where SA is in g, θ1= 5.87504, θ4= 0.80277, θ5= -0.33487, θ2= -1.75360, θ3= 0.13125, θ6= -0.00039,
θ14= -0.73080, θ10= 4.53143, θ11= 0.00567, θ12= 1.01495, θ7= 1.0988, θ8= -1.420, θ15= 0.9969,
θ16= -1.000, θ9= 0.4, ΔC1,interface= 0.200, Δ1,in-slab= -0.300, Vlin= 865.1, b = -1.186, n = 1.18,
C4= 10, C1= 7.2; τ = 0.47462 (inter-event), ϕS2S= 0.56436 (site-to-site), ϕ =SS= 0.39903 (single
station intra-event) and σ = 0.83845 (total) for the standard model; and τ = 0.48274 (inter-event),
ϕS2S= 0.35438 (site-to-site), ϕ =SS= 0.29315 (single station intra-event) for the high-quality model.
PGA1000 is median PGA for Vs,30= 1000m∕s.
Characterise sites using Vs,30, some measured for study. Only 57 stations (with 744 records) have measured
Vs,30. For others (178 stations) use topographic slope and site’s predominant period as proxy for Vs,30
(using a weighted average). Vs,30 between 108 and 1951m∕s but believe model only valid from 100–1000m.
Insufficient data to constrain nonlinear model so adopt coefficients from Abrahamson et al. (2016) for this
part of model.
Use data from networks of Integrated Plate boundary Observatory Chile and Red Nacional de Acelerografos
and Seismometer Network of Centro Sismológico Nacional from 1985 to 2015.
Classify earthquakes into 2 types using its location w.r.t. trench axis and focal mechanism, when
Generally associated with reverse faulting, occur between the Peru-Chile trench and Chile’s coast and
at depths ≤ 50km. Shallow reserve-faulting events were interface earthquakes whereas other shallow
events were crustal (and excluded). Fevent= 0.
Generally normal faulting and have depths > 50km. For events without focal mechanism, classify
using a slab subduction model. Fevent= 1.
Use finite-fault rupture models to compute distances, when available, and empirical relationships to
estimate fault location, otherwise.
Individually bandpass filter each record using a smoothed signal-to-noise ratio of three to choose low cut-off
frequency and Nyquist and frequency at which Fourier amplitude spectrum becomes flat for high cut-off.
Use data down to 1.25 times the low cut-off frequency.
Focal depths, Zh, of interface events between about 5 and about 50km and for intraslab between about
40 and about 280km.
About 70% of events have ≥ 3 records. Nearly 60% of stations have ≥ 3 records.
Regress using all data. Remove outliers (defined using the Rosner algorithm) and then regress again. Force
coefficient θ6 to be negative to avoid unrealistic distance attenuation. Do not smooth coefficients as believe
this can be done by hazard analyst if necessary.
Derive second model using only high-quality data (measured Vs,30 and Mw from Global CMT catalogue,
411 records from 151 interface events and 109 records from 57 intraslab events). Find much lower intra-event
variabilities but higher uncertainties in coefficients due to fewer records. This model only valid for interface
events because of limited intraslab data.
Define 95% confidence intervals for coefficients using 1000 bootstrap replications using datasets with same
number of records as original database but accepting duplicate data.
Create 100 random data subsets with various sizes from 500 to 3500 records and regress. Assess the
convergence of statistical tests to evaluate models.
Examine inter-event residuals w.r.t. Mw, single-station residuals w.r.t. R and site-to-site residual w.r.t.
Vs,30. Find no trends so conclude regression is robust and reliable.
Note that model shows reasonable behaviour up to 1000km but may only be valid for ≤ 300km considering
data distribution. Also note that model strictly valid from 5 ≤ Mw≤ 8 but could be extended to Mw9
because of presence of Mw8.8 Maule event, which is well represented.