  Multiple vertical fracture sets, possibly combined with horizontal fine
layering, produce an equivalent medium of monoclinic symmetry with a horizontal
symmetry plane. Here, we show that multi component wide azimuth reflection data
(combined with known vertical velocity or reflector depth) or multi-azimuth
walkaway $VSP$ surveys provide enough information to invert for all but one
anisotropic parameters of monoclinic media. To facilitate the inversion
procedure, we introduce a Thomsen style parametrization that includes the
vertical velocities of the $P$-wave and one of the split $S$ waves and a set of
dimensionless anisotropic coefficients. This notation captures the combinations
of the stiffnesses responsible for the normal moveout $(NMO)$ ellipses of all
three pure modes. Our parameter-estimation algorithm, based on NMO equations
valid for any strength of the anisotropy, is designed to obtain anisotropic
parameters of monoclinic media by inverting the vertical velocities and NMO
ellipses of the waves $P$, S$_1$ and S$_2$. A Dix type representation of the
NMO velocity of mode-converted waves makes it possible to replace the pure
shear modes in reflection surveys with the waves PS$_1$ and PS$_2$. Numerical
tests show that our method yields stable estimates of all relevant parameters
for both a single layer and a horizontally stratified monoclinic medium.
