Estimation of radius and thickness of a thin spherical shell in water using the midfrequency enhancement of a short tone burst response

Abstract

The midfrequency enhancement phenomenon for tone burst backscattering by thin spherical shells in water has been discussed by several investigators. In their works, it is found that the earliest elastic tone burst echo is enhanced relative to the specular reflection, and this enhancement is mainly due to the lowest subsonic antisymmetric Lamb wave. In this paper, the tone burst backscattering obtained from the convolution integral of the incident tone burst and the impulse response by a submerged spherical shell is investigated to display the midfrequency enhancement. The modified ray approximations are used to calculate the echo contributions from different Lamb waves. The numerical results show that the ratio of a∕h and the dimensionless echo delay have nearly linear relationship with the frequency of greatest enhancement. Based on this property, two linear approximate equations are formulated to evaluate the radius and thickness of a thin spherical shell. A simple method is developed to estimate the frequency of greatest enhancement and the corresponding echo delay from a short tone burst echo with a higher carrier frequency. The evaluated results show that the present method is effective on determination of the radius and thickness of a thin spherical shell in water.