### 2.71 Youngs et al. (1988)

• Ground-motion model is:

where amax is in g, C1 = 19.16, C2 = 1.045, C3 = 4.738, C4 = 205.5, C5 = 0.0968, B = 0.54 and σ = 1.55 - 0.125Mw.

• Use only rock records to derive equation but use some (389 records) for other parts of study. Classification using published shear-wave velocities for some sites.
• Exclude data from very soft lake deposits such as those in Mexico City because may represent site with special amplification characteristics.
• Data from subduction zones of Alaska, Chile, Peru, Japan, Mexico and Solomon Islands.
• Use two basic types of earthquake:
Zt = 0
Interface earthquakes: low angle, thrust faulting shocks occurring on plate interfaces.
Zt = 1
Intraslab earthquakes: high angle, predominately normal faulting shocks occurring within down going plate.

Classification by focal mechanisms or focal depths (consider earthquakes with depths > 50km to be intraslab). Note that possible misclassification of some intraslab shocks as interface events because intraslab earthquakes do occur at depths < 50km.

• Plots PGA from different magnitude earthquakes against distance; find near-field distance saturation.
• Originally include anelastic decay term -C6R but C6 was negative (and hence nonphysical) so remove.
• Plot residuals from original PGA equation (using rock and soil data) against Mw and R; find no trend with distance but reduction in variance with increasing Mw. Assume standard deviation is a linear function of Mw and find coefficients using combined rock and soil data (because differences in variance estimation from rock and soil are not significant).
• Use derived equation connecting standard deviation and Mw for weighted (weights inversely proportional to variance defined by equation) nonlinear regression in all analyses.
• Plot residuals from original PGA equation; find that hypothesis that coefficients of equations for interface and intraslab earthquakes are the same can be rejected (using likelihood ratio test for nonlinear regression models) at 0.05 percentile level for both soil and rock. Try including a term proportional to depth of rupture into equation (because intraslab deeper than interface events) but find no significant reduction in standard error. Introduce BZt term into equation; find B is significant at 0.05 percentile level. Try including rupture type dependence into other coefficients but produces no further decrease in variance so reject.
• Use only data from sites with multiple recordings of both interface and intraslab earthquakes and include dummy variables, one for each site, to remove differences due to systematic site effects. Fix C1 to C5 to values from entire set and find individual site terms and B; find B is very similar to that from unconstrained regression.
• Examine residuals for evidence of systematic differences between ground motion from different subduction zones; find no statistically significant differences in PGA among different subduction zones.
• Use geometric mean of two horizontal components to remove effect of component-to-component correlations that affect validity of statistical tests assuming individual components of motion represent independent measurements of ground motion. Results indicate no significant difference between estimates of variance about median relationships obtained using geometric mean and using both components as independent data points.
• Extend to Mw > 8 using finite difference simulations of faulting and wave propagation modelled using ray theory. Method and results not reported here.