Abstract
Wavelets scattered from a spherical heterogeneity were computed from solutions of the wave equation for a plane wave incident on a spherical inhomogeneity. The solution is expressed as an orthogonal function expansion that is asymptotically correct for all wavelengths. In this paper we computed the spectral response and corresponding time-domain impulse response for wavelengths greater than one tenth the radius. The frequency content and amplitude of the scattered wave from an incident compressional wave systematically varies with scattering angle. A comparison of the scattered waves with arrival times and amplitudes computed using ray theory shows that the variations in response with scattering angle are closely tied to arrival times and amplitudes of the internally reflected and refracted waves. Use of the minimum phase criterion in order to generate a wavelet does not replicate the wavelet shape, but can be used to generate wavelets where the spectral amplitudes are the principal objective. The Born approximation, the first two terms in the orthogonal function expansion, underestimates the high-frequency energy.
