Stochastic Representations of Seismic Anisotropy: Verification of Effective Media Models for Locally Isotropic 3D Heterogeneity

Xin Song, Thomas H. Jordan, & David A. Okaya

Submitted August 15, 2017, SCEC Contribution #7842, 2017 SCEC Annual Meeting Poster #039

A self-consistent theory for the effective elastic parameters of stochastic media with small-scale 3D heterogeneities has been developed using a 2nd-order Born approximation to the scattered wavefield [Jordan,2015]. The theory has been applied to heterogeneities in the Los Angeles basin determined from well-log analysis and its predicted anisotropy has been compared with seismic constraints [Song and Jordan, 2017]. Here we verify this theory through a series high-resolution numerical experiments using isotropic wave-propagation codes. In the low-frequency limit, where the seismic wavenumbers are small compared to the characteristic wavenumbers of the heterogeneity, the locally isotropic stochastic medium can be replaced by a homogeneous “effective medium” with a transversely isotropic (TI) stiffness tensor that depends only on the one-point covariance matrix of the two Lamé parameters and a dimensionless number η that measures the horizontal-to-vertical aspect ratio of the heterogeneity. Three types of seismic velocity models are used in the experiment: (1) heterogeneous, locally isotropic models generated by a Gaussian random process with an RMS relative variability in the Lamé parameters of ε and a Matérn correlation structure described by the aspect ratio η, a characteristic outer scale l, and a fractal dimension D; (2) homogenous, isotropic models given by the Voigt average of the heterogeneous models; (3) homogeneous, anisotropic models calculated from the heterogeneous models using the effective media theory. If the seismic wavelength λ is large compared to l and small compared to the total propagation distance L, the effective-medium theory predicts that the scattering caused by isotropic heterogeneity (η = 1) with ε = 10% relative variations reduces the effective travel time by about 0.25% compared to the Voigt travel time. Calculations of wave propagation through models of type (1) yield modulus reductions of the same magnitude within a numerical resolution of about 10% (0.025% in travel time). Similar agreement is found between predicted and computed shear-wave splitting for geometrically anisotropic structures with η = 0.3 and η = 3, although, with the mesh-size limitations of the current calculations, the numerical resolution degrades at these values to as much as 50% of the total splitting effect. Strategies for increasing the numerical resolution, which require maintaining the relationship l << λ << L, will be discussed.

Song, X., Jordan, T. H., & Okaya, D. A. (2017, 08). Stochastic Representations of Seismic Anisotropy: Verification of Effective Media Models for Locally Isotropic 3D Heterogeneity. Poster Presentation at 2017 SCEC Annual Meeting.

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