A numerical investigation of scattering effects for teleseismic plane wave propagation in a heterogeneous layer over a homogeneous half-space

Numerical simulations of teleseismic wave propagation in a heterogeneous layer over a homogeneous half-space are conducted to further our understanding of teleseismic coda generation. Acoustic and elastic finite difference synthetics are generated for more than 150 different layer-over-a-half-space models. The models vary in scattering layer thickness (L), heterogeneity correlation distance (a, or a_x and a_z), and heterogeneity standard deviation (σ). The synthetic data are analysed by examining coda intensity envelopes and frequency-wavenumber spectra.

The level of scattered energy is found to be controlled by the ka and σ values. Coda levels increase with increasing ka from ka > 1 to ka∼ 1, and decrease with increasing ka for ka > 1. Scattered energy levels always increase with increasing σ. Models that vary in scattering layer thickness alone did not consistently produce changes in the coda level or rate of decay independently of the values of ka and/or σ. The rate of coda decay is controlled by the heterogeneity aspect ratio (a_x/a_z). Models with spatially isotropic heterogeneities (a_x/a_z = 1) produce the slowest rate of decay, while those with an infinite aspect ratio (homogeneous, plane-layered models) produce the most rapid rate of decay. Any decay rate between these two extremes can be obtained by varying the heterogenity aspect ratio. Acoustic and elastic models exhibit similar coda intensity envelope characteristics. Apparent scattering attenuation of the direct pulse is a function of ka and is strongest for models with spatially isotropic heterogeneities.

Frequency-wavenumber analysis showed that coda for models with spatially isotropic heterogeneities is composed largely of low apparent velocity energy in the form of P-to-S and/or body-to-surface wave scattered energy. Coda for models with spatially anisotropic heterogeneities is composed largely of vertically propagating layer reverberations. Coda for extreme anisotropic models is composed solely of vertically propagating layer reverberations. The onset time of low apparent velocity energy is also controlled by the heterogeneity aspect ratio. For models with anisotropic heterogeneities, low apparent velocity energy appears immediately after the first arrival, for models with an infinite heterogeneity aspect ratio (1-D models), low apparent velocity energy never appears.