- Ground-motion model is:
where y is in m∕s2, a

_{1}= -1.296, a_{2}= 0.556, a_{3}= -1.582, a_{B}= 0.22, a_{C}= 0.304, a_{D}= 0.332 and σ = 0.344 for horizontal PGA. - Use four site categories based on Eurocode 8:
- A
- Rock-like. V
_{s,30}≥ 800m∕s. S_{B}= S_{C}= S_{D}= 0. - B
- Stiff ground. 360 ≤ V
_{s,30}< 800m∕s. S_{B}= 1, S_{C}= S_{D}= 0. - C
- 180 ≤ V
_{s,30}< 360m∕s. S_{C}= 1, S_{B}= S_{D}= 0. - D
- Very soft ground. V
_{s,30}< 180m∕s. S_{D}= 1, S_{B}= S_{C}= 0.

Try to retain only records from stations of known site class but keep records from stations of unknown class (4% of total), which assume are either B or C classes. Use various techniques to extend 20m profiles of K-Net down to 30m. Vast majority of data with V

_{s,30}≤ 500m∕s. - Use mechanism classification scheme of Boore and Atkinson (2007) based on plunges of P-, T- and
B-axes:
- Normal
- 16 earthquakes. 5 ≤ M
_{w}≤ 6.9. - Strike-slip
- 32 earthquakes. 5 ≤ M
_{w}≤ 7.2. - Reverse
- 12 earthquakes. 5.3 ≤ M
_{w}≤ 6.6.

- Develop for use in displacement-based design.
- Select records with minimal long-period noise so that the displacement ordinates are reliable. Restrict
selection to digital records because their displacement spectra are not significantly affected by correction
procedure and for which reliable spectral ordinates up to at least 10s are obtainable. Include 9 analogue
records from 1980 Irpinia (M
_{w}6.9) earthquake after careful scrutiny of long-period characteristics. - Use approach of Paolucci et al. (2008) to estimate cut-off frequencies for bandpass filtering. Compute noise
index I
_{V }for each record based on PGV and average value computed from coda of velocity time-history. Compare I_{V }with curves representing as a function of M_{w}the probability P that the long-period errors in the displacement spectrum are less than a chosen threshold. Use probability P ≥ 0.9 and drifts in displacement spectrum < 15% using I_{V }from geometric mean. Rejections closely correlated with instrument type (less data from high-bit instruments rejected than from low-bit instruments). Process records by removing pre-even offset from entire time-history. Following this 57% of records satisfied criterion of Paolucci et al. (2008). Remaining records filtered using fourth-order acausal filter with cut-off 0.05Hz after zero padding and cosine tapering. After this step records pass criterion of Paolucci et al. (2008). Note that filtering of 43% of records may affect reliability beyond 15s. - Use data from K-Net and Kik-Net (Japan) (84%); California (5%); Italy, Iceland and Turkey (5%); and Iran (6%). Try to uniformly cover magnitude-distance range of interest. All data from M > 6.8 are from events outside Japan.
- Exclude data from M
_{w}< 5 because probabilistic seismic hazard deaggregation analyses show contribution to spectral displacement hazard from small events is very low. - Exclude data from M
_{w}> 7.2 because 7.2 is representative of the largest estimated magnitude in historical catalogue of Italy. Most records from M_{w}≤ 6.6. - Exclude data from subduction zone events.
- Focal depths between 2 and 22km. Exclude earthquakes with focal depth > 22km to be in agreement with focal depths of most Italian earthquakes.
- Use r
_{hypo}for greater flexibility in seismic hazard analyses where source zones have variable depth. Exclude data from r_{hypo}> 150km based on deaggregation results. - Test regional dependence of ground motions using analysis of variance. Divide dataset into intervals of
10km×0.3M
_{w}units and consider only bins with ≥ 3 records. Apply analysis for 18 bins on logarithmically transformed ground motions. Transform observed motions to site class A by dividing by site amplification factor derived by regression. Find no strong evidence for regional dependence. - Apply pure error analysis to test: i) standard logarithmic transformation, ii) magnitude-dependence of
scatter and iii) lower bound on standard deviation using only M and r
_{hypo}. Divide dataset into bins of 2km × 0.2M_{w}units and consider only bins with ≥ 2 records (314 in total). Compute mean and standard deviation of untransformed ground motion and calculate coefficient of variation (COV). Fit linear equation to plots of COV against mean. Find no significant trend for almost all periods so conclude logarithmic transformation is justified for all periods. Compute standard deviation of logarithmically-transformed ground motions and fit linear equations w.r.t. M_{w}. Find that dependence of scatter on magnitude is not significant. Compute mean standard deviation of all bins and find limit on lowest possible standard deviation using only M_{w}and r_{hypo}. - Aim for simplest functional form and add complexity in steps, checking the statistical significance of each
modification and its influence on standard error. Try including an anelastic term, quadratic M
_{w}dependence and magnitude-dependent decay term but find none of these is statistically significant and/or leads to a reduction in standard deviation. - Try one-stage maximum likelihood regression but find higher standard deviation so reject it. Originally use two-stage approach of Joyner and Boore (1981).
- Find that coefficients closely match a theoretical model at long periods.
- Consider style-of-faulting by adding terms: a
_{N}E_{N}+ a_{R}E_{R}+ a_{S}E_{S}where E_{x}are dummy variables for normal, reverse and strike-slip mechanisms. Find that reduction in standard deviation is only appreciable for limited period ranges but keep terms in final model. - Replace terms: a
_{B}S_{B}+a_{C}S_{C}+a_{D}S_{D}by b_{V }log_{10}(V_{s,30}∕V_{a}) so that site amplification factor is continuous. V_{s,30}available for about 85% of records. To be consistent between both approaches constrain V_{a}to equal 800m∕s. Find b_{V }closely matches theoretical values 1 close to resonance period and 0.5 at long periods. - Examine residuals w.r.t. r
_{hypo}and M_{w}. Find no trends.