Diffuse fields in open systems and the emergence of the Green’s function (L)

As is now well known, the relation between diffuse field correlations and the Green’s function follows directly from a definition of a diffuse field as an uncorrelated smooth spectral superposition of normal modes. Such a definition is, however, inapplicable in most open structures, the earth in particular. A preferable definition might be that of room acoustics: a diffuse field is an uncorrelated isotropic superposition of plane waves. But that definition is inapplicable to heterogeneous structures, or near boundaries. Here, a definition of a local diffuse field applicable to open heterogeneous systems is proposed. A local diffuse field is taken to be one in steady‐state equilibrium with the field in a homogeneous region having an uncorrelated isotropic superposition of incident plane waves. This definition is applicable to both heterogeneous and open systems, and is shown using a reciprocity argument to lead to the familiar identity between the local Green’s function of the structure and the diffuse fields correlations.

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