Propagation of sound pulses in a homogeneous layer under an inhomogeneous half space

Abstract

We consider the propagation of two-dimensional sound pulses in a homogeneous layer −y ₁⩽y⩽0. It is bounded by a plane stratified inhomogeneous half spacey⩾0 on one side and a perfectly reflecting boundary on the other. A line source is situated in the layer. The boundary condition isφ=0 or∂φ/∂y=0 aty=−y ₁, whereφ is the acoustic velocity potential. We suppose that the velocity of wave propagationc is given byc ⁻²=p−qe ^−αy iny>0, wherep, q, α are real and positive andp>q. It is equal to C′ in the layer where C′ is a constant. The method of dual integral transformation is used and the velocity potentialφ is obtained after using asymptotic expressions for some of the functions which are in the integrand. We obtain the incident, reflected, multiply-reflected and diffracted pulses in the layer.