- Ground-motion model is:
where A is in g, c1 = -1.072, c2 = 0.3903, b = 1.21, c3 = 0.5873 and σ = 0.14.
- Considers two site categories but does not model:
- Rock: generally granite/quartzite/sandstone, 41 records.
- Soil: exposed soil covers on basement, 25 records.
- Focal depths between 7.0 and 50.0km.
- Most records from distances > 50km. Correlation coefficient between M and X is 0.63.
- Does not include source mechanism as parameter because not well defined and including many terms may
lead to errors. Also neglects tectonic type because set is small and small differences are expected.
- Fit log A = -blog X + c to data from each earthquake separately and find average b equal to 1.292. Then
fit log A = aM -blog X +c to data from all earthquakes and find b = 0.6884. Fit log A = -blog X +∑
to all data, where li = 1 for ith earthquake and 0 otherwise and find b = 1.21, use this for rest of analysis.
- Use weighted regression, due to nonuniform sampling over all M and X. Divide data into distance bins
2.5km wide up to 10km and logarithmically dependent for larger distances. Within each bin each earthquake
is given equal weight by assigning a relative weight of 1∕nj,l, where nj,l is the number of recordings for jth
earthquake in lth distance bin, then normalise so that sum to total number of recordings.
- Original data included two earthquakes with focal depths 91.0km and 119.0km and M = 6.8 and 6.1 which
caused large errors in regression parameters due to large depths so excluded them.
- Check capability of data to compute coefficients by deleting, in turn, c1, c2 and c3, find higher standard
- Makes one coefficient at a time equal to values given in Abrahamson and Litehiser (1989), finds sum of
- Notes lack of data could make relationship unreliable.