2.58 Sabetta and Pugliese (1987)

• Ground-motion model is:

  where y is in g and for distance to surface projection of fault a = -1.562, b = 0.306, e = 0.169, h = 5.8 and σ = 0.173.

• Use two site categories:

  S = 0

  Stiff and deep soil: limestone, sandstone, siltstone, marl, shale and conglomerates (V _s > 800m∕s) or depth of soil, H, > 20m, 74 records.

  S = 1

  Shallow soil: depth of soil, H, 5 ≤ H ≤ 20m, 21 records.

• Select records which satisfy these criteria:

  1.

  Reliable identification of the triggering earthquake.

  2.

  Magnitude greater than 4.5 recorded by at least two stations.

  3.

  Epicentres determined with accuracy of 5km or less.

  4.

  Magnitudes accurate to within 0.3 units.

  5.

  Accelerograms from free-field. Most are from small electric transformer cabins, 4 from one- or two-storey buildings with basements and 5 from near abutments of dams.

• Depths between 5.0 and 16.0km with mean 8.5km.
• Focal mechanisms are: normal and oblique (7 earthquakes, 48 records), thrust (9 earthquakes, 43 records) and strike-slip (1 earthquake, 4 records).
• Notes lack of records at short distances from large earthquakes.
• Records baseline-, instrument-corrected and filtered with cutoff frequencies determined by visual inspection in order to maximise signal to noise ratio within band. Cutoff frequencies ranged from 0.2 to 0.4Hz and from 25 to 35Hz. This correction routine thought to provide reliable estimates of PGA so uncorrected PGA do not need to be used.
• For well separated multiple shocks, to which magnitude and focal parameters refer, use only first shock.
• Magnitude scale assures a linear relationship between logarithm of PGA and magnitude and avoids saturation effects of M_L.
• Distance to surface projection of fault rupture thought to be a more physically consistent definition of distance for earthquakes having extensive rupture zones and is easier to predict for future earthquakes. Also reduces correlation between magnitude and distance.
• Use Exploratory Data Analysis using the ACE procedure to find transformation functions of distance, magnitude and PGA.
• Include anelastic attenuation term but it is positive and not significant.
• Include magnitude dependent h equal to h₁ exp(h₂M) but find h₂ not significantly different than zero. Note distribution of data makes test not definitive.
• Find geometric attenuation coefficient, c, is close to -1 and highly correlated with h so constrain to -1 so less coefficients to estimate.
• Consider deep soil sites as separate category but find difference between them and stiff sites is not significant.
• Also use two-stage method but coefficients and variance did not change significantly with respect to those obtained using one-stage method, due to uniform distribution of recordings among earthquakes.
• Find no significant trends in residuals, at 99% level and also no support for magnitude dependent shape for attenuation curves.
• Exclude records from different seismotectonic and geological regions and repeat analysis. Find that predicted PGA are similar.
• Plot residuals from records at distances 15km or less against magnitude; find no support for magnitude dependence of residuals.
• Note some records are affected by strong azimuthal effects, but do not model them because they require more coefficients to be estimated, direction of azimuthal effect different from region to region and azimuthal effects have not been used in other relationships.