- Ground-motion model for rupture distance is:
where A is in cm∕s2, a = 0.50, h = 0.0036, d1 = 0, d2 = 0.09, d3 = 0.28, e = 0.60, k = 0.003 and σ = 0.27 (c1 and
c2 are not given).
Ground-motion model for equivalent hypocentral distance (EHD) is:
where A is in cm∕s2, a = 0.50, h = 0.0043, d1 = 0, d2 = 0.01, d3 = 0.22, e = 0.61, k = 0.003 and σ = 0.28.
- Use two site categories for most records following Joyner and Boore (1981):
- Records from free-field or small buildings where soil-structure interaction effects are negligible.
- Records from three different type of instrument so instrument correct. Filter with corner frequencies,
chosen according to noise level, a) 0.08 & 0.15Hz, b) 0.10 & 0.20Hz or c) 0.15 to 0.33Hz.
- Exclude records obviously affected by soil liquefaction.
- Focal depth (defined as average depth of fault plane), D, between 6 and 120km; most less than 40km.
- Select records satisfying: distances < 300km for Mw > 7, distances < 200km for 6.6 ≤ Mw ≤ 7, distances
< 150km for 6.3 ≤ Mw ≤ 6.5 and distances < 100km for Mw < 6.3.
- Fix k = 0.003.
- Multiply rock PGAs by 1.4 to get soil PGA based on previous studies.
- Use three fault types: crustal (<719 records from 9 earthquakes) ⇒ S1 = 1,S2 = 0,S3 = 0, inter-plate
(<291 records from 7 earthquakes) ⇒ S2 = 1,S1 = 0,S3 = 0 and intra-plate (<127 records from 5
earthquakes) ⇒ S3 = 1,S1 = 0,S2 = 0.
- Use weighted regression giving more weight to near-source records (weight factor of 8 for records < 25km,
4 for records between 20 and 50km, 2 for records between 50 and 100km and 1 for records > 100km). Use
only three earthquakes with sufficient near-source data to find c1 and c2 then use all earthquakes to find a,
h, di, e in second stage using weighted regression dependent on number of recordings for each earthquake
(weight factor of 3 for >83 records, 2 for between 19 and 83 records, 1 for <19 records.
- Note that Mw and D are positively correlated so a and h may not be correctly determined when using
rupture distance. Constrain a for rupture distance model to that obtained for EHD and constrain PGA to
be independent of magnitude at 0km and repeat regression. Coefficients given above.