Time-domain reciprocity theorems for acoustic wave fields in fluids with relaxation

Time-domain reciprocity theorems of the time-convolution and the time-correlation type for acoustic wave fields in linear, time-invariant, and locally reacting fluids are discussed. Inhomogeneity, inertial anisotropy, and arbitrary relaxation effects in inertia and compressibility properties, both of the active and the passive type, are included. The theorems also apply to the ‘‘equivalent fluid model’’ of a solid in which only compressional waves are considered and shear is neglected. The analysis is entirely carried out in space-time, without intermediate recourse to the frequency or the wave vector domains. The application to inverse source and inverse constituency (or inverse profiling/scattering, or imaging) problems is briefly indicated.