Time-Domain Analysis of Echoes from Solid Spheres and Spherical Shells with Separated Transmit-Receive Configurations

The complexity of bistatic echo pulse sequences surpasses that of monostatic echo pulse sequences. Based on the scattering acoustic field of elastic spheres and spherical shells, a method is employed to calculate the time-domain echoes of solid spheres and spherical shells with transceiver separation under the condition of plane wave incidence. This is achieved by constructing the incident signal and performing a multiplication operation in the frequency domain with the target scattering acoustic field. Employing the contour integral method, we derive phase velocity and group velocity dispersion curves for circumferential waves propagating around these structures. Furthermore, under the assumption of plane wave incidence, we analyze the propagation paths of Rayleigh echoes for solid spheres and anti-symmetric Lamb waves for spherical shells. Estimation formulas for the arrival times of separated transmit-receive echoes are provided for both solid spheres and spherical shells. Our findings indicate that bistatic waves can be classified into clockwise and counterclockwise circulation patterns around the surfaces of these structures. Through a comparison with the time-angle spectrum of echoes, we demonstrate the accuracy of the proposed estimation formulas for echo arrival times. This study offers valuable insights for the identification of underwater targets.