Thomsen's parameter defined by Eq. (3)
is pertinent for near vertical quasi-*P*-waves and can also be rewritten as

(25) |

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.

The analysis of Berryman *et al.* (1999)
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 layered models and this fact also plays a role in these comparisons,
determining the unoccupied upper left hand corner of a vs.
plot.

10/16/2003