Emergence of the coherent reflected field for a single realisation of spherical scatterer locations in a solid matrix

The acoustic field reflected from a region containing spherical scatterers is most often estimated by use of the coherent field; that is, the field resulting from the summed scattered fields from the scatterers, averaged over all possible configurations of scatterer locations. It is this ensemble-averaged coherent field which is equivalent to the field reflected from a homogeneous medium with properties which can be derived mathematically using ensemble-averaging techniques. Such properties include the effective density, and the effective wavenumber, which can be derived from multiple scattering theories, or by other homogenisation methods. Experimentally, although ensemble-averaging can be effected in practice in fluid systems due to the motion of the scatterers during the measurement time-scale, measurements in solid materials have fixed locations of scatterers. Averaging can only be achieved by using "large" sample areas, multiple samples or measurements in different locations, or "large" receiver areas. However, in the context of NDE applications we are interested in the field resulting from a specific region of material, rather than the average over a large region. Our study addresses the question of when the coherent field (resulting from averaging over many scatterer configurations) can be used as an accurate description of the field reflected by a region of scatterers at fixed locations. In this paper we present results of simulations of the scattered reflected field from a region of solid material containing spherical cavities. Simulations of single realisations of scatterer locations are compared with the coherent field, to demonstrate the validity or otherwise of the use of the coherent field to describe the response of a particular configuration of scatterers.