- Ground-motion model is:
- Response parameter is acceleration for an unspecified damping (but assumed to be 5%).
- Use two site classes:
- Rock. Generally granite/quartzite/sandstone.
- Soil. Sites with exposed soil cover with different levels of consolidation.
- Data from three strong-motion (SMA-1) arrays: Kangra, Uttar Pradesh and Shillong, in the Himalayas.
- Instruments generally from ground floors of buildings.
- Rotate components into NS and EW directions.
- Focal depths between 7 and 121km.
- Note that distribution of records is uneven. Five events have less than 9 records and one earthquake has
- Note that Mw avoids magnitude saturation problems.
- Note that lack of near-field data (all but one record from > 20km) means that results are not stable.
Therefore introduce nine European records from seven reverse-faulting earthquakes for M ≥ 6.0 and
de ≤ 20km.
- Use method of Campbell (1981) to avoid problems due to correlation between magnitude and distance.
Divide data into a number of subsets based on distance. For each interval, each earthquake is given equal
weight by assigning a relative weight of 1∕nj,l to the record where nj,l is the total number of records from
the jth earthquake within ith distance bin. Normalise weights so that they sum to total number of records.
Use distance bins of 5km wide up to 10km and then bins of equal width w.r.t. logarithmic distance.
- Use rhypo rather than rrup because: a) large depth of some events and b) poorly known fault geometries.
Note that rhypo has a reasonable seismological basis and can be reliably and easily determined for most
significant (including hypothetical design) earthquakes.
- Regress all data using: ln(A) = c - bln(X) and find b = 1.22 ± 0.69. Next regress using: ln(A) =
aM - bln(X) + c and find b = 0.515 ± 0.081. Conclude that this is due to correlation between magnitude
and distance and hence conduct the first step of a two-step regression with dummy variables for each
earthquake. Find a decay rate of -1.20 ± 0.036. Use this fixed decay rate for rest of analysis.
- Try to regress on rock and soil data simultaneously by including a linear site term c4SSR but find that
there are problems during the regression process. Hence regress separately on rock and soil data.