Ward identities for visco-acoustic and visco-elastic propagation media

This study discusses Ward identities in the presence of viscous dissipation. A Ward identity relates the Green function of the medium to the noise correlation function. Our study is focused on two types of mechanical waves: the scalar (1-component) pressure field, and the 3-component displacement field. Under some realistic (from a practical point of view) low attenuation and far-field assumptions, the first-order time-derivative of the noise correlation is shown not to be proportional to the odd part of the Green function any longer. New algebraic relations are derived in the Fourier domain, and a new form of the Ward identity is obtained that relates the third-order time-derivative of the noise correlation function to the odd part of the Green function. ► We address the problem of passive identification in viscous media. ► The Ward identity is derived for a viscous attenuation model. ► We show that usual Ward identity is not acceptable for the realistic dissipation model. ► Green correlation and Ward identities are given in time/frequency/space domains. ► The expressions in different domains allow us to exhibit physical meaning of the derived expressions.