Reflected and lateral waves for the Sommerfeld model

Abstract

The Sommerfeld model, a constant-density isospeed half space over a second constant-density isospeed half space, has offered extensive insight into the role of the ocean bottom in acoustic propagation by exploiting properties of the ground or lateral wave and the specularly reflected waves. This paper presents some new results for this model. A uniform asymptotic expansion is obtained for the source and receiver on the interface, which reduces to the exact solution as either the density ratio or the sound-speed ratio approaches unity. In addition, this result shows the ground or lateral wave decays initially—not like 1/kr2, the classical result, but like 1/r, and as the index ratio approaches unity this region increases. For the source and receiver above the interface, the reflected fields are expressed in a uniform expansion involving the parabolic cylinder functions. Away from the critical ray these expressions reduce to the usual specular and lateral fields. The expressions reduce to the interface results and are not singular as the sound-speed index approaches unity, and confirm the above decay predictions for the lateral wave. Subject Classification: [43]30.20, [43]30.30; [43]20.15.