Astronomy and Astrophysics – Astronomy
Scientific paper
Jun 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009geoji.177..958s&link_type=abstract
Geophysical Journal International, Volume 177, Issue 3, pp. 958-965.
Astronomy and Astrophysics
Astronomy
1
Fractals And Multifractals, Tsunamis, Wave Scattering And Diffraction
Scientific paper
The scattering coefficient is one of the most fundamental parameters by which to quantify the scattering intensity for waves as a function of scattering angle and wave frequency. This study presents a derivation of the scattering coefficient for linear long-wave tsunami equations in randomly fluctuating sea-bottom topography using the first-order Born approximation. The scattering coefficient is directly related to the power spectrum density function of fluctuations in the bottom topography and shows a strong tsunami-wavelength dependence. The scattering regime is determined by the normalized wavenumber ak, where k is the tsunami wavenumber and a is the correlation distance of the fluctuating sea-bottom topography. The scattering pattern for small wavenumbers, ak << 1, is symmetric in the forward and backward directions, whereas the pattern for large wavenumbers, ak >> 1, shows small-angle scattering around the forward direction. Based on the theoretically derived scattering coefficient, we evaluate the excitation of tsunami coda and leading-wave attenuation as a function of the normalized wavenumber. The coda energy for small wavenumber ak << 1 is proportional to k3, whereas the energy for large wavenumber ak >> 1 is proportional to k-p+3 when the power spectral density function of the sea-bottom fluctuation is characterized by a power law with the exponent of -p in large wavenumber. The scattering attenuation represented by the inverse of the quality factor ScQ-1 is proportional to k2 for small wavenumber ak << 1, whereas ScQ-1 is proportional to k-p+2 for large wavenumber ak >> 1.
Furumura Takashi
Saito Tatsuhiko
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