- Ground-motion model is: where PSA(T) is in cm∕s2, b1 = 0.0031, b2 = 1.0848, b3 = -0.0835, b4 = -2.4423, b5 = 0.2081, b6 = 8.0282,
b7 = 0.0781, b8 = 0.0208, b9 = -0.0292, b10 = 0.0963, σ1 = 0.599 ± 0.041 - 0.058 ± 0.008Mw (intra-event)
and σ2 = 0.323 ± 0.075 - 0.031 ± 0.014Mw (inter-event).
- Use three site categories:
- V s,30 < 360m∕s. SS = 1, SA = 1. 75 records from 3 ≤ Mw < 5.
- 360 < V s,30 < 750m∕s. SA = 1, SS = 0. 173 records from 3 ≤ Mw < 5.
- V s,30 ≥ 750m∕s. SS = 0, SA = 0. 217 records from 3 ≤ Mw < 5.
- Use three faulting mechanism categories:
- FN = 1, FR = 0. 291 records from 3 ≤ Mw < 5.
- FN = 0, FR = 0. 140 records from 3 ≤ Mw < 5.
- FR = 1, FN = 0. 24 records from 3 ≤ Mw < 5. 12% of all records. Note that reverse events poorly
- 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 ≤ Mw < 5. Search
ISESD for records from earthquakes with Mw < 5, known site class and known faulting mechanism. Find
one record from a Mw2 event but only 11 for events with Mw < 3 therefore use Mw3 as lower limit.
Select 465 records from 158 events with 3 ≤ Mw < 5. Many additional records from Greece (mainly
singly-recorded events), Italy, Spain, Switzerland, Germany and France. Few additional records from Iran
- Data well distributed w.r.t. magnitude, distance and site class but for Mw < 4 data sparse for distances
- 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 Mw 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
- Compute residuals with respect to Mw 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. Mw 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.