- Ground-motion model is:
where y is in m∕s2, a1 = 2.522, a2 = -0.142, a3 = -3.184, a4 = 0.314, a5 = 7.6, a6 = 0.137, a7 = 0.050,
a8 = -0.084, a9 = 0.062, a10 = -0.044, σ1 = 0.665 - 0.065Mw (intra-event) and σ2 = 0.222 - 0.022Mw
- Use three site categories:
SS = 1, SA = 0
- Soft soil (S), 180 < V s,30 ≤ 360m∕s. 143 records.
SS = 0, SA = 1
- Stiff soil (A), 360 < V s,30 ≤ 750m∕s. 238 records.
SS = 0, SA = 0
- Rock (R), V s,30 > 750m∕s. 203 records.
Originally include a fourth category, very soft soil (V s,30 ≤ 180m∕s), but only included 11 records so
combined with soft soil records. Note that measured V s,30 only exist for 89 of 338 stations contributing
161 records so use descriptions of local site conditions to classify stations. Exclude records from stations
with unknown site conditions because could not be handled by chosen regression method.
- Use only data from Europe and Middle East because believe their databank is reasonably complete for
moderate and large earthquakes that occurred in region. Also these data have been carefully reviewed in
previous studies. Finally based on a previous study believe motions in California could be significantly
higher than those in Europe. Note that including these data would increase the quantity of high-quality
near-source data available.
- Combine data from all seismically active parts of Europe and the Middle East into a common dataset
because a previous study shows little evidence for regional differences between ground motions in different
regions of Europe.
- Only use earthquakes with a M0 estimate for which to calculate Mw. Do not convert magnitudes from other
scales because this increases the uncertainty in the magnitude estimates. Exclude records from earthquakes
with Mw < 5 in order to have a good distribution of records at all magnitudes. Note that this also excludes
records from small earthquakes that are unlikely to be of engineering significance.
- Use rjb because does not require a depth estimate, which can be associated with a large error.
- Exclude records from > 100km because: excludes records likely to be of low engineering significance,
reduces possible bias due to non-triggering instruments, reduces effect of differences in anelastic decay
in different regions and it gives a reasonably uniform distribution w.r.t. magnitude and distance, which
reduces likelihood of problems in regression analysis.
- Use only earthquakes with published focal mechanism in terms of trends and plunges of T, B and P axes
because estimating faulting type based on regional tectonics or to be the same as the associated
mainshock can lead to incorrect classification. Classify earthquakes using method of Frohlich and
- Plunge of T axis > 50∘. 26 earthquakes, 91 records, FT = 1, FN = 0, FO = 0.
- Plunge of P axis > 60∘. 38 earthquakes, 191 records, FT = 0, FN = 1, FO = 0.
- Plunge of B axis > 60∘. 37 earthquakes, 160 records, FT = 0, FN = 0, FO = 0.
- All other earthquakes. 34 earthquakes, 153 records, FT = 0, FN = 0, FO = 1.
Use this method because does not require knowledge of which plane is the main plane and which the
- Do not exclude records from ground floors or basements of large buildings because of limited data.
- Exclude records from instruments that triggered late and those that were poorly digitised.
- Instrument correct records and then apply a low-pass filter with roll-off and cut-off frequencies of 23 and
25Hz for records from analogue instruments and 50 and 100Hz for records from digital instruments. Select
cut-off frequencies for high-pass bidirectional Butterworth filtering based on estimated signal-to-noise ratio
and also by examining displacement trace. For records from digital instruments use pre-event portion of
records as noise estimate. For those records from analogue instruments with an associated digitised fixed
trace these were used to estimate the cut-offs. For records from analogue instruments without a fixed trace
examine Fourier amplitude spectrum and choose the cut-offs based on where the spectral amplitudes do
not tend to zero at low frequencies. Note that there is still some subjective in the process. Next choose a
common cut-off frequency for all three components. Use a few records from former Yugoslavia that were
only available in corrected form.
