This paper is concerned with the application of the Boundary Integral Equation (BIE) method to acoustic radiation and scattering in a three-dimensional half space. Problems in this class include the radiation of sound from vibrating machines near reflecting surfaces and the scattering of sound from objects in air or water that are in close proximity to rigid or free surfaces. Written in the usual way, the Helmholtz integral formula involves integrations over all surfaces that border the acoustic domain. For half-space problems these integrations include the infinite plane that forms the half-space boundary. For half-space radiation and scattering problems, it is shown that the integrals on the infinite plane may be removed by using a modified Green’s function in the Helmholtz integral. Thus, all element discretization and numerical approximation are confined to the body or obstacle. This feature simplifies the engineering effort required to set up a problem and improves the accuracy of the results. Gone also is the question of where to terminate the discretization of the infinite plane. Examples of radiation and scattering near a rigid boundary are used as illustration of the method.

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