### Tsunami numerical simulation

For the 349 rupture scenarios, tsunami simulations were initiated using seafloor displacements obtained from Okada’s (1985) analytical solution for coseismic dislocation. Finite-difference computations were conducted for the nonlinear long-wave equation, including the bottom friction (Satake 1995). Bathymetry grids for the simulation were constructed from various data sets: JTOPO30, 30 arcsec gridded bathymetry data provided by the Japan Hydrographic Association; M7000 series, digitized bathymetry charts provided by the Japan Hydrographic Association; and the General Bathymetric Chart of the Oceans (GEBCO). We used nested bathymetry grids with spatial resolutions of 27 and 9 arcsecs. The time step for calculations was set at 0.5 s to satisfy the stability condition of the finite-difference method, and the tsunami was simulated for 5 h after the earthquake. The Manning’s roughness coefficient was assumed as 0.025 m^{−1/3} s (Goto and Sato 1993).

Coastal tsunami heights from various scaling relations and slip angles considering their uncertainties were compared with those calculated from Recipe A and standard slip angles, that is, slip angles evaluated from the regional stress fields, using the following geometric mean (*G*):

$$\log G = { }\frac{1}{n}\mathop \sum \limits_{i = 1}^{n} \log \frac{{H_{i} }}{{R_{i} }},$$

where \(n\) is the number of coastal points at which the maximum tsunami heights were evaluated. For the comparison of different scaling relations, \({H}_{i}\) and \({R}_{i}\) represent the tsunami heights at the *i*th coastal point using the fault slip amounts from Takemura (1998) and those from Recipe A, respectively. For the evaluation of the uncertainty of fault slip angles, \({H}_{i}\) and \({R}_{i}\) denote the tsunami heights at *i*th coastal point with varied fault slip angles and those from the standard fault slip angle, respectively, using the slip amount derived from Recipe A.

### Effects of the fault rupture scenario

The coastal tsunami heights differ for the various fault combinations, including those with the same moment magnitude. An example is the two possible multi-segment rupture scenarios for the tsunami from the 1993 off the southwest coast of Hokkaido earthquake from the similar moment magnitude with different fault segment combinations (ST08 + ST09 + OK01; *M*_{w} 7.5 and ST09 + OK01 + OK02; *M*_{w} 7.6). The former rupture scenario (ST08 + ST09 + OK01) exhibits greater coastal tsunami heights along the southwestern coast of Hokkaido, reaching areas of the northern Hokkaido coast, such as Haboro Town and Rishiri Island. In contrast, the latter model (ST09 + OK01 + OK02) produces a lower coastal tsunami height in northern Hokkaido that becomes higher along the coast of Okushiri Island, which is similar to what was observed in the 1993 tsunami (Fig. 6). Murotani et al. (submitted to *Earth, Planets and Space*) further compared tsunami simulation results with the 1993 observations, both in terms of tsunami waveforms and coastal runup heights. The geometric mean *K* and logarithmic standard deviation *κ* of the observed to simulated coastal heights (Aida 1977) are 4.41 and 2.35 for ST08 + ST09 + OK01, while they are 3.56 and 2.12 for ST09 + OK01 + OK02. Murotani et al. (submitted to *Earth, Planets and Space*) concluded that the likely causative faults were OK03a, OK03b, and OK05 with *K* = 2.26 and *κ* = 1.54 (see Additional file 1: Fig. S1 for the locations of these faults).

### Effects of scaling relations

The tsunami heights depend on the slip amounts, which were derived using the scaling relations; therefore, the tsunami heights vary significantly with the selection of these relations. The slip amounts obtained from Recipe A are larger than those obtained from TM for wide faults with gentle (~ 30°) dip angles, resulting in greater coastal heights. As an example of the single-segment rupture scenario, the fault model MMS01 off Tohoku region (*L* = 53.2 km, *W* = 33.4 km, dip angle = 25°) produces a higher maximum tsunami (6.08 m) for Recipe A due to a larger slip amount (2.88 m) than that of TM (maximum tsunami height of 4.90 m from a slip amount of 2.03 m; Fig. 7). The geometric mean *G* of the coastal tsunami heights from the TM compared to those of Recipe A is 0.72, which is similar to the ratio of slip amounts 0.70 (2.03/2.88). As a common characteristic of the MMS01 rupture scenario, the tsunami heights are also great along the Noto Peninsula and Oki Islands due to bathymetric effects, such as the Yamato bank. In fact, the coastal tsunami heights from the 1983 central Sea of Japan earthquake (*M* 7.7; Satake 1985, 1989) indicated significant tsunamis along these coasts as well as the eastern coast of the Korean peninsula, resulting in three casualties.

In contrast, the slip amounts obtained from the TM for steeply dipping faults with narrow widths, or multi-segment rupture scenarios with long total fault lengths are larger than those from Recipe A, resulting in a higher tsunami. An example is the single-segment rupture scenario YM18D off the Yamaguchi Prefecture, which is a steeply dipping fault with *L* = 44.6 km, *W* = 17.1 km, and dip angle = 60°. The tsunami is higher for TM (maximum coastal tsunami height = 5.61 m), due to a larger slip amount (3.32 m) than that of Recipe A (maximum coastal tsunami height = 2.33 m with a slip amount of 1.24 m; Fig. 8). The geometric mean *G* of the coastal tsunami height in this case is 2.38.

