TY - JOUR

T1 - Statistical characteristics of scattered waves in three-dimensional random media

T2 - Comparison of the finite difference simulation and statistical methods

AU - Emoto, Kentaro

AU - Sato, Haruo

N1 - Funding Information:
We would like to thank Piero Poli, an anonymous reviewer and the editor, Ana Ferreira for their helpful comments to improve this manuscript. Computations were conducted on the Earth Simulator at the JAMSTEC under the support of a joint research project between Earthquake Research Institute, the University of Tokyo, and Center of Earth Information Science and Technology entitled 'Numerical simulations of seismic-and tsunami-wave propagation in 3-D heterogeneous earth'. We have used the computer system of the Earthquake and Volcano Information Center of the Earthquake Research Institute, the University of Tokyo to create random media. We used the Hi-net data in Fig. 1, provided by National Research Institute for Earth Science and Disaster Resilience (http://www.hinet.bosai.go.jp/)
Publisher Copyright:
© The Author(s) 2018.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - Random velocity fluctuations distributed in the solid Earth function as sources of seismic wave scattering. Scattering effects are often observed in high-frequency seismograms of earthquakes as the broadening of the apparent duration of an S-wavelet and the emergence of coda waves. We conduct large-scale 3-D finite difference (FD) simulations of the scalar wave equation to analyse the intensities of scattered waves propagating through random small-scale heterogeneous media. First, we compare ensemble averaged intensities (mean square amplitudes) derived by the FD simulation with those synthesized based on statistical methods such as the radiative transfer equation with the Born approximation and the newly developed spectrum division methods.We consider several types of random media characterized by von Kármán type autocorrelation functions with different characteristic distances and mean square fractional fluctuations. In the case of a large characteristic distance, the forward scattering is dominant and the fluctuation of the traveltime is large. Even in that case, the newly developed spectrum division method can reproduce the average intensity derived by FD simulations in the entire lapse time range. We further investigate the characteristics of scattered waves. To know the property of the fluctuation of intensities due to the small-scale heterogeneity is important for the ground motion prediction. We reveal the gradual shift of intensity fluctuations from the log-normal distribution to the exponential one with the increase of lapse time. The timing of the shift varies depending on the random medium parameters. This can be explained as the shift from the multiple forward scattering regime to the incoherent wide-angle scattering one. The decay rate of the intensity changes from r-2 to r-4 with the increase of the propagation distance r, which corresponds to the empirical relationship of the observed intensity. This timing of the change also depends on the random medium parameters.

AB - Random velocity fluctuations distributed in the solid Earth function as sources of seismic wave scattering. Scattering effects are often observed in high-frequency seismograms of earthquakes as the broadening of the apparent duration of an S-wavelet and the emergence of coda waves. We conduct large-scale 3-D finite difference (FD) simulations of the scalar wave equation to analyse the intensities of scattered waves propagating through random small-scale heterogeneous media. First, we compare ensemble averaged intensities (mean square amplitudes) derived by the FD simulation with those synthesized based on statistical methods such as the radiative transfer equation with the Born approximation and the newly developed spectrum division methods.We consider several types of random media characterized by von Kármán type autocorrelation functions with different characteristic distances and mean square fractional fluctuations. In the case of a large characteristic distance, the forward scattering is dominant and the fluctuation of the traveltime is large. Even in that case, the newly developed spectrum division method can reproduce the average intensity derived by FD simulations in the entire lapse time range. We further investigate the characteristics of scattered waves. To know the property of the fluctuation of intensities due to the small-scale heterogeneity is important for the ground motion prediction. We reveal the gradual shift of intensity fluctuations from the log-normal distribution to the exponential one with the increase of lapse time. The timing of the shift varies depending on the random medium parameters. This can be explained as the shift from the multiple forward scattering regime to the incoherent wide-angle scattering one. The decay rate of the intensity changes from r-2 to r-4 with the increase of the propagation distance r, which corresponds to the empirical relationship of the observed intensity. This timing of the change also depends on the random medium parameters.

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U2 - 10.1093/gji/ggy298

DO - 10.1093/gji/ggy298

M3 - Article

AN - SCOPUS:85056585391

SN - 0956-540X

VL - 215

SP - 585

EP - 599

JO - Geophysical Journal International

JF - Geophysical Journal International

IS - 1

ER -