### 2.408 Landwehr et al. (2016)

• Ground-motion is:
where y is in g, β1 = 2.4228, β2 = -0.17267, β4 = 0.1983, β7 = 0.074761, β8 = -0.1 (fixed a priori as few normal events), σ0 = 0.5219 and σT = 0.8127. Values are not given for all coefficients as some are spatially varying and only shown on maps.
• Characterise sites using V s,30.
• Classify events into 3 mechanisms:
S
Strike-slip. FNM = FR = 0.
N
Normal. FNM = 1 and FR = 0.
R
Reverse. FR = 1 and FNM = 0.
• Assume spectral acceleration at 0.01s is PGA.
• Use subset of data from California and Nevada from Abrahamson et al. (2014) as data from other regions will be spatially uncorrelated.
• Data well distributed from about 5km to 200km and for Mw < 7, although a slight lack of data between Mw5 and 6.
• Data from most of coastal California, although limited data north of 38N. Data from 1425 different stations.
• Develop a varying-coefficient model to relax the ergodic assumption. Coefficients β-1, β3 and β5 depend on earthquake location (horizontal projection of the geographical centre of the rupture) and coefficients β0 and β6 depend on station location. Constrain coefficients to be similar for nearby locations by imposing a Gaussian process prior because insufficient data to estimate independent models for every location. Choose certain coefficients to spatially vary to capture expected physics as well as avoiding problems of extrapolating the predictions to large magnitudes and due to a lack of data from different mechanisms.
• Also derive a model with spatially-fixed coefficients. Find that this model leads to higher generalisation error (estimated using a 10-fold cross validation approach to compute the root mean squared prediction error) as well as total σ compared with the nonergodic σ0 of the model with spatially-varying coefficients.