Shallow water propagation from an embedded source

The method of plane wave decomposition is used to model acoustic propagation in shallow water from a point source in the sea-bed. The research was prompted by the need to model blast waves emanating from explosive charges buried in boreholes, which are used to fragment unwanted bedrock. The water channel is assumed to be a homogenous medium of constant depth, and a point spherical source is located below the rock-water boundary. By using the analytical decomposition of a spherical wave into plane wave components, the resulting pressure due to the spherical source is given as a single, one-dimensional integral. This integral is of a similar form to the established expression for the case of a point source located within the water channel, and in fact the denominator is identical.Rather than form an approximate solution to the integrals, the integrals are solved numerically using reliable adaptive integration routines and advanced computational power. By integrating the real and imaginary parts separately, exact results are produced for both the case of the point source in the sea-bed and the point source in the water. Exact results are produced in both the frequency and time domains. The presence of shear waves in the sea-bed is incorporated into the model by using the fluid-solid plane wave reflection and transmission coefficients in the integrands. By approximating the position of the poles of the integrand in the complex plane, it is seen how an evanescent wave component of the source in the sea-bed can excite a propagating mode in the water. This has implications on the dependence of the acoustic field with the depth that the source is buried, since the modes excited by evanescent wave components become weaker as the source is buried deeper, while the modes excited by propagating plane wave components stay strong. This effect was observed in the frequency domain numerical results.