- Ground-motion model is for combined model using both surface and borehole
records
^{28}(same as Boore and Atkinson (2008)):_{med}^{A}is in g, M_{ref}= 4.5, R_{ref}= 1km, V_{ref}= 760m∕s, h_{ref}= 60m and Vshole_{ref}= 3000m∕s (reference values); c_{1}= -1.2534, c_{2}= 0.4271, c_{3}= -0.0140, e_{1}= -0.0663, e_{5}= -0.5997, e_{6}= -0.5012, e_{7}= 0, b_{lin}= -0.4665, bh800 = -0.1801, a_{100}= -1.4372, a_{200}= -1.6518, b_{100}= -0.0269, b_{200}= -0.1884, c_{100}= -0.2666, c_{200}= -0.3793, ϕ = 0.6293 (intra-event) for M_{w}< 5, ϕ = 0.6202 (intra-event) for M_{w}> 6.5, τ = 0.4929 (inter-event) for M_{w}< 5, τ = 0.9164 (inter-event) for M_{w}> 6.5 (linear interpolation of ϕ and τ between M_{w}5 and 6.5) and τ^{*}= 0.4981 for M_{w}> 6.5 (computed using inter-event residuals corrected for the observed bias using a linear term)^{29}. - Characterise sites by V
_{s,30}, depth to reach V_{s}of 800m∕s (h800) and V_{s}at bedrock (Vshole). - Uses an NGA functional form to reflect state of the art in ground-motion prediction and the form of Boore and Atkinson (2008) specifically because it can be constrained by the data.
- Extension of analysis by Rodriguez-Marek and Montalva (2010) (see Section 4.201).
- Analysis conducted to investigate single-site variability of ground motions.
- Data from KiK-net on surface and at depth as processed by Pousse et al. (2005) and Cotton et al. (2008) (see Sections 4.131 and 2.294 for details). Note that although Cotton et al. (2008) state that spectral accelerations up to 3s can be used, in fact some spectral accelerations at long periods are less than the number of decimals used for storing the data. Hence limit analysis to periods < 1.3s.
- Majority of data is for M
_{w}≤ 6.1, which will have an impact on the regression. - Presents histogram of V
_{s,30}at surface stations: peak around 500m∕s with very few records for V_{s,30}> 1000m∕s. - Presents histogram of borehole depths: almost all at 100 and 200m. Use flag to indicate borehole instrument depth ≤ 150m or > 150m.
- Presents histogram of V
_{s,30}at borehole stations: roughly uniformly distributed between 1000m∕s and 2500m∕s with some higher and lower. - Notes that geographical distribution of earthquakes shows clusters that could enable a further separation of source and path effects from site effects in future studies.
- Only uses data from earthquake that were recorded by ≥ 5 stations to adequately constrain inter-event residuals.
- Uses multiple step regression method. First, uses only data from earthquakes recorded by > 100 stations
to constrain c
_{3}and h by maximum-likelihood regression (after fixing c_{1}to a value between -0.2 and -1.1 and fixing c_{2}to 0). Next finds M_{h}and e_{7}. Originally find that e_{7}is negative (oversaturation) but note that lack of data from large earthquakes so constrain it to be positive. M_{h}is chosen by inspection. Rest of coefficients found by random-effects regression. - Combined model assumes source and path terms are independent of near-surface layering, which note is desired from a phenomenological view.
- Plots inter-event residuals against M
_{w}and find overestimation for M_{w}> 6.5 due to constraint that ground motions do not oversaturate. Plots inter-event residuals against depth and find that motions from deeper events underestimated, which relate to less attenuation than shallower events and possibly different stress drops in shallow and deep earthquakes. - Plots intra-event residuals against M
_{w}and r_{rup}and site parameters and find no trends. However, finds trend in residuals from earthquakes recorded at r_{rup}< 20km, which relate to lack of near-fault-effects and nonlinear soil terms. Also finds decreasing variation in the intra-event residuals for r_{rup}> 200km. - Examines correlation between normalised inter- and intra-event residuals and concludes that they are uncorrelated.
- Finds combined, surface and borehole inter-event residuals well correlated.
- Recommends use of combined model rather than the surface or borehole only models.
- Computes single-station residuals and σs, by defining site terms for each station based on intra-event residuals, from 131 stations that recorded > 10 earthquakes. Finds slight magnitude dependence of residuals. Finds no correlation between intra-event residuals corrected by site terms and inter-event residuals. Examine in detail single-station residuals, associated σs and their various components w.r.t. to their use in PSHA without the ergodic assumption. Report these single-station σs: surface ϕ = 0.4967, borehole ϕ = 0.5060, surface σ = 0.6725 and borehole σ = 0.6684.
- Examine effect of selecting data from a station-to-event azimuthal bracket of 8
^{∘}and finds that sigma is reduced.