- Ground-motion model is (it is not clear which coefficients were fixed and which obtained by the regression
algorithm): where y is in cm∕s2, a1 = 6, a2 = -1∕6, a3 = 1∕6, a4 = 6, a5 = 64, a6 = -8, a7 = 5, a8 = -7 and
σ = 0.602 (training set) and σ = 0.624 (testing set).
- Characterize sites using V s,30. Most sites have 350 ≤ V s,30 ≤ 850m∕s.
- Characterize faulting mechanism using rake angle λ. Most records have 60 ≤ λ ≤ 180∘. Tried using classes
for mechanism (strike-slip, normal and reverse) instead but did not find better results.
- Use variant of genetic programming (multi-expression programming, MEP) for derivation.
Technique seeks best functional form and coefficients.
- Use PEER-NGA database. Select 2815 records by excluding those with missing information and duplicates.
- Most data from Mw > 5.5 and rrup < 100km.
- Note that the distribution of data w.r.t. parameter is not uniform and that MEP works best with uniform
- Randomly divide data into learning (1971 records), validation (281 records) and testing (563 records)
subsets. Learning data used for the genetic evolution; validation data used to specify the generalization
capability of the models on data not used for training; and testing data used to measure performance of
the models on independent data.
- Examine correlations between independent variables (Mw, rrup, V s,30 and λ) because strong
interdependency can exaggerate strength of relations between variables. Do not find strong correlations.
- Choose best models based on: a) simplicity (although not a predominant factor), which was controlled
by parameter settings; b) best fitness value (objective function, which is a function of root-mean-square
error, mean absolute error and coefficient of determination) on learning set; and c) best fitness value on
- Compare observed and predicted PGAs for training and testing data. Compute various statistics to check
model. Conclude that derived models have predictive capability within the data range used for their