- Ground-motion model for crustal earthquakes is:
_{15}′(T) = C_{17Y }(T). For both models:where PGA′

_{A∕B}= SA′_{A∕B}(T = 0). Final model given by:where SA

_{A∕B,C,D}is in g, r_{V OL}is length in km of source-to-site path in volcanic zone and F_{HW }(M,r) is hanging wall factor of Abrahamson and Silva (1997). Coefficients for PGA (larger component) are: C_{1}= 0.28815, C_{3}= 0, C_{4}= -0.14400, C_{5}= -0.00967, C_{6}= 0.17000, C_{8}= -0.70494, C_{10}= 5.60000, C_{11}= 8.68354, C_{12}= 1.41400, C_{13}= 0, C_{15}= -2.552000, C_{17}= -2.56727, C_{18}= 1.78180, C_{19}= 0.55400, C_{20}= 0.01550, C_{24}= -0.50962, C_{29}= 0.30206, C_{30}= -0.23000, C_{32}= 0.20000, C_{33}= 0.26000, C_{43}= -0.31769, C_{46}= -0.03279, σ_{M6}= 0.4865, σ_{slope}= -0.1261, where σ = σ_{M6}+ σ_{slope}(M_{w}- 6) for 5 < M_{w}< 7, σ = σ_{M6}-σ_{slope}for M_{w}< 5 and σ = σ_{M6}+σ_{slope}for M_{w}> 7 (intra-event), and τ = 0.2687 (inter-event). Coefficients for PGA′ (larger component) are: C_{1}= 0.18130, C_{3}= 0, C_{4}= -0.14400, C_{5}= -0.00846, C_{6}= 0.17000, C_{8}= -0.75519, C_{10}= 5.60000, C_{11}= 8.10697, C_{12}= 1.41400, C_{13}= 0, C_{15}= -2.552000, C_{17}= -2.48795, C_{18}= 1.78180, C_{19}= 0.55400, C_{20}= 0.01622, C_{24}= -0.41369, C_{29}= 0.44307, C_{30}= -0.23000, C_{32}= 0.20000, C_{33}= 0.26000, C_{43}= -0.29648, C_{46}= -0.03301, σ_{M6}= 0.5035, σ_{slope}= -0.0635 and τ = 0.2598. - Use site classes (combine A and B together and do not use data from E):
- A
- Strong rock. Strong to extremely-strong rock with: a) unconfined compressive strength > 50MPa,
and b) V
_{s,30}> 1500m∕s, and c) not underlain by materials with compressive strength < 18MPa or V_{s}< 600m∕s. - B
- Rock. Rock with: a) compressive strength between 1 and 50MPa, and b) V
_{s,30}> 360m∕s, and c) not underlain by materials having compressive strength < 0.8MPa or V_{s}< 300m∕s. - C
- δ
_{C}= 1, δ_{D}= 0. Shallow soil sites. Sites that: a) are not class A, class B or class E sites, and b) have low-amplitude natural period, T, ≤ 0.6s, or c) have soil depths ≤ these depths:Soil type Maximum and description soil depth (m) Cohesive soil Representative undrained shear strengths (kPa) Very soft < 12.5 0 Soft 12.5–25 20 Firm 25–50 25 Stiff 50–100 40 Very stiff or hard 100–200 60 Cohesionless soil Representative SPT N values Very loose < 6 0 Loose dry 6–10 40 Medium dense 10–30 45 Dense 30–50 55 Very dense > 50 60 Gravels > 30 100 - D
- δ
_{D}= 1, δ_{C}= 0. Deep or soft soil sites. Sites that: a) are not class A, class B or class E sites, and b) have a low-amplitude T > 0.6s, or c) have soil depths > depths in table above, or c) are underlain by < 10m of soils with an undrained shear-strength < 12.5kPa or soils with SPT N-values < 6. - E
- Very soft soil sites. Sites with: a) > 10m of very soft soils with undrained shear-strength < 12.5kPa,
b) > 10m of soils with SPT N values < 6, c) > 10m of soils with V
_{s}< 150m∕s, or d) > 10m combined depth of soils with properties as described in a), b) and c).

