Observed Seismograms
The characteristics of high-frequency S and S-coda waves confirmed in Fig. 1b and 1c were also observed in other earthquakes (Figures S2–S51). We recognized that coda signals for frequency ranges 0.5 to 1.0 Hz and 0.75 to 1.5 Hz could be available in only a few moderate (MJMA > 4) earthquakes. Therefore, we focused our attention on the characteristics of seismic wave propagation at frequencies > 1 Hz. The coda amplitudes of the horizontal and vertical components at the DONET stations were larger than those at the F-net stations; however, the vertical Smax amplitudes at both DONET and F-net stations obeyed similar attenuation characteristics. DONET stations were deployed just above the thick sedimentary layers (Fig. 2a). The characteristic differences between S and S-coda waves within sedimentary basins were first described by Idei et al. (1985), who pointed out that the amplification characteristics of S and S-coda waves may be different if the seismic station is located within a thick sedimentary basin. Additionally, we confirmed a similar possibility at DONET stations, where thick (> 2 km) oceanic sediments exist (e.g., Kamei et al. 2012; Tonegawa et al. 2017).
Figure 3 shows the relationship between hypocenter depths and relative coda amplitudes at four DONET stations (KMA03, KMB06, KMC09, and KMD13) normalized against those at N.KISF (the station locations are shown in Fig. 1a). In the coda-normalization method, these values are considered as the site-amplification factors of S waves. An earthquake that occurred at 11:39 on April 1, 2016 (JST), was located at a depth of 28 km in the JMA catalog; however, this earthquake was an interplate earthquake at a depth of approximately 10 km (e.g., Wallace et al. 2016a; Takemura et al. 2020a). Therefore, we modified the depth of the earthquake to 10 km (Table S1). Excluding the interplate earthquake at a depth of 10 km, the relative coda amplitudes increased with increasing hypocenter depth. This tendency appeared to be due to the effects of depth-difference coda generation rather than local site effects.
We calculated horizontal-to-vertical (H/V) ratio envelopes and discarded envelopes with coda-to-noise ratios less than 5. Figure 4 shows the H/V ratio envelopes at M.KMB06 for available earthquakes. Owing to the differences in earthquake locations and source radiation patterns, the H/V ratios at lapse times of 20 s to 40 s (body wave parts) were relatively unstable. The H/V ratios were almost constant at lapse times ≥ 70 s, despite the variance in epicenter locations and earthquake depths (Fig. 1a). Figure 5 shows the map of the coda H/V ratios for frequency ranges of 1.0 to 2.o Hz, 1.5 to 3.0 Hz, 2.0 to 4.0 Hz, and 3.0 to 6.0 Hz. The coda H/V ratios were calculated using the average H/V ratios at lapse times of 70 s to 90 s. The coda H/V ratios at F-net stations were almost 1. Although methods for estimating site amplifications at OBSs have been discussed (e.g., Kubo et al. 2020), these values correspond well with the horizontal site amplifications estimated by Yabe et al. (2019) except for M.KMC10 and M.KMC11. The H/V ratio has been widely used for site-amplification and shallower structure estimations (e.g., Lermo and Chávez-García 1993; Field and Jacob 1995; Konno and Ohmachi 1998; Kawase et al. 2018). We corrected the horizontal Smax amplitudes at the DONET stations using the average coda H/V ratio at each station. Figure 6 shows the relationships between the Smax amplitudes and epicentral distances for an earthquake that occurred at 08:00 on November 30, 2014 (JST). Both the vertical and corrected horizontal Smax amplitudes at the DONET stations obeyed similar attenuation characteristics. This result indicated that the H/V ratios for the coda part were practically able to correct site amplifications for horizontal ground motions at OBSs. This possibility will be numerically validated in a later section.
Simulations Of Seismic Wave Propagation
Numerical simulations of seismic wave propagation within various heterogeneous models help us understand the observed characteristics of high-frequency S and S-coda waves. Figure 7 shows the simulated envelopes for Events 1 and 2 at stations N.KISF and M.KMB06. The amplitudes of the coda waves at M.KMB06 were larger than those at N.KISF. Although the observed horizontal coda amplitudes at the DONET stations were much larger than those in the vertical component, the simulated horizontal and vertical coda amplitudes did not differ significantly.
