Approximate results if Thomsen parameters have small values

Using the definitions of the Thomsen parameters, we can also rewrite the terms appearing in (27) in order to make connection with this related point of view. Recalling (5) and the fact that b = a - 2m, we have

$$\begin{eqnarray} {{a+b-c}\over{f}} \simeq 1 + {{3}\over{c-2l}}(c\delta + 4l\gamma) + {{4}\over{c-2l}}\left[c(\epsilon - \delta) - 4l\gamma\right], \end{eqnarray}$$ (28)

with some higher order corrections involving powers of $\delta$and products of $\delta$ with $\epsilon$ and $\gamma$ that we neglected in this equation. We have added and subtracted equally some terms proportional to $\delta$, and others proportional to $\gamma$, in order to emphasize the similarities between the form (28) and that found previously in (27). In particular, the difference $\epsilon - \delta$ is known (Postma, 1955; Berryman, 1979) to be non-negative and its deviations from zero depend on fluctuations in $\mu$ from layer to layer, behavior similar to that of the final term in (27). Since the formula (28) is only approximate and its interpretation requires the use of various other results we derive subsequently for other purposes, for now we will delay further discussion of this to a point later in the paper. [See the discussion of Eq. (62).]