We note that we did not observe the coherent backscattering (Margerin et al. This indicates that coda waves are affected by the 3-D small-scale heterogeneities even in the long period (>2 s). This uniform distribution of the energy is well known as the characteristic of short-period seismic waves resulting from wave scattering by small-scale subsurface heterogeneities (Aki 1969 Sato et al. In the spatial distribution, the energy at the epicentral distance smaller than the direct wave front corresponds to the energy of the coda waves. The coda means the later part of the seismograms. The energy density between the source and the epicentral distance of 200 km is flat at all three period bands, which corresponds to the energy of the coda waves. The maximum energy can be seen at the epicentral distance between 300 and 350 km, which corresponds to the direct S or surface waves. The front of the direct wave is located at the epicentral distance between 400 and 500 km. 1, recorded by the Hi-net stations shown in Fig. For example, we show the snapshot of the energy density distribution of a local earthquake in Fig. 2005) revealed that, similar to short period signals, the coda of long-period seismograms is affected by small-scale heterogeneities. However, the nationwide dense high sensitivity seismograph network(Hi-net Okada et al. For example, a 1-D layered velocity structure is often used to estimate the moment tensor of the source (e.g. It is difficult to deterministically model the entire waveform of the short-period seismogram (∼2 s). These effects are important for the propagation of short-period seismic waves as well as the intrinsic attenuation. Numerical modelling, Wave propagation, Wave scattering and diffraction 1 INTRODUCTIONĪ small-scale velocity inhomogeneity generates coda waves and decreases the peak amplitude of the direct phase due to the scattering of seismic waves. The method proposed in this study is suitable for quantifying the statistical properties of long-wavelength subsurface random inhomogeneity, which leads the way to characterizing a wider wavenumber range of spectra, including the corner wavenumber. Finally, we estimate the intrinsic attenuation by modelling the decay rate of the energy. Our result reveals the spectrum of the random inhomogeneity in a wide wavenumber range including the intensity around the corner wavenumber as P( m) = 8πε 2 a 3/(1 + a 2 m 2) 2, where ε = 0.05 and a = 3.1 km, even though past studies analysing higher-frequency records could not detect the corner. By taking the ratio of the energy of the coda area to that of the entire area, we can separately estimate the scattering and the intrinsic absorption effects.
It is not necessary to assume a uniform background velocity, body or surface waves and scattering properties considered in general scattering theories. Compared to conventional methods based on statistical theories, we can calculate more realistic synthetics by using the FD simulation. We calculate the spatial distribution of the energy density recorded by a dense seismograph network in Japan at the period bands of 8–16 s, 4–8 s and 2–4 s and model them by using 3-D finite difference (FD) simulations. We analyse three moderate-size earthquakes that occurred in southwest Japan. We estimate the statistical parameters that characterize the small-scale random heterogeneity by modelling the spatiotemporal energy distribution of long-period seismograms. This phenomenon is well known in short-period seismograms and results from the scattering by small-scale heterogeneities. We found that the energy of the coda of long-period seismograms shows a spatially flat distribution.