Scattering attenuation ratios of P and S waves in elastic media

The variation of scattering attenuation ratios of P and S waves (Q_P^-1/Q_S^-1) is investigated in elastic media by using numerical simulations and theoretical expressions based on the first-order Born approximation. Numerical results from stochastic random media (von Karman, exponential, Gaussian) with mild velocity perturbation (10 per cent in this study) are represented well by theoretical attenuation curves with a minimum scattering angle of 60-90°. The level of scattering attenuation ratios is dependent on the velocity ratio (γ = α₀/β₀) and the type of medium. The change of perturbation in the density introduces a relatively small variation in attenuation ratio. Attenuation ratios are proportional to normalized frequency (fa, frequency-by-correlation length) at the intermediate-frequency range (0.1 km s^-1 < f a < 10 km s^-1) and determined constant at the high-frequency (f a > 10 km s^-1) and low-frequency (f a < 1 km s^-1) regimes. The von Karman-type models look appropriate for the representation of small-scale variation in the Earth. The scattering attenuation ratios can be implemented for the investigation of small-scale heterogeneities in the Earth.