GTD for backscattering from elastic spheres and cylinders in water and the coupling of surface elastic waves with the acoustic field

The geometrical theory of diffraction (GTD) has been extended to describe surface elastic wave (SEW) contributions to backscattering from spheres and cylinders in water at high frequencies. The coupling (described by a coefficient Gl ) of the lth class of SEW with the acoustic field and the resulting contribution fl to the form function for solid spheres were previously derived [K. L. Williams and P. L. Marston, J. Acoust. Soc. Am. 79, 1702–1708 (1986)] via a Sommerfeld–Watson transformation (SWT). That work gave a Fabry–Perot representation of fl . A similar representation was postulated by applying the principles of GTD to the Lamb wave contributions to backscattering from empty cylindrical shells [V. Borovikov and N. Veksler, Wave Motion 7, 143–152 (1985)]. In either case, ‖ fl ‖=‖Gl  exp[−2βl ×(π−θl )]/[1+j exp(−2πβl +i2πkac/cl )]‖ ,where j=1 for spheres and j=−1 for cylinders, each of radius a. The SEW phase velocity and attenuation coefficient are cl and βl , sin θl =c/cl , and c and k are the veloc...