[S03-1] Imaging of heterogeneities in the Earth with seismic scattered waves and ambient noise I

[S03-1-03] Propagation of a Scalar Wavelet through von Karman-type Random Media

^○Haruo Sato, Kentaro Emoto (Tohoku University, Sendai, Japan)

Short-period seismograms of small earthquakes show envelope broadening of an S-wavelet with travel distance increasing and excitation of long lasting coda waves. Their durations are much larger than the source duration. We may interpret the collapse of a seismic wavelet as result of scattering by earth medium heterogeneities. As a mathematical model, we study the propagation of a scalar wavelet through von Karman-type random media. When the center wavenumber of the wavelet is lower than the corner wavenumber, the radiative transfer equation with the Born approximation is useful for the synthesis of wavelet intensity. When the center wavenumber is in the power-law spectral range higher than the corner wavenumber, the Markov approximation method based on the parabolic approximation is useful for the synthesis of wavelet intensity; however, this approximation fails to synthesize coda excitation. In this case, we propose the following method for the synthesis of intensity time trace from the onset through the peak until coda for an impulsive radiation from a point source. Taking the center wavenumber of the wavelet as a reference, we divide the random medium spectrum into high– and low-wavenumber spectral components. Applying the Born approximation to the high–wavenumber component, we calculate the scattering coefficient, which is used in the radiative transfer equation for the calculation of intensity. Applying the Markov approximation to the low–wavenumber component, we calculate the envelope broadening and wandering factors. Convolution of these factors with the intensity calculated in the previous step leads to the Green function in the random media. By comparing the synthesized intensity time traces with FD simulations, we have confirmed the usefulness of the proposed synthesis from the onset through the peak until early coda.