(= τ_{0}(M,T)) are intra-event and inter-event standard deviations, σ_{0}and τ_{0}are intra-event and inter-event standard deviations of the observed ground motions for low levels of outcrop rock motions (directly from regression), σ_{amp}is intra-event variability of the site amplification factors (assumed equal to 0.3 for all periods based on 1D site response results), c_{1}= 6.75, c_{4}= 4.5, a_{3}= 0.265, a_{4}= -0.231, a_{5}= -0.398, N = 1.18, c = 1.88, c_{2}= 50, V_{LIN}= 865.1, b = -1.186, a_{1}= 0.804, a_{2}= -0.9679, a_{8}= -0.0372 ,a_{10}= 0.9445, a_{12}= 0.0000, a_{13}= -0.0600, a_{14}= 1.0800, a_{15}= -0.3500, a_{16}= 0.9000, a_{18}= -0.0067, s_{1}= 0.590 and s_{2}= 0.470 for V_{S30}estimated, s_{1}= 0.576 and s_{2}= 0.453 for V_{S30}measured, s_{3}= 0.470, s_{4}= 0.300 and ρ(T,PGA) = 1.000. - Characterise sites using V
_{S30}and depth to engineering rock (V_{s}= 1000m∕s), Z_{1.0}. 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 soil profile. - Classify events in three fault mechanism categories:
- Reverse(-oblique)
- F
_{RV }= 1, F_{NM}= 0. Earthquakes defined by rake angles between 30 and 150^{∘}. - Normal
- F
_{RV }= 0, F_{NM}= 1. Earthquakes defined by rake angles between -60 and -120^{∘}. - Strike-slip
- F
_{RV }= 0, F_{NM}= 0. All other earthquakes.

- Believe that model applicable for 5 ≤ M
_{w}≤ 8.5 (strike-slip) and 5 ≤ M_{w}≤ 8.0 (dip-slip) and 0 ≤ d_{r}≤ 200km. - Use simulations for hard-rock from 1D finite-fault kinematic source models for 6.5 ≤ M
_{w}≤ 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 d
_{r}< 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 d_{r}> 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 d_{r}> 200km. - Classify earthquakes by event class: AS (aftershock) (F
_{AS}= 1); MS (mainshock), FS (foreshock) and swarm (F_{AS}= 0). Note that classifications not all unambiguous. - Use depth-to-top of rupture, Z
_{TOR}, fault dip in degrees, δ and down-dip rupture width, W. - Use r
_{jb}and R_{x}(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, F_{HW }= 1. T_{1}, T_{2}and T_{3}constrained by 1D rock simulations and the Chi-Chi data. T_{4}and T_{5}constrained by well-recorded hanging wall events. Only a_{14}was estimated by regression. State that hanging-wall scaling is one of the more poorly-constrained parts of model^{22}. - Records well distributed w.r.t. M
_{w}and r_{rup}. - 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 variability.
- Only used records from 5 ≤ M ≤ 6 to derive depth-to-top of rupture (Z
_{TOR}) dependence to limit the effect on the relation of the positive correlation between Z_{TOR}and M. - Constrain (outside the main regression) the large distance (R
_{rup}> 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 (Z_{1.0}), which believe to be unreliable in NGA Flat-File. Therefore, develop soil-depth dependence based on 1D (for Z_{1.0}< 200m) and 3D (for Z_{1.0}> 200m) site response simulations. Motion for shallow soil sites do not fall below motion for V_{S30}= 1000m∕s. - T
_{D}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 T_{D}as log_{10}(T_{D}) = -1.25 + 0.3M. For T > T_{D}compute rock spectral acceleration at T_{D}and then scale this acceleration at T_{D}by (T_{D}∕T)^{2}for constant spectral displacements. The site response and soil depth scaling is applied to this rock spectral acceleration, i.e. Sa(T_{D},V_{S30}= 1100) +f_{5}(,V_{S30},T)+ f_{10}(Z_{1.0},V_{S30},T). - Reduce standard deviations to account for contribution of uncertainty in independent parameters M, R
_{rup}, Z_{TOR}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 PGA
_{1100}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 Z
_{1.0}then use median Z_{1.0}estimated from equations given and do not adjust standard deviation.

^{22}Model for T_{5} reported here is that given in 2009 errata. In original reference: T_{5} = 1 - (δ - 70)∕20 for δ ≥ 70 and 1 otherwise).