Wavefield separation in anisotropic media (and why it's not what you expect)
, by Joe Dellinger
The divergence and curl operatiors are commonly used to separate P and S
waves in two-dimensional isotropic media (Clayton, 1981). In the Fourier
domain a wavefield is viewed as a sum of plane wave components. In this
domain the divergence and curl operatiors separate P and S waves by their
orthogonal particle motion directions on each plan wave.
In generalizing this simple scheme to three dimensions, a complication
arises even for the isotropic case. It is not enough merely to identify
three wavetypes at each (k-subscript x, k-subscript y, k-subscript x);
three global modes must be identified for the Fourier-domain as a whole.
Ideally each mode should be continuous and well behaved everywhere.
Unfortunately, in three dimensions a mode cannot exhibit quasi-S motion
everywhere and still be continuous.
A more confusing problem, mode-mode coupling, occurs with certain ani-
sotropic media. For isotropic or tansversely isotropic media, three modes
can always be picked out (usually called quasi-P, quasi-SV, and SH). One
might expect that slight perturbations away from transverse isotropy to
orthorhombic symmetry should always leave these three modes identifiable.
Instead, the three original modes can exchange fragments and pull apart
from each other. This creates new continuous distinct modes that appear
to be patched together out of the fragments of the orginal quasi-P, quasi-
SV, and SH modes. This phenomena can create new arrivals in the impulse
response of the orthorhomic medium with no cournterpart in the unperturbed
transversely isotropic medium (Crampin, 1981).
STANFORD