- Ground-motion model is (following Abrahamson et al. (2016)):
_{1}= 5.87504, θ_{4}= 0.80277, θ_{5}= -0.33487, θ_{2}= -1.75360, θ_{3}= 0.13125, θ_{6}= -0.00039, θ_{14}= -0.73080, θ_{10}= 4.53143, θ_{11}= 0.00567, θ_{12}= 1.01495, θ_{7}= 1.0988, θ_{8}= -1.420, θ_{15}= 0.9969, θ_{16}= -1.000, θ_{9}= 0.4, ΔC_{1,interface}= 0.200, Δ_{1,in-slab}= -0.300, V_{lin}= 865.1, b = -1.186, n = 1.18, C_{4}= 10, C_{1}= 7.2; τ = 0.47462 (inter-event), ϕ_{S2S}= 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), ϕ_{S2S}= 0.35438 (site-to-site), ϕ = SS = 0.29315 (single station intra-event) for the high-quality model. PGA_{1000}is median PGA for V_{s,30}= 1000m∕s. - Characterise sites using V
_{s,30}, some measured for study. Only 57 stations (with 744 records) have measured V_{s,30}. For others (178 stations) use topographic slope and site’s predominant period as proxy for V_{s,30}(using a weighted average). V_{s,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
available:
- Interface
- 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). F
_{event}= 0. - Intraslab
- Generally normal faulting and have depths > 50km. For events without focal mechanism, classify
using a slab subduction model. F
_{event}= 1.

- Classify records into 2 classes:
- Back-arc
- f
_{FABA}= 1 - Fore-arc
- f
_{FABA}= 0

No data from back-arc sites so adopt coefficients from Abrahamson et al. (2016).

- 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, Z
_{h}, 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 θ
_{6}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 V
_{s,30}and M_{w}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. M
_{w}, single-station residuals w.r.t. R and site-to-site residual w.r.t. V_{s,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 ≤ M
_{w}≤ 8 but could be extended to M_{w}9 because of presence of M_{w}8.8 Maule event, which is well represented.