As for the multi-segment rupture scenarios, the tsunami is generally higher for the TM than that of Recipe A (Additional file 2: Table S2), due to the larger slip amounts. For example, the multi-segment rupture scenario SHN09 + MRK01 + ECG03 + ECG05 off the Niigata Prefecture that is a total length of 100.2 km based on the TM, exhibits coastal tsunami heights with a maximum of 9.39 m, which is substantially higher than those from Recipe A (maximum coastal tsunami height = 4.93 m; Fig. 9). The calculated geometric mean *G* of the coastal tsunami height in this case is 1.74.

The geometric mean *G* histogram of the coastal tsunami heights from the TM relative to Recipe A is shown in Fig. 10a and the Additional file 2: Tables S1 and S2. The *G* values for both the single- and multi-segment rupture scenarios range from 0.69 to 4.30 and has an average of 2.01. Therefore, the coastal tsunami heights from the TM are on average about twice higher than those from Recipe A. For the single-segment rupture scenarios, the correlation coefficient between the slip ratios and *G* ratios is 1.0, indicating that the coastal heights can be predicated once they are computed for a unit slip amount. This means that the costal tsunami heights are mostly linear process. The *G* values range from 0.69 to 3.45 with an average of 1.84, and the distribution has clear spatial characteristics reflecting the fault aspect ratio (*L/W*), that is, the *G* values are relatively small for the faults off Hokkaido and Tohoku, while they are comparatively large for those off Chugoku and Kyushu. The *G* values are larger for faults with a larger aspect ratio (relatively narrow faults due to steep dip angles or thin seismogenic thickness) and vice versa (Fig. 10b). In contrast, the *G* values are > 1 for most of the multi-segment rupture scenarios, indicating that TM models produce higher tsunamis for multi-segment faults. The *G* values for multi-segment rupture scenarios range from 0.84 to 4.30 with an average of 2.17. Our results indicate that the selection of the scaling relation influences the coastal tsunami height differently depending on the fault geometry, due to systematic differences in the relation between fault geometry and slip.

### Uncertainty of fault slip angles

The effects of uncertainty of fault slip angles on coastal tsunami heights were examined by changing these angles from the standards of the regional tectonic stress fields. The effects are expected to be large for strike-slip faults; therefore, we conducted sensitivity analyses for the faults in the central and southwestern parts of the Sea of Japan, where most of the strike-slip faults are located (Fig. 2d).

Ishibe et al. (2021a) investigated the accuracy of the regional stress fields with the Wallace–Bott hypothesis in reproducing the fault slip angles of actual earthquakes using two different catalogs of focal mechanism solutions. The misfit angles between the observed and calculated fault slip angles were shown to generally be small (< 30°), except for the source and surrounding regions of large earthquakes (e.g., the 2011 earthquake off the Pacific coast of Tohoku) and the swarm-like activities started after the 2011 earthquake. Therefore, in the present study, we conducted tsunami simulations by modifying the fault slip angles by 15° or 30° from the standards estimated from three-dimensional tectonic stress fields. Here, + 15° and + 30° are in the direction of the increasing dip-slip component, while − 15° and − 30° are in the direction of the increasing strike-slip component. The varied fault slip angles saturate at ± 90° for + 15° and + 30°, and at 0° or ± 180° for the − 15° and − 30° cases (Fig. 11).

As a typical example, the changes in tsunami heights due to the variable fault slip angles for the single-segment rupture scenario FO04D off the Kyushu fault are shown in Fig. 12. The standard slip angle of this fault is 176°, which indicates an almost pure right-lateral fault, and the calculated maximum tsunami height is 0.44 m at Iki City, Nagasaki Prefecture. When the fault slip angle is changed to 161° (+ 15°), the coastal tsunami height increases to 1.03 m. The coastal tsunami height increases (1.70 m) when the fault slip angle is changed to 146° (+ 30°). Another important issue is that the coastal point with the maximum tsunami height changes from Iki City to Tsushima City (Tsushima Island, northwest of Iki Island). In contrast, cases of − 15° and − 30° show little change in tsunami heights, because slip angle changes of − 15° and − 30° result in the same fault slip angle (180°), which is the specified saturation limit explained previously, thus producing identical tsunami heights. Changes in coastal tsunami heights and the geometric means (*G*) for other rupture scenarios are shown in the Additional file 1: Figs. S5 and S6, Additional file 2: Table S3.

The changes in tsunami heights with fault slip angles for the multi-segment rupture scenario YM07a + YM07b + YM07c, located off Yamaguchi Prefecture, are shown in Fig. 13. Similarly, coastal tsunami heights increase as the dip-slip component of the fault slip increases. Considering uncertainties of the fault slip angles of ± 30°, the maximum tsunami heights range from 0.20 m to 1.71 m. The location of the maximum tsunami height also changes. For the standard fault slip angle, the maximum coastal tsunami height of 0.85 m is located on the coast of Mishima Island, whereas it moves eastward to Hamada at + 30° and southeastward to Hagi at − 15° and − 30°.

The variation in coastal tsunami heights due to the changes in fault slip angles in the southwestern and central parts of the Sea of Japan is summarized in Fig. 14. The *G* values for modifying the fault slip angles range from 0.23 to 5.88. These values are comparable or larger than the *G* values for the scaling relations of the TM and Recipe A. This indicates that the variation in coastal tsunami heights due to uncertainty in fault slip angle is similar or greater than those from the choice of scaling relations for pure strike-slip faults. The sensitivity of the uncertainty in the fault slip angles for coastal tsunami heights depends on the standard fault slip angle (Fig. 14b). For pure strike-slip faults, the coastal tsunami heights vary significantly, and the resulting changes in geometric means (*G*) are substantial. However, for pure dip-slip faults, changes in *G* due to the uncertainty of fault slip angles are relatively small.