We consider a long-wave transversely isotropic (TI) medium equivalent to a series 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 authors method citep{Adamus}, using anisotropy parameter $varphi$. Both methods are based on detecting variations of the Lame parameter, $lambda$, in a series of thin isotropic layers, and we treat these variations as potential change of the fluid content. To verify these methods, we use Monte Carlo (MC) simulations; for certain range of Lame parameters $lambda$ and $mu$---relevant to particular type of rocks---we generate numerous combinations of these parameters in thin layers and, after the averaging process, we obtain their TI media counterparts. Subsequently, for each of the aforementioned media, we compute $varphi$ and citet{Thomsen} parameters $epsilon$ and $delta$. We exhibit $varphi$, $epsilon$ and $delta$ in a form of cross-plots and distributions that are relevant to chosen range of $lambda$ and $mu$. We repeat that process for various ranges of Lame parameters. Additionally, to support the MC simulations, we consider several numerical examples of growing $lambda$, by using scale factors. As a result of the thorough analysis of the relations among $varphi$, $epsilon$ and $delta$, we find eleven fluid detectors that compose a new fluid detection method. Based on these detectors, we show the quantified pattern of indicating change of the fluid content.
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