Small frequency approximation of (causal) dissipative pressure waves
This provides a theoretical justification for using noncausal approximations in wave propagation models, but the result is incremental and specific to a particular causal wave model.
The paper shows that the Green function of a causal dissipative pressure wave model can be approximated by a noncausal Green function with frequencies limited to a small range, with the approximation error being small in the L2 sense.
In this paper we discuss the problem of small frequency approximation of the causal dissipative pressure wave model proposed in \cite{KoScBo:11}. We show that for appropriate situations the Green function $G^c$ of the causal wave model can be approximated by a noncausal Green function $G_M^{pl}$ that has frequencies only in the small frequency range $[-M,M]$ ($M\leq 1/τ_0$, $τ_0$ relaxation time) and obeys a power law. For such cases, the noncausal wave $G^{pl}_M$ contains partial waves propagating arbitrarily fast but the sum of the noncausal waves is small in the $L^2-$sense.