- Ground-motion model is:
_{h}= 1 when h ≥ h_{c}and 0 otherwise, a = 1.101, b = -0.00564, c = 0.0055, d = 1.080, e = 0.01412, S_{R}= 0.251, S_{I}= 0.000, S_{S}= 2.607, S_{SL}= -0.528, C_{H}= 0.293, C_{1}= 1.111, C_{2}= 1.344, C_{3}= 1.355, C_{4}= 1.420, σ = 0.604 (intra-event) and τ = 0.398 (inter-event). Use h_{c}= 15km because best depth effect for shallow events. - Use five site classes (T is natural period of site):
- Hard rock
- NEHRP site class A, V
_{s,30}> 1100m∕s. 93 records. Use C_{H}. - SC I
- Rock, NEHRP site classes A+B, 600 < V
_{s,30}≤ 1100m∕s, T < 0.2s. 1494 records. Use C_{1}. - SC II
- Hard soil, NEHRP site class C, 300 < V
_{s,30}≤ 600m∕s, 0.2 ≤ T < 0.4s. 1551 records. Use C_{2}. - SC III
- Medium soil, NEHRP site class D, 200 < V
_{s,30}≤ 300m∕s, 0.4 ≤ T < 0.6s. 629 records. Use C_{3}. - SC IV
- Soft soil, NEHRP site classes E+F, V
_{s,30}≤ 200m∕s, T ≥ 0.6s. 989 records. Use C_{4}.

Site class unknown for 63 records.

- Focal depths, h, between about 0 and 25km for crustal events, between about 10 and 50km for interface events, and about 15 and 162km for intraslab events. For earthquakes with h > 125km use h = 125km.
- Classify events into three source types:
- 1.
- Crustal.
- 2.
- Interface. Use S
_{I}. - 3.
- Slab. Use S
_{S}and S_{SL}.

and into four mechanisms using rake angle of ±45

^{∘}as limit between dip-slip and strike-slip earthquakes except for a few events where bounds slightly modified:- 1.
- Reverse. Use F
_{R}if also crustal event. - 2.
- Strike-slip
- 3.
- Normal
- 4.
- Unknown

Distribution of records by source type, faulting mechanism and region is given in following table.

Region Focal Mechanism Crustal Interface Slab Total Japan Reverse 250 1492 408 2150 Strike-slip 1011 13 574 1598 Normal 24 3 735 762 Unknown 8 8 Total 1285 1508 1725 4518 Iran and Western USA Reverse 123 12 135 Strike-slip 73 73 Total 196 12 208 All Total 1481 1520 1725 4726

- Exclude data from distances larger than a magnitude-dependent distance (300km for intraslab events) to eliminate bias introduced by untriggered instruments.
- Only few records from < 30km and all from < 10km from 1995 Kobe and 2000 Tottori earthquake. Therefore add records from overseas from < 40km to constrain near-source behaviour. Note that could affect inter-event error but since only 20 earthquakes (out of 269 in total) added effect likely to be small.
- Do not include records from Mexico and Chile because Mexico is characterised as a ‘weak’ coupling zone and Chile is characterised as a ‘strong’ coupling zone (the two extremes of subduction zone characteristics), which could be very different than those in Japan.
- Note reasonably good distribution w.r.t. magnitude and depth.
- State that small number of records from normal faulting events does not warrant them between considered as a separate group.
- Note that number of records from each event varies greatly.
- Process all Japanese records in a consistent manner. First correct for instrument response. Next low-pass filter
with cut-offs at 24.5Hz for 50 samples-per-second data and 33Hz for 100 samples-per-second data. Find that this
step does not noticeably affect short period motions. Next determine location of other end of usable period range.
Note that this is difficult due to lack of estimates of recording noise. Use the following procedure to select
cut-off:
- 1.
- Visually inspect acceleration time-histories to detect faulty recordings, S-wave triggers or multiple events.
- 2.
- If record has relatively large values at beginning (P wave) and end of record, the record was mirrored and tapered for 5s at each end.
- 3.
- Append 5s of zeros at both ends and calculate displacement time-history in frequency domain.
- 4.
- Compare displacement amplitude within padded zeros to peak displacement within the record. If displacement in padded zeros was relatively large, apply a high-pass filter.
- 5.
- Repeat using high-pass filters with increasing corner frequencies, f
_{c}, until the displacement within padded zeros was ‘small’ (subjective judgement). Use 1∕f_{c}found as maximum usable period.

Verify method by using K-Net data that contains 10s pre-event portions.

- Conduct extensive analysis on inter- and intra-event residuals. Find predictions are reasonably unbiased w.r.t. magnitude and distance for crustal and interface events and not seriously biased for slab events.
- Do not smooth coefficients.
- Do not impose constraints on coefficients. Check whether coefficient is statistically significant.
- Note that the assumption of the same anelastic attenuation coefficient for all types and depths of earthquakes could lead to variation in the anelastic attenuation rate in a manner that is not consistent with physical understanding of anelastic attenuation.
- Derive C
_{H}using intra-event residuals for hard rock sites. - Residual analyses show that assumption of the same magnitude scaling and near-source characteristics for all
source types is reasonable and that residuals not not have a large linear trend w.r.t. magnitude. Find that
introducing a magnitude-squared term reveals different magnitude scaling for different source types and a sizable
reduction in inter-event error. Note that near-source behaviour mainly controlled by crustal data. Derive correction
function from inter-event residuals of each earthquake source type separately to avoid trade-offs. Form of
correction is: log
_{e}(S_{MSst}) = P_{st}(M_{w}- M_{C}) + Q_{st}(M_{w}- M_{C})^{2}+ W_{st}. Derive using following three-step process:- 1.
- Fit inter-event residuals for earthquake type to a quadratic function of M
_{w}- M_{C}for all periods. - 2.
- Fit coefficients P
_{st}for (M_{w}-M_{C}) and Q_{st}for (M_{w}-M_{C})^{2}(from step 1) where subscript st denotes source types, to a function up to fourth oder of log_{e}(T) to get smoothed coefficients. - 3.
- Calculate mean values of differences between residuals and values of P
_{st}(M_{w}-M_{C})+Q_{st}(M_{w}-M_{C})^{2}for each earthquake, W_{st}, and fit mean values W_{st}to a function of log_{e}(T).

For PGA Q

_{C}= W_{C}= Q_{I}= W_{I}= 0, τ_{C}= 0.303, τ_{I}= 0.308, P_{S}= 0.1392, Q_{S}= 0.1584, W_{S}= -0.0529 and τ_{S}= 0.321. Since magnitude-square term for crustal and interface is not significant at short periods when coefficient for magnitude-squared term is positive, set all coefficients to zero. Find similar predicted motions if coefficients for magnitude-squared terms derived simultaneously with other coefficients even though the coefficients are different than those found using the adopted two-stage approach. - Compare predicted and observed motions normalized to M
_{w}7 and find good match for three source types and the different site conditions. Find model overpredicts some near-source ground motions from SC III and SC IV that is believed to be due to nonlinear effects.