Categories based on classes in existing New Zealand Loadings Standard but modified following statistical analysis. Note advantage of using site categories related to those in loading standards. Site classifications based on site periods but generally categories from site descriptions.

- Classify earthquakes in three categories:
- Crustal
- Earthquakes occurring in the shallow crust of overlying Australian plate. 24 earthquakes. Classify
into:
- Strike-slip
- -33 ≤ λ ≤ 33
^{∘}, 147 ≤ λ ≤ 180^{∘}or -180 ≤ λ ≤ -147^{∘}where λ is the rake. 6 earthquakes. Centroid depths, H_{c}, 4 ≤ H_{c}≤ 13km. 5.20 ≤ M_{w}≤ 6.31. CN = 0, CR = 0. - Normal
- -146 ≤ λ ≤-34
^{∘}. 7 earthquakes. 7 ≤ H_{c}≤ 17km. 5.27 ≤ M_{w}≤ 7.09. CN = -1, CR = 0. - Oblique-reverse
- 33 ≤ λ ≤ 66
^{∘}or 124 ≤ λ ≤ 146^{∘}. 3 earthquakes. 5 ≤ H_{c}≤ 19km. 5.75 ≤ M_{w}≤ 6.52. CR = 0.5, CN = 0. - Reverse
- 67 ≤ λ ≤ 123
^{∘}. 8 earthquakes. 4 ≤ H_{c}≤ 13km. 5.08 ≤ M_{w}≤ 7.23. CR = 1, CN = 0.

- Interface
- Earthquake occurring on the interface between Pacific and Australian plates with H
_{c}< 50km. 5 reserve and 1 strike-slip with reverse component. Use data with 15 ≤ H_{c}≤ 24km. Classify using location in 3D space. 6 earthquakes. 5.46 ≤ M_{w}≤ 6.81. SI = 1, DS = 0. - Slab
- Earthquakes occurring in slab source zone within the subducted Pacific plate. Predominant mechanism
changes with depth. 19 earthquakes. 26 ≤ H
_{c}≤ 149km. Split into shallow slab events with H_{c}≤ 50km (9 normal and 1 strike-slip, 5.17 ≤ M_{w}≤ 6.23) and deep slab events with H_{c}> 50km (6 reverse and 3 strike-slip, 5.30 ≤ M_{w}≤ 6.69). SI = 0, DS = 1 (for deep slab events).

Note seismicity cross sections not sufficient to distinguish between interface and slab events, also require source mechanism.

- Find that mechanism is not a significant extra parameter for motions from subduction earthquakes.
- State that model is not appropriate for source-to-site combinations where the propagation path is through the highly attenuating mantle wedge.
- Note magnitude range of New Zealand is limited with little data for large magnitudes and from short
distances. Most data from d > 50km and M
_{w}< 6.5. - Only include records from earthquakes with available M
_{w}estimates because correlations between M_{L}and M_{w}are poor for New Zealand earthquakes. Include two earthquakes without M_{w}values (M_{s}was converted to M_{w}) since they provide important data for locations within and just outside the Central Volcanic Region. - Only include data with centroid depth, mechanism type, source-to-site distance and a description of site conditions.
- Only include records with PGA above these limits (dependent on resolution of instrument):
- 1.
- Acceleroscopes (scratch-plates): 0.02g
- 2.
- Mechanical-optical accelerographs: 0.01g
- 3.
- Digital 12-bit accelerographs: 0.004g
- 4.
- Digital 16-bit accelerographs: 0.0005g

