2.338 Anderson and Uchiyama (2011)

• Ground-motion model is:

where Y is in cms2, a1 = 0.97412, a2 = 0.0074138, a3 = -0.0044524 and a4 = 2.1041 for mean horizontal; a1 = 0.95461, a2 = 0.0073811, a3 = -0.0045837 and a4 = 2.4935 for vectorially-resolved component including vertical; a1 = 0.96387, a2 = 0.006973, a3 = -0.00466 and a4 = 2.3969 for vectorially-resolved component using two horizontal components; and a1 = 0.98212, a2 = 0.0073442, a3 = -0.0044279 and a4 = 1.7006 for vertical; a5 = 0.0261 and a6 = 0.9594 for all. σ = 0.70.

• Data from 36 rock sites, which recorded between 1 and 23 events.
• All events recorded by 10 stations so that number of events and stations are comparable.
• Only use earthquakes with Global CMT Mw available.
• Focal depths, Z, between 5 and 69km with most 25km.
• Try a different function for the distance decay (-ln) and find that fits the data almost equally well. Prefer the selected form because it has been used for Japanese models using more data.
• Correlation between parameters is: between M and R 0.49, between M and Z 0.21 and between Z and R 0.41.
• Fit distance decay term of form -ln(R+c) to each earthquake individually. Find a5 and a6 from plot of c against M. Choose a5 and a6 that can be used for all across periods. Next find coefficients a1 to a4 based on data adjusted by distance decay term.
• Find no trends in residuals w.r.t. M, Z or R.
• Plot observations against predictions for magnitude-unit wide intervals and find good fit.
• Note that model is not definitive because many other data available. Believe model is adequate for illustration of how a model can be improved by event, site and path terms.