- Ground-motion model is:
where A is in cm∕s2, a = 0.41, b = 0.0034, c = 0.032, d = 1.30 and σ = 0.21.
- Use four site categories for some Japanese stations (302 Japanese records not classified):
- Rock: 41 records
- Hard: ground above Tertiary period or thickness of diluvial deposit above bedrock < 10m, 44 records.
- Medium: thickness of diluvial deposit above bedrock > 10m, or thickness of alluvial deposit above
bedrock < 10m, or thickness of alluvial deposit < 25m and thickness of soft deposit is < 5m, 66
- Soft soil: other soft ground such as reclaimed land, 33 records.
- Use 1100 mean PGA values from 43 Japanese earthquakes (6.0 ≤ MJMA ≤ 7.9, focal depths
≤ 30km) recorded at many stations to investigate one and two-stage methods. Fits log A = c -
blog X (where X is hypocentral distance) for each earthquake and computes mean of b, b. Also
fits log A = aM - b*log X + c using one-stage method. Find that b > b* and shows that this is
because magnitude and distance are strongly correlated (0.53) in data set. Find two-stage method
of Joyner and Boore (1981) very effective to overcome this correlation and use it to find similar
distance coefficient to b. Find similar effect of correlation on distance coefficient for two other models:
log A = aM - blog(Δ + 30) + c and log A = aM - log X - bX + c, where Δ is epicentral distance.
- Japanese data selection criteria: focal depth < 30km, MJMA > 5.0 and predicted PGA ≥ 0.1m∕s2. US
data selection criteria: dr ≤ 50km, use data from Campbell (1981).
- Because a affects distance and magnitude dependence, which are calculated during first and second steps
respectively use an iterative technique to find coefficients. Allow different magnitude scaling for US and
- For Japanese data apply station corrections before last step in iteration to convert PGAs from different
soil conditions to standard soil condition using residuals from analysis.
- Two simple numerical experiments performed. Firstly a two sets of artificial acceleration data was generated
using random numbers based on attenuation relations, one with high distance decay and which contains
data for short distance and one with lower distance decay, higher constant and no short distance data. Find
that the overall equation from regression analysis has a smaller distance decay coefficient than individual
coefficients for each line. Secondly find the same result for the magnitude dependent coefficient based on
similar artificial data.
- Exclude Japanese data observed at long distances where average acceleration level was predicted (by using
an attenuation relation derived for the Japanese data) to be less than the trigger level (assume to be about
0.05m∕s2) plus one standard deviation (assume to be 0.3), i.e. 0.1m∕s2, to avoid biasing results and giving
a lower attenuation rate.
- Use the Japanese data and same functional form and method of Joyner and Boore (1981) to find an
attenuation relation; find the anelastic coefficient is similar so conclude attenuation rate for Japan is almost
equal to W. USA.
- Find difference in constant, d, between Japanese and W. USA PGA values.
- Plot residuals against distance and magnitude and find no bias or singularity.