- Ground-motion model is for D ≤ 30km:
and for D > 30km:

where pre is in cm∕s2, a

_{1}= 0.56, b_{1}= -0.0031, c_{1}= 0.26, d_{1}= 0.0055, a_{2}= 0.41, b_{2}= -0.0039, c_{2}= 1.56, σ_{1}= 0.37 and σ_{2}= 0.40. - Use V
_{s,30}to characterise site effects using correction formula: G = log(obs∕pre) = plog V_{s,30}+ q. Derive p and q by regression analysis on residuals averaged at intervals of every 100m∕s in V_{s,30}. p = -0.55 and q = 1.35 for PGA. Note that the equation without site correction predicts ground motions at sites with V_{s,30}≈ 300m∕s. - Focal depths, D, for shallow events between 0km and 30km and for deep events between 30km and about 180km.
- Note that it is difficult to determine a suitable model form due to large variability of strong-motion data, correlation among model variables and because of coupling of variables in the model. Therefore choose a simple model to predict average characteristics with minimum parameters.
- Introduce correction terms for site effects and regional anomalies.
- Originally collect 91731 records from 4967 Japanese earthquakes.
- Include foreign near-source data (from California and Turkey, which are compressional regimes similar to Japan) because insufficient from Japan.
- High-pass filter records with cut-off of 0.1Hz. Low-pass filter analogue records using cut-offs selected by visual inspection.
- Choose records where: 1) M
_{w}≥ 5.5, 2) data from ground surface, 3) two orthogonal horizontal components available, 4) at least five stations triggered and 5) the record passed this M_{w}-dependent source distance criterion: f(M_{w},X) ≥ log 10 (for data from mechanical seismometer networks) or f(M_{w},X) ≥ log 2 (for data from other networks) where f(M_{w},X) = 0.42M_{w}- 0.0033X - log(X + 0.02510^{0.43Mw}) + 1.22 (from a consideration of triggering of instruments). - Examine data distributions w.r.t. amplitude and distance for each magnitude. Exclude events with irregular distributions that could be associated with a particular geological/tectonic feature (such as volcanic earthquakes).
- Do not include data from Chi-Chi 1999 earthquake because have remarkably low amplitudes, which could be due to a much-fractured continental margin causing different seismic wave propagation than normal.
- Data from 2236 different sites in Japan and 305 in other countries.
- Note relatively few records from large and deep events.
- Note that maybe best to use stress drop to account for different source types (shallow, interface or intraslab) but cannot use since not available for all earthquakes in dataset.
- Investigate effect of depth on ground motions and find that ground-motions amplitudes from earthquakes with D > 30km are considerably different than from shallower events hence derive separate equations for shallow and deep events.
- Select 0.5 within function from earlier study.
- Weight regression for shallow events to give more weight to near-source data. Use weighting of 6.0 for X ≤ 25km, 3.0 for 25 < X ≤ 50km, 1.5 for 50 < X ≤ 75km and 1.0 for X > 75km. Note that weighting scheme has no physical meaning.
- Note that amplitude saturation at short distances for shallow model is controlled by crustal events hence
region within several tens of kms of large (M
_{w}> 8.0) interface events falls outside range of data. - Note standard deviation decreases after site correction term is introduced.
- Introduce correction to model anomalous ground motions in NE Japan from intermediate and deep
earthquakes occurring in the Pacific plate due to unique Q structure beneath the island arc. Correction
is: log(obs∕pre) = (αR
_{tr}+ β)(D - 30) where R_{tr}is shortest distance from site to Kuril and Izu-Bonin trenches. α and β are derived by regression on subset fulfilling criteria: hypocentre in Pacific plate, station E of 137^{∘}E and station has V_{s,30}measurement. For PGA α = -6.73 × 10^{-5}and β = 2.09 × 10^{-2}. Find considerable reduction in standard deviation after correction. Note that R_{tr}may not be the best parameter due to observed bias in residuals for deep events. - Examine normalised observed ground motions w.r.t. predicted values and find good match.
- Examine residuals w.r.t. distance and predicted values. Find residuals decrease with increasing predicted amplitude and with decreasing distance. Note that this is desirable from engineering point of view, however, note that it may be due to insufficient data with large amplitudes and from short distances.
- Examine total, intra-event and inter-event residuals w.r.t. D for D > 30km. When no correction terms are used, intra-event residuals are not biased but inter-event residuals are. Find mean values of total error increase up to D = 70km and then are constant. Find depth correction term reduces intra-event residuals considerably but increases inter-event error slightly. Overall bias improves for D < 140km. Find site corrections have marginal effect on residuals.
- Find no bias in residuals w.r.t. magnitude.