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We consider a long-wave transversely isotropic (TI) medium equivalent to aseries of finely parallel-layered isotropic layers, obtained using the\citet{Backus} average. In such a TI equivalent medium, we verify the\citet{Berrymanetal} method of indicating fluids and the author's method\citep{Adamus}, using anisotropy parameter $\varphi$. Both methods are based ondetecting variations of the Lam\'e parameter, $\lambda$, in a series of thinisotropic layers, and we treat these variations as potential change of thefluid content. To verify these methods, we use Monte Carlo (MC) simulations;for certain range of Lam\'e parameters $\lambda$ and $\mu$---relevant toparticular type of rocks---we generate numerous combinations of theseparameters in thin layers and, after the averaging process, we obtain their TImedia counterparts. Subsequently, for each of the aforementioned media, wecompute $\varphi$ and \citet{Thomsen} parameters $\epsilon$ and $\delta$. Weexhibit $\varphi$, $\epsilon$ and $\delta$ in a form of cross-plots anddistributions that are relevant to chosen range of $\lambda$ and $\mu$. Werepeat that process for various ranges of Lam\'e parameters. Additionally, tosupport the MC simulations, we consider several numerical examples of growing$\lambda$, by using scale factors. As a result of the thorough analysis of therelations among $\varphi$, $\epsilon$ and $\delta$, we find eleven fluiddetectors that compose a new fluid detection method. Based on these detectors,we show the quantified pattern of indicating change of the fluid content.

On anisotropy parameters and fluid detection in equivalent TI medium