- Ground-motion model is: h0 = 50km, Mr = 5, SI = 0, SII = -0.584, SIII = -0.322, SIV = -0.109, SV = -0.095, SV I = -0.212,
c1 = -2.8548, Δc1 = 2.5699, c2 = 0.7741, Δc2 = -0.4761, c3 = -0.97558, Δc3 = -0.52745, c4 = 0.1
(fixed to avoid trade-offs in regression), c5 = -0.00174, c6 = 5 (fixed), c7 = 0.35 (fixed), c8 = 0.00586,
c9 = -0.03958, σe = 0.172 (inter-event), σr = 0.232 (intra-event) and σt = 0.289 (total).
- Use V s,30 to characterise sites as well as 6 site classes based on predominant period of the soil (T*) from
horizontal-to-vertical response spectral ratios (HVRSR):
- Not identifiable: HVRSR ≤ 2
- T*≤ 0.2s
- 0.2 < T*≤ 0.4s
- 0.4 < T*≤ 0.8s
- T* > 0.8s
- Not identifiable: broadband amplification or two or more peaks
- Classify events into 2 classes using hypocentral depth and dip and strike criteria:
- Focal depth, H, between 10 and 50km and dip of 20∘±5∘ and strike of 0∘±20∘ and they occur close
to subduction contact zone Feve = 0.
- Intraslab events have greater depths (exclude events with H > 150km). Feve = 1.
- Use data from National Seismological Center and National Accelerometer Network of the Department
of Civil Engineering (RENADIC), University of Chile. Collect 1207 records from 184 events. Apply
magnitude-dependent limits to avoid bias from trigger thresholds. Also exclude records based on
- Data from 154 different stations, most in northern and central Chile (near Santiago).
- Data quite well distributed w.r.t. Mw and rhypo but few intraslab records between Mw6.5 and 7.5.
- 22% of records from analogue (SMA-1 and QDR) instruments. Recent records generally digital (CMG-5
and FBA ES-T).
- Baseline correct to remove trend. Apply cosine taper over 5% of total length of detrended signal. Zero
pad (30s length) beginning and end of signal. Bandpass filter using 4th order Butterworth acausal filter.
Highpass corner frequencies chosen based on instrument (0.2, 0.1 and 0.06Hz for SMA-1, QDR and digital
sensors, respectively). Lowpass corner frequency for analog and QDR instruments is 25Hz. For digital
instruments lowpass filtering was applied when the Fourier amplitude spectra showed an unusual high
frequency amplitude (e.g. for sensors with natural frequencies lower than the Nyquist). For only 3% of
digital records was such filtering required. Remove 91 records (mainly from rock sites at short source-to-site
distances) because believe they are significantly affected by high-frequency noise.
- Chose functional form based on iterative approach. Start with a simple model and add terms by examining
plots of data w.r.t. R and Mw. Only include terms that are identified by the data (e.g. no quadratic
magnitude-scaling seen in intraslab data), which note could mean certain dependencies are not included
because of lack of data.
- Use a 2-stage approach fixing certain coefficients and using simplified functional forms to avoid trade-offs.
- Smooth coefficients with a linear fit using 20% of the total coefficient vector length.
- Examine first-stage residuals w.r.t. distance (grouped by Mw and site class) and find no trends.
- Show event terms w.r.t. predictions from second stage and find good fit.
- Compare observations grouped by Mw against predictions w.r.t. R and when good match.