The effects of thick sedimentary and seawater layers on S and S-coda waves are presented in Fig. 8, which shows the simulated horizontal envelopes at M.KMB06 and N.KISF for the various-type heterogeneous models (Models 1–3). The coda amplitudes of Model 1 (Fig. 8a) were smaller than those of Model 0. Additionally, the effects of the thick sedimentary layer appeared at N.KSF, because N.KISF is located close to the coastline. The influence of the thick, low-velocity sedimentary layer at M.KMB06 appeared to be stronger than that at N.KISF. Owing to the lack of a seawater layer (Model 2; Fig. 8b), the coda amplitude at M.KMB06 became slightly smaller than those in Model 0. Based on these comparisons, we confirmed that thick, low-velocity sediments had the strongest effect on S-coda amplitudes. However, the Smax amplitudes of each heterogeneous model did not drastically change relative to those of Model 0.
The simulated vertical Smax and S-coda amplitudes (Figs. 9 and 10) were in good agreement with the observations (Figs. 1c and S27–51). The simulated Smax at the DONET and F-net (Figs. 9a, c, and 10, blue diamonds and triangles, respectively) stations exhibited similar attenuation characteristics, even for Model 0. Although S-coda amplitudes in Model 3 (Fig. 9b and d) were almost the same irrespective of epicentral distance, coda amplitudes at DONET stations in Model 0 were larger than those at F-net stations (Figs. 9a, c, and 10). As the frequency increased, the differences in the S-coda amplitudes of Model 0 between the F-net and DONET stations also increased (Figs. 9a, c, and 10). Figure 11 (top panels) show the spatial distributions of the horizontal coda amplitudes for Event 1 at the F-net, DONET, and virtual seismic stations at an interval of 0.05°. Moreover, we plotted the thickness of the Japan Integrated Velocity Structure Model (JIVSM) sedimentary layer and confirmed that areas with large coda amplitudes corresponded well to areas with thick (> 2 km) sedimentary layers. Furthermore, the coda amplitudes for sediments > 2-km thick were almost constant (Fig. 11, bottom panels). This suggested that the energies of the coda waves were trapped and averaged within the thick sedimentary layers.
We then calculated the energy fluxes at M.KMB06 for the simulations of Event 1 for each model. Using the stress (τ) and velocity (v) wavefields, we obtained the energy flux of the j-th component, ej, by − τjkvk. We evaluated the propagation directions of coda waves using energy flux vectors. Figure 12 shows the histograms of the propagation directions for coda waves at lapse times of 70 s to 90 s in each model. We used a simulated time series of the velocity and stress fields at M.KMB06 from the simulation results of Event 1. The angle θ was measured from the z-axis, and θ = 0 indicated downward propagation. Angle ϕ represents the horizontal azimuth measured from the X-axis, which is the same as that in Fig. 2a. The horizontal azimuth, ϕ, was uniformly distributed irrespective of the heterogeneous models. This indicated that scattered waves were randomly incident from the scatterers to the M.KMB06 station. In Model 3 (typical crust), the angle θ tended to be concentrated around 60° to 120º, indicating that scattered waves propagated horizontally from far scatterers. However, in the heterogeneous models, except for Model 3, angle θ was not localized around 60° to 120º. This suggested that scattering within the sedimentary layer and/or multiple reflections between the bedrock and sea surface generates vertically-propagating S-waves, which causes the amplification and elongation of coda waves.
According to the observed seismograms and simulations in various-type heterogeneous models, we found that coda waves at DONET stations mostly comprise a superposition of scattered or reflected waves within a thick (> 2 km) sedimentary layer. Low-velocity sedimentary basin was developed in 100-kmscale along both strike and dip directions (Figs. 2a and 11). Once S waves radiated from a seismic source incident within thick low-velocity sediments, S-wave energy is trapped within the sediments; consequently, coda waves at DONET stations mostly comprise multiple scattered waves within the sediments. By contrast, direct S waves propagated through the sediments just beneath the stations only once. Thus, the amplification characteristics of high-frequency S and S-coda waves due to thick low-velocity sediments are completely different.
