- Ground-motion model is:
where PGA is in g, for unconstrained model a = 0.0159, b = 0.868, c1 = 0.0606, c2 = 0.700, d = 1.09 and
σ = 0.372 (on natural logarithm) and for constrained model a = 0.0185, b = 1.28, c1 = 0.147, c2 = 0.732, d = 1.75
and σ = 0.384 (in terms of natural logarithm).
Uses this functional form because capable of modelling possible nonlinear distance scaling in near field
and because distance at which transition from near field to far field occurs probably proportional to fault
rupture zone size.
- Considers six site classifications but does not model:
- Recent alluvium: Holocene Age soil with rock ≥ 10m deep, 71 records.
- Pleistocene deposits: Pleistocene Age soil with rock ≥ 10m deep, 22 records.
- Soft rock: Sedimentary rock, soft volcanics, and soft metasedimentary rock, 14 records.
- Hard rock: Crystalline rock, hard volcanics, and hard metasedimentary rock, 9 records.
- Shallow soil deposits: Holocene or Pleistocene Age soil < 10m deep overlying soft or hard rock, 17
records. Not used in analysis.
- Soft soil deposits: extremely soft or loose Holocene Age soils, e.g. beach sand or recent floodplain,
lake, swamp, estuarine, and delta deposits, 1 record. Not used in analysis.
- Notes that data from areas outside western USA may be substantially different than those from western
USA due to tectonics and recording practices but far outweighed by important contribution these data
can make to understanding of near-source ground motion.
- Notes use of only near-source data has made differences in anelastic attenuation negligible to inherent
scatter from other factors.
- Selects data from shallow tectonic plate boundaries generally similar to western N. America, deep
subduction events excluded because of differences in travel paths and stress conditions.
- Selects data from instruments with similar dynamic characteristics as those used in USA to avoid bias,
therefore excludes data from SMAC accelerographs in Japan.
- Selects data which meet these criteria:
- Epicentres known with an accuracy of 5km or less, or accurate estimate of closest distance to fault
rupture surface known.
- Magnitudes accurate to within 0.3 units.
- Distances were within 20, 30, and 50km for magnitudes less than 4.75 between 4.75 and 6.25 and
greater than 6.25 respectively. Only uses data from earthquakes with magnitude ≥ 5.0 because of
greatest concern for most design applications.
- Hypocentres or rupture zones within 25km of ground surface.
- PGA≥ 0.2m∕s2 for one component, accelerographs triggered early enough to capture strong phase of
- Accelerograms either free-field, on abutments of dams or bridges, in lowest basement of buildings, or
on ground level of structures without basements. Excluded Pacoima Dam record, from San Fernando
(9/2/1971) earthquake due to topographic, high-frequency resonance due to large gradation in wave
propagation velocities and amplification due to E-W response of dam.
- Well distributed data, correlation between magnitude and distance only 6%.
- Uses PGA from digitised, unprocessed accelerograms or from original accelerograms because fully processed
PGAs are generally smaller due to the 0.02s decimation and frequency band-limited filtering of records.
- Uses mean of two horizontal components because more stable peak acceleration parameter than either
single components taken separately or both components taken together.
- Magnitude scale chosen to be generally consistent with Mw. Division point between using ML and Ms
varied between 5.5 and 6.5; finds magnitudes quite insensitive to choice.
- Notes rrup is a statistically superior distance measure than epicentral or hypocentral and is physically
consistent and meaningful definition of distance for earthquakes having extensive rupture zones.
- Does not use all data from San Fernando earthquake to minimize bias due to large number of records.
- Uses seven different weighting schemes, to control influence of well-recorded earthquakes (e.g. San Fernando
and Imperial Valley earthquakes). Giving each record or each earthquake equal weight not reasonable
representation of data. Uses nine distance dependent bins and weights each record by a relative weighting
factor 1∕ni,j, where ni,j is total number of recordings from ith earthquake in jth interval.
- Finds unconstrained coefficients and all coefficients statistically significant at 99%.
- Finds coefficients with d constrained to 1.75 (representative of far-field attenuation of PGA) and c2 = b∕d,
which means PGA is independent of magnitude at the fault rupture surface. All coefficients statistically
significant at 99%. Notes similarity between two models.
- Plots normalised weighted residuals against distance, magnitude
and predicted acceleration. Finds that residuals uncorrelated, at 99%, with these variables.
- Normal probability plots, observed distribution of normalised weighted residuals and Kolmogorov-Smirnov
test, at 90%, confirms that PGA can be accepted as being lognormally distributed.
- Finds effects of site geology, building size, instrument location and mechanism to be extensively interrelated
so selects only records from free-field or small structures.
- Analyses all selected data, find sites of classes E and F significantly higher PGA , at 90% level, so removes
records from E and F.
- Finds differences in PGA from other site categories to be negligible but notes that it cannot be extended
to PGV, PGD, spectral ordinates or smaller magnitudes or further distances.
- Distribution with mechanism is: 69 from strike-slip, 40 from reverse, 5 from normal and 2 records from
oblique. Finds that reverse fault PGAs are systematically higher, significant at 90%, than those from other
fault types although size of bias is due to presence of data from outside N. America.
- Considers soil (A and B) records from small buildings (115 components) and in free-field and those obtained
in lowest basement of large buildings (40 components). Finds PGA significantly lower, at 90% level, in
- Finds topographic effects for 13 components used in final analysis (and for 11 components from shallow
soil stations) to be significantly higher, at 90%, although states size of it may not be reliable due to small
number of records.
- Removes Imperial Valley records and repeats analysis. Finds that saturation of PGA with distance is not
strongly dependent on this single set of records. Also repeats analysis constraining c2 = 0, i.e. magnitude
independent saturation, and also constraining c1 = c2 = 0, i.e. no distance saturation, finds variance when
no distance saturation is significantly higher, at 95%, than when there is saturation modelled.
- Finds that magnitude saturation effects in modelling near-source behaviour of PGA is important and c2 is
significantly greater than zero at levels of confidence exceeding 99%. Also variance is reduced when c2≠0
although not at 90% or above.
- Repeats analysis using distance to surface projection of fault, finds reduced magnitude saturation but
similar magnitude scaling of PGA for larger events.