- Ground-motion model is:
where y is in g, a = 0.46, b = 0.35, c = 0.07, d = -4.79, e = 0.60, h = 8.9km and σ = 0.33.
- Investigates effect of nontriggering stations on derivation of empirical Ground-motion model based on the
assumption that the triggering level is known (or can be estimated from data) but do not know which
stations triggered (called left truncated data).
- Develops mathematical theory and computational method (after trying various alternative methods) for
truncated regression analysis (TRA) and randomly truncated regression analysis (RTRA) (where triggering
level changes with time).
- Tests developed methods on 1000 lognormally-distributed synthetic data points simulated using the
equation of Ambraseys et al. (1996) for 4 ≤ Ms ≤ 7 and 1 ≤ df ≤ 100km. A fixed triggering threshold of
0.02g is imposed. Regresses remaining 908 samples using TRA and RTRA. Finds a very similar equation
using TRA but large differences for df > 20km by using standard regression analysis (SRA) due to slower
attenuation. Also apply TRA to randomly truncated synthetic data and find a close match to original
curve, which is not found using SRA.
- Applies method to 189 records from rock sites downloaded from ISESD with M > 4.5 (scale not specified)
and d < 80km (scale not specified) using functional form: log 10(y) = a + bm + clog 10(). Uses
these selection criteria to allow use of simple functional form and to avoid complications due to crustal
reflections that reduce attenuation. Discards the five points with PGA < 0.01g (assumed threshold of
SMA-1s). Applies TRA and SRA. Finds both M-scaling and distance attenuation are larger with TRA
than with SRA because TRA accounts for larger spread in original (not truncated) data. Differences are
relevant for M < 6 and d > 20km.
- Applies method to dataset including, in addition, non-rock records (456 in total). Finds no differences
between TRA and SRA results. Believes that this is due to lack of data in range possibly affected by
truncation (small M and large d). Finds similar results to Ambraseys et al. (1996).
- Applies method to NE Italian data from seven seismometric and ten accelerometric digital stations
assuming: log 10(y) = a + bm + clog 10(). Accelerometric stations used usually trigger at 0.001g.
Seismometric stations used trigger based on ratio of short-term and long-term averages (STA/LTA), which
varies from station to station and acts like a random threshold. Firstly neglects randomness and assumes
trigger level of each station equals lowest recorded PGA and applies TRA and SRA. Finds small differences
for d < 8km and d > 30km.
- Applies method using functional form above, which believes is more physically justified. SRA does not
converge. Studies reason for this by regressing on data from M intervals of 0.3 units wide. Finds behaviour
of PGAs inverts for M < 3. Finds increasing σ with decreasing M for M > 3. TRA does converge and
shows stronger magnitude saturation than SRA.
- Notes that application of RTRA to model effect of STA/LTA for used data is not realistic since probably not
enough data to constrain all 23 parameters and to computational expensive using adopted maximization
technique for RTRA.
- Estimates the random truncation parameters for one station (Zoufplan) and finds that the fixed threshold
assumption made is acceptable since estimated random truncation parameters predict that only 14% of
observations are lost at the earlier assumed fixed threshold level (the lowest PGA recorded).