Large-scale thick sedimentary structures also exist in various inland regions (e.g., the Kanto, Osaka, Niigata, Los-Angeles, Seattle, and Mexico Basins). Additionally, thick oceanic sediments exist in other subduction zones (Straume et al. 2019), such as the Japan Trench (Takagi et al. 2020; Yamaya et al. 2021), Hikurangi margin (Eberhart-Phillips and Bannister 2015; Kaneko et al. 2019), and Cascadia (Ruan et al. 2014; Gomberg 2018). In such regions, as Idei et al. (1985) first pointed out, the coda-excitation mechanism can differ from that in a typical lithosphere. Moreover, we found that the seawater layer also affected the coda at OBSs; however, the impact was limited. The coda-normalization method for estimating or correcting site amplifications cannot be applied to stations within thick sediments.
A Realistic Simulation For The 2016 Southeast Off Mie Earthquake
To directly compare the simulations with the observed strong motions, we conducted a finer-scale simulations of the seismic wave propagation for Event 1 in a model region that covered an area discretized by a finer grid (0.015 km) (Fig. 13a, blue rectangle). We employed the same 3D model and source model of Event 1 as in previous simulations but the minimum S-wave velocity is 0.5 km/s, which allowed evaluation of seismic wave propagation for frequencies less than 4.7 Hz. We conducted simulations of the model using five realizations of small-scale random velocity fluctuations. The simulated envelopes for each frequency band were then calculated by stacking the envelopes of the five random realizations. Each simulation for preparing 75-s seismograms by 150,000 timesteps required 50 TB of computer memory and 6.1 h of computation time using 2,736 vector elements (available full vector elements) of the Earth Simulator.
Owing to our limited knowledge of small-scale heterogeneities, it is difficult to obtain a realistic moment rate function that includes high-frequency (> 1 Hz) components. Thus, after simulations using a 0.1-s Küpper source wavelet, the simulated envelopes for each frequency band were adjusted by ratios between the simulated and observed horizontal Smax amplitudes at N.KISF. Additionally, the horizontal envelopes at DONET stations were multiplied by the observed coda H/V ratios at the corresponding stations (Fig. 5). Because the simulation region was narrowed because of the finer spatial grids for a minimum S-wave velocity of 0.5 km/s, F-net stations were consequently located close to the model boundaries (Fig. 13a). Thus, in our new simulations, we focused on the Smax amplitudes at the F-net and DONET stations and envelope shapes at the DONET stations.
Figure 13b shows a comparison of the Smax amplitudes between the simulations and observations. We discarded the data of the M.KME node (4 northwestern DONET stations just above the source of Event 1) because of strong nonlinear site responses during this event (Kubo et al. 2019). The adjusted simulation results reproduced the observed Smax amplitudes of both horizontal and vertical component. Figure 14 shows examples of comparisons between the observed and simulated envelopes for the frequency range 2.0 Hz to 4 Hz. Although we assumed an unrealistic 0.1-s Küpper pulse, the envelope shapes at the DOENT stations were characterized by spindle shapes. This significant pulse broadening was also caused by thick oceanic sediments beneath the stations (Takemura et al. 2020b).
Figure 15 shows the variance reductions (VRs) between the observed and simulated envelopes. Although detailed parameters for the source time function and stochastic random small-scale heterogeneity within oceanic sediments are not well known, this simulation reproduced the characteristics of seismogram envelopes at the DONET stations, suggesting that the described simulation model and method for adjusting site amplification based on coda H/V ratios worked well. The stations at the KMA node (4 northeastern stations) exhibited low VRs, and the simulation using a point source model could not reproduce envelopes in directions close to the null axis of the Event 1 focal mechanism. The 10.6×3.4-km2 rectangle fault of this earthquake reproduced tsunami records at DONET stations (e.g., Wallace et al. 2016a; Kubota et al. 2018); therefore, a complicated rupture process for generating high-frequency seismic energy is expected on the fault of this earthquake. By introducing detailed source rupture heterogeneities, the discrepancies between the observed and simulated envelopes will be improved in future studies.