### 2.349 Yuen and Mu (2011)

• Ground-motion model is:

where PGA is in cms2, M0 = 3.5, b1 = 2.8, b2 = 0.72, b3 = -0.038, b4 = -0.0060, b5 = -0.0095, b6 = 0.72, b7 = 0.035 and σ = 0.77. nonlinearterms are not given but stated to be almost negligible.

• Use 3 site classes:
Class A
Granite, sandstone, bedrock, siltstone and conglomerate. 14 stations, 72 records. Both stations in Guangdong on granite. GB = GC = 0.
Class B
Alluvium, diluvium, weathered conglomerate. 12 stations (none in Guangdong), 146 records. GB = 1 and GC = 0.
Class C
Soft soil, clay and subclay. 8 stations (none in Guangdong), 48 records. GC = 1 and GB = 0.

Cannot use V s,30 as information not available.

• Use data from China Earthquake Data Center for three regions: Tangshan (94 records, 18 earthquakes, 19 stations), Xinjiang (155 records, 125 earthquakes, 13 stations) and Guangdong (17 records, 4 earthquakes, 2 stations).
• Use Bayesian model class selection approach to find the model that balances data-fitting capability and sensitivity to noise. Believe that this approach reduces the chance of overfitting. Compute the plausibility of each model conditional on the database. For the linear models use an analytical solution for this and for the nonlinear models (in this case including a term b8 ln[r + b9 exp(b10M)]) use a Monte Carlo approach to evaluate the plausibility.
• Derive 48 models (by including different combinations of terms) for Tangshan and Xinjiang separately as well as for all data. Find σ smaller for regional models. Recommend using the regional models but note that the model for all regions is best for prediction in another region without sufficient data.
• Derive many models assuming different functional forms. Choose model that is the most plausible using the Bayesian model class selection approach as final one.
• Plot predictions versus observations and find strong correlation.