Characterizing seismic scattering in 3D heterogeneous Earth by a single parameter

Abstract

<p>We analyze the power spectral density (PSD) of von Karman autocorrelation function (ACF) to derive a theoretical parameter which characterizes the scattering of seismic wavefield due to random heterogeneities in 3D Earth structure. We then verify our analytical findings by performing ground-motion simulations. We characterize scattering using root-mean-square (RMS) fluctuations of normalized seismic wave speed, which represents wavefield scattering due to random heterogeneities in 3D Earth under the diffraction condition. The isotropic von Karman ACF is parameterized by correlation length a, standard deviation σ, and Hurst exponent H. To compute the RMS value, we simplify the von Karman PSD for three regimes: k·a ≫ 1 (λ ≪ a), k·a ≈ 1 (λ ≈ a) and k·a ≪ 1 (λ ≫ a), where λ is wavelength and k wavenumber of the seismic waves. The analysis of the RMS values reveals that 1) scattering is proportional to the standard deviation σ of small-scale velocity variations in all three regimes, 2) scattering is inversely proportional to the correlation length in the k·a ≫ 1 regime, but directly proportional to the correlation length in the other two regimes, 3) a small Hurst exponent H for the k·a ≫ 1 regime leads to scattering controlled solely by the standard deviation of small-scale velocity variations (for the other two regimes, it leads to weaker scattering). The seismic scattering effectively vanishes for H approaching zero. Our theoretical findings are purely physics based and are furthermore verified by 3D high resolution numerical simulations. Hence, we developed solid physics-based understanding of 3D seismic scattering due to random heterogeneities in the Earth which will be helpful for future modeling studies.</p>