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Additional file 3: Figure S4. PGV ratio for four realizations of random heterogeneity that are different from that in Fig. 6. Heterogeneous velocity model with a = 5 km and the source model S1_3.3 are used.

Additional file 1. Estimation of corner frequencies.

We obtain a new attenuation distance-relation of seismic intensity for Japan using the strongmotion data-base constructed by Kanno et al.（2006）. We also obtain additional correction terms corresponding to the site amplification, anomalous seismic intensity and event type（plate-boundary or intra-slab）. Although we used strong-motion data until the 2003 Tokachi-oki earthquake, the attenuation relation agrees to observed records during recent large earthquakes.

We examine source characteristics of intraslab earthqakes based on the eleven source models estimated by the empirical Green’ｓfunction method. This method provides strong motion generation areas that reproduce near-source ground motions in a broadband period range(0.1～10sec). The storong motion generation areas roughly coincide with the asperity areas where stresses are largely released. Fault parameters of the asperity source model are outer fault parameters (entire source area and total seismic moment) and inner fault prameters (area of asperities,stress drop on each asperity and short-period level of the S-wave acceleration source spectrum). We find self-similar scaling of total seismic moment to the asperity areas. The number of asperities is one for Mw6 events,two to three for Mw7 events and five for Mw8 events. We also find self-similar scaling of total seismic moment to the short-period level of the S-wave acceleration source spectrum that is directly related to the asperity parameters (area of asperities and stress drop on each asperity ).Further we find that the aftershock area overestimates the entire source area.This means that estimation of the entire source area is somewhat difficult for intraslab earthquakes. Based on our results we propose a procedure for characterizing the source model for future intraslab earthquakes. Step 1:setting the total seismic moment (Mo), Step 2:setting the asperity areas (Sa) from the empirical relationship of Sa-Mo, Step 3: setting the short-period level (A) from the empirical relationship of A-Mo, Step 4: setting the number of asperities, Step 5: setting the stress drop (Δσ）on each asperity from the theoretical relation of A, Sa and Δσ, Step 6: setting the entire source area (S) from the theoretical relation of Mo, Sa, Δσ and S. The theoretical relations are derived from the multiple-asperity model.

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