### 2.226 Midorikawa and Ohtake (2004)

• Ground-motion models are:
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 σinter-event = 0.16.
• Use two site categories [definitions of Joyner and Boore (1981)]:
Rock
Soil

Use V s,30 where available. Multiply PGA values from rock sites by 1.4 to normalise them w.r.t. PGA at soil sites.

• 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:
Crustal
S1 = 1, S2 = S3 = 0. 12 earthquakes, 1255 records. Focal depths, D, between 3 and 30km.
Inter-plate
S2 = 1, S1 = S3 = 0. 10 earthquakes, 640 records. 6 D 49km.
Intra-plate
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 earthquakes.
• Plot histograms of residuals and conclude that they are lognormally distributed.
• Compute σ for 4 M ranges: 5.55.9, 6.06.5, 6.66.9 and 7.68.3. 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 Q-structure).
• Believe site effects do not contribute greatly to the variance.
• Plot PGA versus distance and observe a saturation at several hundred cms2, which suggest may be due to nonlinear soil behaviour.
• Plot σ w.r.t. PGA for three site categories: 100 V s,30 300ms, 300 V s,30 600ms and 600 V s,30 2600ms. 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.