2.64 Fukushima et al. (1988) & Fukushima and Tanaka (1990)

• 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):

  1.

  Rock: 41 records

  2.

  Hard: ground above Tertiary period or thickness of diluvial deposit above bedrock < 10m, 44 records.

  3.

  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 records.

  4.

  Soft soil: other soft ground such as reclaimed land, 33 records.

• Use 1100 mean PGA values from 43 Japanese earthquakes (6.0 ≤ M_JMA ≤ 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, M_JMA > 5.0 and predicted PGA ≥ 0.1m∕s2. US data selection criteria: d_r ≤ 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 Japanese data.
• 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.