Acoustic Tomographic Reconstruction of Anomalies in Three-Dimensional Bodies

Abstract

We present a theory of acoustic tomography based on data processing shear wave scattered field over an observational plane, including frequency and polarization diversities. The theory is based on the Gubernatis formulation of scattering and does not require solution of the Fredholm equation for material displacement u. An essential feature of the theory is an expansion of VjkUk in even powers of frequency to obtain an "equivalent frequency insensitive" source in the anomaly.We treat data inversion both in cartesian coordinates via the twodimensional fast-Fourier transform (FFT) and in cylindrical coordinates via the one-dimensional Hankel transform. We note the advantages of polarization diversity. Sampling formulae are quoted. AR (auto regressive) and ARMA (auto regressive moving-average) modeling are mentioned as means of improving anomaly resolution. Both frequency and polarization diversities tend to reduce speckle noise.