- Only use records with three usable components in order that ground-motion estimates are unbiased and
that mutually consistent horizontal and vertical equations could be derived.
- Note lack of data from large (Mw > 6.5) earthquakes particularly from normal and strike-slip earthquakes.
- Data from: Italy (174 records), Turkey (128), Greece (112), Iceland (69), Albania (1), Algeria (3), Armenia
(7), Bosnia & Herzegovina (4), Croatia (1), Cyprus (4), Georgia (14), Iran (17), Israel (5), Macedonia (1),
Portugal (4), Serbia & Montenegro (24), Slovenia (15), Spain (6), Syria (5) and Uzbekistan (1).
- Note that much strong-motion data could not be used due to lack of local site information.
- Select one-stage maximum-likelihood regression method because accounts for correlation between ground
motion from same earthquake whereas ordinary one-stage method does not. Note that because there is
little correlation between Mw and distance in the data used (correlation coefficient of 0.23) ordinary
one-stage and one-stage maximum-likelihood methods give similar coefficients. Do not use two-stage
maximum-likelihood method because underestimates σ for sets with many singly-recorded earthquakes (35
earthquakes were only recorded by one station). Do not use method that accounts for correlation between
records from same site because records are used from too many different stations and consequently method
is unlikely to lead to an accurate estimate of the site-to-site variability (196 stations contribute a single
record). Do not use methods that account for uncertainty in magnitude determination because assume all
magnitude estimates are associated with the same uncertainty since all Mw are derived from published
- Apply pure error analysis of Douglas and Smit (2001). Divide dataspace into 0.2Mw units by 2km intervals
and compute mean and unbiased standard deviation of untransformed ground motion in each bin. Fit
a linear equation to graphs of coefficient of variation against ground motion and test if slope of line is
significantly different (at 5% significance level) than zero. If it is not then the logarithmic transformation is
justified. Find that slope of line is not significantly different than zero so adopt logarithmic transformation
of ground motion.
- Use pure error analysis to compute mean and unbiased standard deviation of logarithmically transformed
ground motion in each 0.2Mw × 2km bin. Plot the standard deviations against Mw and fit linear
equation. Test significance (5% level) of slope. Find that it is significantly different than zero and hence
magnitude-independent standard deviation is not justified. Use the reciprocals of fitted linear equations
as weighting functions for regression analysis.
- Using the standard deviations computed by pure error analysis for each bin estimate lowest possible σ for
- Investigate possible magnitude-dependence of decay rate of ground motions using ten best-recorded
earthquakes (total number of records between 13 and 26). Fit PGAs for each earthquake with equation of
form: log y = a1 + a2 log . Plot decay rates (a2) against Mw and fit a linear equation. Find that
the fitted line has a significant slope and hence conclude that data supports a magnitude-dependent decay
rate. Assume a linear dependence between decay rate and Mw due to limited data.
- Try including a quadratic magnitude term in order to model possible differences in scaling of ground
motions for earthquakes that rupture entire seismogenic zone. Find that term is not significant at 5% level
- Could not simultaneously find negative geometric and anelastic decay coefficients so assume decay
attributable to anelastic decay is incorporated into geometric decay coefficient.
- Test significance of all coefficients at 5% level. Retain coefficients even if not significant.
- Note that there is not enough data to model possible distance dependence in effect of faulting mechanism
or nonlinear soil effects.
- Compute median amplification factor (anti-logarithm of mean residual) for the 16 stations that have
recorded more than five earthquakes. Find that some stations show large amplifications or large
deamplifications due to strong site effects.
- Compute median amplification factor for the ten best recorded earthquakes. Find that most earthquakes
do not show significant overall differences but that a few earthquakes do display consistently lower or
higher ground motions.
- Plot residual plots w.r.t. weighted Mw and weighted distance and find no obvious dependence of scatter
on magnitude or distance.
- Plot histograms of binned residuals.
- Compare predicted and observed PGAs from the 2004 Parkfield earthquake and find a close match. Note
that this may mean that the exclusion of data from California based on possible differences in ground
motions was not justified.