- Ground-motion model is:
- Use V s,30 to characterise sites.
- Use 3 faulting mechanisms:
- Reverse. FR = 1 and FN = 0.
- Normal. FN = 1 and FR = 0.
- Strike-slip. FR = FN = 0.
- Coefficients not reported.
- Use same data as Gianniotis et al. (2014).
- Data from 359 different stations.
- Develop a hierarchical/multi-level model, which is slightly adjusted from Kuehn and Scherbaum (2015),
to account for regional differences, which are at a higher level than event and station effects.
- Scaling of PGA is assumed to be similar but not identical in 9 different regions: Alps (29 earthquakes, 91
records), Apennines (78 earthquakes, 303 records), south Greece (41 earthquakes, 87 records), north Greece
(18 earthquakes, 58 records), north Turkey (53 earthquakes, 324 records), south Turkey (70 earthquakes,
250 records), east Turkey/Caucasus/Israel (62 earthquakes, 122 records), Iran/Central Asia (6 earthquakes,
19 records) and Sicily (5 earthquakes, 7 records). Coefficients are treated as random variables which are
sampled from an underlying global distribution.
- Coefficients estimated by Bayesian inference using the program Stan, which performs Hamiltonian Monte
Carlo sampling. Regions with only few records borrow strength from regions with more data.
- Prior distributions of the global coefficients are normal distributions based on the model of Abrahamson
et al. (2014), which is chosen as works well for large magnitudes and short distances and it is based on a
global database and hence has only partial overlap with data used to derive model. Prior distributions of
the standard deviations are half-Cauchy distributions.
- Evaluate Abrahamson et al. (2014) for many Mw, R, V s,30 and mechanism. Fit model to these predictions
to find means and their standard errors as the parameters of the prior normal distributions of the
coefficients. Constrain coefficients (except c0) to be either positive or negative to avoid unphysical
- Run 4 chains of samples from different starting values. Discard first 1000 samples. Each chain run for
another 1000 samples. Keep every fifth sample, leading to 800 draws from posterior distribution. Assess
convergence using Gelman-Rubin statistics.
- Use the Widely-Applicable Information Criterion (WAIC) to estimate the generalisation error. Use this to
compare: a global model using all the data, a individual model were all coefficients are regionalised and
models where various sets of coefficients are regionalised. Assume σ is the same for all regions to avoid
trade-offs. Find that all regionalised models are better in terms of WAIC and components of σ than the
global model. Select model where all coefficients except c3, c4 and c7 vary by region.
- Use Sammon’s map (Scherbaum et al., 2010) to examine similarity between regional models.