Thomsen's parameter defined by Eq. (3) is pertinent for near vertical quasi-P-waves and can also be rewritten as
Because of a controversy surrounding the sign of for finely layered media (e.g., Levin, 1988; Thomsen, 1988; Anno, 1997), Berryman et al. (1999) performed a series of Monte Carlo simulations with the purpose of establishing the existence or nonexistence of layered models having positive .Those simulation results should be interpreted neither as modeling of natural sedimentation processes nor as an attempt to reconstruct any petrophysical relationships. The main goal was to develop a general picture of the distribution of the sign of using many choices of constituent material properties. This analysis established a similarity in the circumstances between the occurrence of positive and the occurrence of small positive (i.e., both occur when Lamé is fluctuating greatly from layer to layer). The positive values of are in fact most highly correlated with the smaller positive values of . We should also keep in mind the fact that is always true for models with isotropic layers (Postma, 1955; Berryman, 1979) and this fact also plays a role in these comparisons, determining the unoccupied upper left hand corner of a vs. plot.