  Anderson localization of $p$-polarized waves and the Brewster anomaly
phenomenon, which is the delocalization of $p$-polarized waves at a special
incident angle, in randomly-stratified anisotropic media are studied
theoretically for two different random models. In the first model, the random
parts of the transverse and longitudinal components of the dielectric tensor,
between which the longitudinal component is the one in the stratification
direction, are assumed to be uncorrelated, while, in the second model, they are
proportional to each other. We calculate the localization length in a precise
way using the invariant imbedding method. From analytical considerations, we
provide an interpretation of the Brewster anomaly as a phenomenon arising when
the wave impedance is effectively uniform. Similarly, the ordinary Brewster
effect is interpreted as an impedance matching phenomenon. We derive the
existence condition for the Brewster anomaly and concise analytical expressions
for the localization length, which are accurate in the weak disorder regime. We
find that the Brewster anomaly can arise only when disorder is sufficiently
weak and only in the second model with a positive ratio of the random parts.
The incident angle at which the anomaly occurs depends sensitively on the ratio
of the random parts and the average values of the tensor components. In the
cases where the critical angle of total reflection exists, the angle at which
the anomaly occurs can be either bigger or smaller than the critical angle.
When the transverse and longitudinal components are uncorrelated, localization
is dominated by the the transverse component at small incident angles. When
only the longitudinal component is random, the localization length diverges as
$\theta^{-4}$ as the incident angle $\theta$ goes to zero and is also argued to
diverge for all $\theta$ in the strong disorder limit.
