where A is in gal, a = 0.59, c = 0.0060 × 100.5Mw (adopted from Si and Midorikawa (2000)), d1= 0.00
(for crustal earthquakes), d2= 0.08 (for inter-plate earthquakes), d3= 0.30 (for intra-plate earthquakes),
e = 0.02, h = 0.0023, k = 0.003 [adopted from Si and Midorikawa (2000)], σintra-event= 0.27 and
Use Vs,30 where available. Multiply PGA values from rock sites by 1.4 to normalise them w.r.t. PGA at
All records from the free-field or small buildings where soil-structure interaction is negligible.
Data from different types of instruments hence instrument correct and bandpass filter.
Classify earthquakes into these three types:
S1= 1, S2= S3= 0. 12 earthquakes, 1255 records. Focal depths, D, between 3 and 30km.
S2= 1, S1= S3= 0. 10 earthquakes, 640 records. 6 ≤ D ≤ 49km.
S3= 1, S1= S2= 0. 11 earthquakes, 1440 records. 30 ≤ D ≤ 120km.
Most data from Mw< 7. No data between 6.9 and 7.6.
Use separate functional forms for D ≤ 30km and D > 30km because of significantly faster decay for deeper
Plot histograms of residuals and conclude that they are lognormally distributed.
Compute σ for 4 M ranges: 5.5–5.9, 6.0–6.5, 6.6–6.9 and 7.6–8.3. Find slight decrease in σ w.r.t. M.
Compute σ for ranges of 20km. Find significantly smaller σs for distances < 50km and almost constant σs
for longer distances.
Compute σ for ranges of PGA of roughly 50km. Find much larger σs for small PGA than for large PGA.
Believe that main cause of M-dependent σ is that stress-drop is M-dependent and that radiation pattern
and directivity are not likely to be significant causes.
Believe that distance-dependent σ is likely to be due to randomness of propagation path (velocity and
Believe site effects do not contribute greatly to the variance.
Plot PGA versus distance and observe a saturation at several hundred cm∕s2, which suggest may be due
to nonlinear soil behaviour.
Plot σ w.r.t. PGA for three site categories: 100 ≤ Vs,30≤ 300m∕s, 300 ≤ Vs,30≤ 600m∕s and
600 ≤ Vs,30≤ 2600m∕s. Find σ lower for soft soils than for stiff soils, which believe may demonstrate that
nonlinear soil response is a cause of PGA-dependent σ.
Note that because inter-event σ is significantly smaller than intra-event σ, source effects are unlikely to be
the main cause for observed σ dependencies.