Xy. Li et al., INTERPRETING NONORTHOGONAL SPLIT SHEAR-WAVES FOR SEISMIC ANISOTROPY IN MULTICOMPONENT VSPS, Geophysical prospecting, 46(1), 1998, pp. 1-27
There are two main sources of non-orthogonality in multicomponent shea
r-wave seismics: inherent non-orthogonal split shear waves arising fro
m substantial ray deviation in off-symmetry planes due to strong aniso
tropy or complex overburden, and apparent non-orthogonal split shear w
aves in the horizontal plane due to variation of the angle of incidenc
e even if the two shear waves along the raypath are orthogonal. Many t
echniques for processing shear-wave splitting in VSP data ignore these
kinds of non-orthogonality of the split shear waves. Assuming inheren
t non-orthogonality in zero-offset VSPs, and apparent nonorthogonality
in offset VSPs, we derive equations for the four-component data matri
x. These can be solved by extending the linear-transform technique (LT
T) to determine the shear-wave polarizations in zero-offset and offset
VSPs. Both full-wave synthetic and field data are used to evaluate th
e technique and to examine the effects of non-orthogonal polarized spl
it shear waves. If orthogonality is incorrectly assumed, errors in pol
arization measurements increase with the degree of non-orthogonality,
which introduces a consistent decreasing trend in the polarization mea
surements. However, the effect of non-orthogonality on the estimation
of geophone orientation and time delays of the two split shear waves i
s small and negligible in most realistic cases. Furthermore, for most
cases of weak anisotropy (less than 5% shear-wave anisotropy) apparent
non-orthogonality is more significant than inherent non-orthogonality
. Nevertheless, for strong anisotropy (more than 10% shear-wave anisot
ropy) with complicated structure (tilted or inclined symmetry axis), i
nherent non-orthogonality may no longer be negligible. Applications to
both synthetic and real data show that the extended linear-transform
techniques permit accurate recovery of polarization measurements in th
e presence of both significant inherent and apparent non-orthogonality
where orthogonal techniques often fail.