- Exclude data from two sites: Athene A (topographic effect) and Hanmer Springs (site resonance at 1.5–1.7Hz) that exhibit excessive amplifications for their site class.
- Exclude data from sites of class E (very soft soil sites with ≳ 10m of material with V
_{s}< 150m∕s) to be consistent with Abrahamson and Silva (1997) and Youngs et al. (1997). Not excluded because of large amplifications but because spectra appear to have site-specific characteristics. - Exclude records from bases of buildings with > 4 storeys because may have been influenced by structural response.
- Exclude data from very deep events with travel paths passing through the highly attenuating mantle were excluded.
- Only use response spectral ordinates for periods where they exceed the estimated noise levels of the combined recording and processing systems.
- Lack of data from near-source. Only 11 crustal records from distances < 25km with 7 of these from 3 stations. To constrain model at short distances include overseas PGA data using same criteria as used for New Zealand data. Note that these data were not intended to be comprehensive for 0–10km range but felt to be representative. Note that it is possible New Zealand earthquakes may produce PGAs at short distances different that those observed elsewhere but feel that it is better to constrain the near-source behaviour rather than predict very high PGAs using an unconstrained model.
- In order to supplement limited data from moderate and high-strength rock and from the volcanic region, data from digital seismographs were added.
- Data corrected for instrument response.
- Derive model from ‘base models’ (other Ground-motion models for other regions). Select ‘base model’ using residual analyses of New Zealand data w.r.t. various models. Choose models of Abrahamson and Silva (1997) for crustal earthquakes and Youngs et al. (1997). Link these models together by common site response terms and standard deviations to get more robust coefficients.
- Apply constraints using ‘base models’ to coefficients that are reliant on data from magnitude, distance and other model parameters sparsely represented in the New Zealand data. Coefficients constrained are those affecting estimates in near-source region, source-mechanism terms for crustal earthquakes and hanging-wall terms. Eliminate some terms in ‘base models’ because little effect on measures of fit using Akaike Information Criterion (AIC).
- Apply the following procedure to derive model. Derive models for PGA and SA using only records with response spectra available (models with primed coefficients). Next derive model for PGA including records without response spectra (unprimed coefficients). Finally multiply model for SA by ratio between the PGA model using all data and that using only PGA data with corresponding response spectra. Apply this method since PGA estimates using complete dataset for some situations (notably on rock and deep soil and for near-source region) are higher than PGA estimates using reduced dataset and are more in line with those from models using western US data. This scaling introduces a bias in final model. Do not correct standard deviations of models for this bias.
- Use r
_{rup}for 10 earthquakes and r_{c}for rest. For most records were r_{c}was used, state that it is unlikely model is sensitive to use r_{c}rather than r_{rup}. For five records discrepancy likely to be more than 10%. - Free coefficients are: C
_{1}, C_{11}, C_{8}, C_{17}, C_{5}, C_{46}, C_{20}, C_{24}, C_{29}and C_{43}. Other coefficients fixed during regression. Coefficients with subscript AS are from Abrahamson and Silva (1997) and those with subscript Y are from Youngs et al. (1997). Try varying some of these fixed coefficients but find little improvement in fits. - State that models apply for 5.25 ≤ M
_{w}≤ 7.5 and for distances ≤ 400km, which is roughly range covered by data. - Note possible problems in applying model for H
_{c}> 150km therefore suggest H_{c}is fixed to 150km if applying model to deeper earthquakes. - Note possible problems in applying model for M
_{w}< 5.25. - Apply constraints to coefficients to model magnitude- and distance-saturation.
- Try including an anelastic term for subduction earthquakes but find insignificant.
- Investigate possibility of different magnitude-dependence and attenuation rates for interface and slab earthquakes but this required extra parameters that are not justified by AIC.
- Investigate possible different depth dependence for interface and slab earthquakes but extra parameters not justified in terms of AIC.
- Try adding additive deep slab term but not significant according to AIC.
- Cannot statistically justify nonlinear site terms. Believe this could be due to lack of near-source records.
- Find that if a term is not included for volcanic path lengths then residuals for paths crossing the volcanic zone are increasingly negative with distance but this trend is removed when a volcanic path length term is included.
- Compare predictions to observed ground motions in 21/08/2003 Fiordland interface (M
_{w}7.2) earthquake and its aftershocks. Find ground motions, in general, underestimated.