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In this paper, we consider a long-wave equivalent medium to a finelyparallel-layered inhomogeneous medium, obtained using the Backus average.Following the work of Postma and Backus, we show explicitly the derivations ofthe conditions to obtain the equivalent isotropic medium. We demonstrate thatthere cannot exist a transversely isotropic (TI) equivalent medium with thecoefficients $c^{\overline{\rm TI}}_{1212} \neq c^{\overline{\rm TI}}_{2323}$,$c^{\overline{\rm TI}}_{1111} = c^{\overline{\rm TI}}_{3333}$ and$c^{\overline{\rm TI}}_{1122} = c^{\overline{\rm TI}}_{1133}$. Moreover, weconsider a new parameter, $\varphi$, indicating the anisotropy of theequivalent medium, and we show its range and properties. Subsequently, wecompare $\varphi$ to the Thomsen parameters, emphasizing its usefulness as asupportive parameter showing the anisotropy of the equivalent medium or as analternative parameter to $\delta$. We argue with certain Berryman et al.considerations regarding the properties of the anisotropy parameters $\epsilon$and $\delta$. Additionally, we show an alternative way---to the one mentionedby Berryman et al.---of indicating changing fluid content in layered Earth.

On conditions for long-wave equivalent medium to be isotropic and on analysis of parameters indicating anisotropy of equivalent TI medium