[SSS12-P19] Angular distribution of energy fluxes of seismic waves in two-dimensional random heterogeneous media
Keywords:Scattering, Angular spectrum, coda
The energy flux of seismic waves can be calculated by taking the product of the velocity and the stress at a certain point. The angular distribution of the energy fluxes, that is the angular spectrum is the ensemble of energy fluxes. The medium size of the finite difference simulation is 384 x 384 km and the grid separation is 100 m. The background velocities are 6.00 and 3.46 km/s for P and S waves, respectively. The random heterogeneous medium is characterized by an exponential type auto-correlation function with the characteristic scale of 0.5 or 5 km and the RMS fractional fluctuation of 5 %. The strike-slip type source located at the center of the medium. The source time function if the Kupper wavelet whose dominant frequency is 3 Hz. Receivers are located at propagation distances 25, 50, 75 and 100 km. At a distance, 8 receivers are located with the interval of the azimuth of 45 degrees. According to the radiation pattern, we stack the energy fluxes of along and perpendicular directions (E90), and oblique directions (E45), respectively. The maximum lapse time of the simulation is 45 s.
The angular spectrum never becomes isotropic within the maximum lapse time of the simulation for both cases (characteristic scales of 0.5 and 5 km). The anisotropy of the angular spectrum at the P coda is stronger than that at the S coda. The difference between the two cases is not strong in terms of the shape of the angular distribution at the S coda. This is the same result as obtained by the scalar wave simulation. Conversely, the angular distribution at the P coda of the case of the characteristic scale of 5 km is anisotropic compared to that of 0.5 km. After the onset of S wave, the angular spectrum approaches the isotropic distribution. This approaching speed of E90 direction is faster than that of E45 direction.
The numerical simulation revealed that the dependence of the angular distribution of scattered waves at the S coda on the medium parameter is weak. However, at the P coda, P to S scattering plays an important role to determine the angular distribution of the energy flux. We will extend our simulation to three-dimensional heterogeneous media in the future.