### 2.130 Molas and Yamazaki (1995)

• Ground-motion model is:

where y is in cms2, b0 = 0.206, b1 = 0.477, b2 = -0.00144, b3 = -1, b4 = 0.00311, σ = 0.276 and ci is site coefficient for site i (use 76 sites), given in paper but are not reported here due to lack of space.

• Records from accelerometers on small foundations detached from structures; thus consider as free-field.
• Exclude records with one horizontal component with PGA < 1cms2[0.01ms2] because weaker records not reliable due to resolution (±0.03cms2[0.0003ms2]) of instruments.
• Exclude earthquakes with focal depths equal to 0km or greater than 200km, due to lack of such data. Depths (depth of point on fault plane closest to site), h, between about 1km to 200km.
• Apply a low-cut filter with cosine-shaped transition from 0.01 to 0.05Hz.
• Positive correlation between magnitude and distance so use two-stage method.
• Note different definition for MJMA for focal depths > 60km.
• Firstly do preliminary analysis with b4 = 0 and no site coefficients; find b2 is positive so constrain to 0 but find b3 < -1.0 so constrain b3 to -1.0 and unconstrain b2. Find linear dependence in residuals on h especially for h < 100km. Find significant improvement in coefficient of determination, R2, using terms b4h and c.
• Find singularity in matrices if apply two-stage method, due to number of coefficients, so propose a iterative partial regression method.
• Also separate data into five depth ranges (A: h = 0.1 to 30km, 553 records from 111 earthquakes; B: h = 30 to 60km, 778 records from 136 earthquakes; C: h = 60 to 90km, 526 records from 94 earthquakes; D: h = 90 to 120km, 229 records from 31 earthquakes; E: h = 120 to 200km, 112 records from 19 earthquakes) and find attenuation equations for each range. Note results from D & E may not be reliable due to small number of records. Find similar results from each group and all data together.
• Find weak correlation in station coefficients with soil categories, as defined in Iwasaki et al. (1980), but note large scatter.