Scattering of elastic waves in 2-D composite media II. Waveforms and spectra

Abstract

The boundary integral representation of the complete seismic wavefield in two-dimensional composite media characterised by the distribution of many cavities (Paper I in this issue) is used to study the waveforms and spectra of the scattered wavefield for three models of media heterogeneity, upon the incidence of P and S plane waves and line sources. First, the case of one circular cavity and S primary waves shows that the scattered wavefield is composed mainly of S waves, and that S-P scattering can be ignored in any frequency range for all forward scattering angles (scattering angle θ measured clockwise with respect to the direction of propagation of the primary wave). The spectra of forward scattering computed for θ ⋍ 0° resemble the spectrum predicted by the Born approximation for acoustic or scalar waves for θ = 0°: of small amplitudes for small values of non-dimensional frequency kd ( k is the wavenumber and d is the cavity diameter), increasing with kd, up to kd ⋍ 2, and becoming constant for larger values of kd. The spectra for backward scattering (θ ⋍ 180°) behave similarly, showing amplitudes as large as those computed for the forward cases. The non-isotropic pattern of scattering predicted by analytical solutions is also confirmed. In the case of P primary waves, P-S scattering appears to be significantly stronger than P-P scattering for most scattering angles, except for θ ⋍ 0° and θ ⋍ 180°. The computation of synthetic seismograms for models with many cavities show scattered waves of low frequency corresponding to wavelengths much larger than the size of the cavities, as well as those of high frequency due to multiple reflections and conversions at the boundaries of the cavities. A cluster of 20 cavities randomly distributed within a small region produces well-defined low frequency waves that appear to be associated with the presence of one low-velocity heterogeneous body, or soft inclusion, represented by the whole cluster. The case of 50 cavities randomly distributed within a horizontally extended region (of narrow thickness) shows coda-like wave arrivals, particularly strong in the horizontal component. Also in this case, nearly horizontally incident plane waves produce low frequency scattered waves of large amplitudes. It appears that while in the long-wavelength limit this model synthesises a coherent wave corresponding to reflection upon a horizontal interface, towards the short-wavelength limit the scattered waves show a rather complex, incoherent pattern immediately after the arrival of the incident wave, as if the region were a transitional zone of effective thickness. The analysis presented in this paper suggests that if the wavelengths are much larger than the size of the cavities, our representation of random media can be used to represent regional heterogeneity in the earth's crust, associated with observed seismic scattering phenomena.