- Ground-motion model is:
_{1}= 0.0031, b_{2}= 1.0848, b_{3}= -0.0835, b_{4}= -2.4423, b_{5}= 0.2081, b_{6}= 8.0282, b_{7}= 0.0781, b_{8}= 0.0208, b_{9}= -0.0292, b_{10}= 0.0963, σ_{1}= 0.599 ± 0.041 - 0.058 ± 0.008M_{w}(intra-event) and σ_{2}= 0.323 ± 0.075 - 0.031 ± 0.014M_{w}(inter-event). - Use three site categories:
- Soft soil
- V
_{s,30}< 360m∕s. S_{S}= 1, S_{A}= 1. 75 records from 3 ≤ M_{w}< 5. - Stiff soil
- 360 < V
_{s,30}< 750m∕s. S_{A}= 1, S_{S}= 0. 173 records from 3 ≤ M_{w}< 5. - Rock
- V
_{s,30}≥ 750m∕s. S_{S}= 0, S_{A}= 0. 217 records from 3 ≤ M_{w}< 5.

- Use three faulting mechanism categories:
- Normal
- F
_{N}= 1, F_{R}= 0. 291 records from 3 ≤ M_{w}< 5. - Strike-slip
- F
_{N}= 0, F_{R}= 0. 140 records from 3 ≤ M_{w}< 5. - Reverse
- F
_{R}= 1, F_{N}= 0. 24 records from 3 ≤ M_{w}< 5. 12% of all records. Note that reverse events poorly represented.

- Investigate whether Ground-motion models can be extrapolated outside the magnitude range for which they were derived.
- Extend dataset of Akkar and Bommer (2007b) by adding data from earthquakes with 3 ≤ M
_{w}< 5. Search ISESD for records from earthquakes with M_{w}< 5, known site class and known faulting mechanism. Find one record from a M_{w}2 event but only 11 for events with M_{w}< 3 therefore use M_{w}3 as lower limit. Select 465 records from 158 events with 3 ≤ M_{w}< 5. Many additional records from Greece (mainly singly-recorded events), Italy, Spain, Switzerland, Germany and France. Few additional records from Iran and Turkey. - Data well distributed w.r.t. magnitude, distance and site class but for M
_{w}< 4 data sparse for distances > 40km. - Additional data has been uniformly processed with cut-offs at 0.25 and 25Hz.
- Use same regression technique as Akkar and Bommer (2007b).
- Observe that equations predict expected behaviour of response spectra so conclude that equations are robust and reliable.
- Compare predicted ground motions with predictions from model of Akkar and Bommer (2007b) and find large differences, which they relate to the extrapolation of models outside their range of applicability.
- Investigate effect of different binning strategies for pure error analysis (Douglas and Smit, 2001). Derive weighting functions for published equations using bins of 2km × 0.2 magnitude units and require three records per bin before computing σ. Repeat using 1km × 0.1 unit bins. Find less bins allow computation of σ. Also repeat original analysis but require four or five records per bin. Find more robust estimates of σ but note that four or five records are still small samples. Also repeating using logarithmic rather than linear distance increments for bins since ground motions shown to mainly decay geometrically. For all different approaches find differences in computed magnitude dependence depending on binning scheme. None of the computed slopes are significant at 95% confidence level.
- Repeat analysis assuming no magnitude dependence of σ. Find predictions with this model are very similar to those assuming a magnitude-dependent σ.
- Find that compared to σs of Akkar and Bommer (2007b) that inter-event σs has greatly increased but
that intra-event σs has not, which they relate to the uncertainty in the determination of M
_{w}and other parameters for small earthquakes. - Repeat analysis exclude data from (in turn) Greece, Italy, Spain and Switzerland to investigate importance of regional dependence on results. Find that results are insensitive to the exclusion of individual regional datasets.
- Compute residuals with respect to M
_{w}for four regional datasets and find that only for Spain (the smallest set) is a significant difference to general results found. - Examine total and intra-event residuals for evidence of soil nonlinearity. Find that evidence for nonlinearity is weak although the expected negative slopes are found. Conclude that insufficient data (and too crude site classification) to adjust the model for soil nonlinearity.
- Plot inter-event and intra-event residuals w.r.t. M
_{w}and find no trend and hence conclude that new equations perform well for all magnitudes. - Do not propose model for application in seismic hazard assessments.