The Acoustic Response of a Sphere in a Two-Layer Half-Space

Abstract

In this paper the acoustic wave equations for a specific cylindrically symmetric model are considered. The model consists of a spherical inhomogeneity in a homogeneous half-space with an overburden layer. A pressure source is located in the top layer, centred on the axis of symmetry. Further details are contained in Section 2. Owing to the geometrical simplicity of the model, the wave equations can be solved analytically to a large extent. Therefore, the results of such a model may be used for the validation of algorithms, solving or dealing with wave equations in more general 3-D models. Moreover, the results for this model give a quantitative impression about the shape and magnitude of the response of a bounded anomaly in comparison with that of a plane layer.