Validation of first-order diffraction theory for the traveltimes and amplitudes of propagating waves

Abstract

Ultrasonic measurements of acoustic wavefields scattered by single spheres placed in a homogenous background medium (water) are presented. The dimensions of the spheres are comparable to the wavelength and the wavelength and represent both positive (rubber) and negative (teflon) velocity anomalies with respect to the background medium. The sensitivity of the recorded wavefield to scattering in terms of traveltime delay and amplitude variation is investigated. The results validate a linear (first-order) diffraction theory for wavefields propagating in heterogeneous media with anomaly contrasts on the order of [Formula: see text]. The diffraction theory is compared further with the exact results known from literature for scattering from an elastic sphere, formulated in terms of Legendre polynomials. To investigate the 2D case, the first-order scattering theory is tested against 2D elastic finite-difference calculations. As the presented theory involves a volume integral, it is applicable to any geometric shape, and the scattering object does not need to be spherical or any other specific symmetrical shape. Furthermore, it can be implemented easily in seismic data inversion schemes, which is illustrated with examples from seismic crosswell tomography and a reflection experiment.