4.200 Rodriguez-Marek and Montalva (2010)

• Ground-motion model is a simplified version of Boore and Atkinson (2008), because it is the simplest NGA functional form¹¹:
  
• Sites characterized by V _s,30, V _s,hole (shear-wave velocity at depth of instrument), S_surface (1 for surface record, 0 otherwise), S₁₀₀ (1 for borehole record from < 150m depth, 0 otherwise) and S₂₀₀ (1 for borehole record from > 150m depth, 0 otherwise).
• Response parameter is pseudo-acceleration for 5% damping.
• Use the same data as Cotton et al. (2008) (see Section 2.292).
• Develop GMPEs for use in the estimation of single-station σ.
• Note that functional form assumes that magnitude and distance dependency are the same for both surface and borehole records. Also assume that site amplification is linear, which note appears to be true for most records but not all but insufficient data to constrain nonlinearity using purely empirical method so ignore it.
• For regression: use only surface data to constrain b_lin, use both surface and borehole records to compute inter-event σs and assume intra-event σs independent of magnitude. Note that final assumption is somewhat limiting but use residual analysis to examine dependency of intra-event terms on depth, V _s,30 and magnitude.
• Compute single-station σs based on residuals from the 44 stations that recorded ≥ 15 earthquakes. Averaged these 44 σs to obtain a single estimate of single-station σ. Note that more work on these σs is being undertaken. Find single-station σs are on average 25% lower than total σ. Find that total σs obtained for borehole stations lower than those at surface but the single-station σs are not considerable different on the surface and in boreholes.