Modified Born approximation for solving scattering problems

Abstract

Scattering of ultrasonic waves in inhomogeneous media is described by the inhomogeneous differential equations. Such equations could be solved using a method of consecutive approximations, such as the Born approximation. The Born approximation is applicable when (n−1)<1 and 2ka(n−1)<1, where n is the refraction index and ka is the wave dimension of the scatterer. For the Born approximation, it is assumed that the acoustic field inside of a scatterer is substituted by the acoustic field of the incident wave, along with the wave number of the surrounding media. In this work, the modified Born approximation is used, where the acoustic field inside of a scatterer is substituted by the acoustic field of the incident wave, along with the wave number of the scatterer. A similar approach is used for solving the scattering problems of multilayered scatterers, which have weak scattering properties. The computed and experimental scattering characteristics for the elastic scatterers with various acoustical impedance are presented. It is demonstrated that the modified Born approximation more accurately describes the scattering problems for the scatterers with ka>1.