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I then consider a 2D anisotropic model similar to the previous model
shown in Figures 10(a)-fig:separate3-ro (with
,
representing the vertical P and S wave velocities), and
additionally characterized by the parameters
and
shown in Figures 10(d) and fig:separate3-delta,
respectively. The parameters
and
vary gradually
from top to bottom and left to right, respectively. The upper left
part of the medium is isotropic and the lower right part is highly
anisotropic. Since the difference of
and
is great
at the bottom part of the model, the qS waves in this region are
severely triplicated due to this strong anisotropy.
Figure 12
illustrates the pseudo derivative operators obtained at different
locations in the model defined by the intersections of
coordinates
0.3, 0.6, 0.9 km and
coordinates 0.3, 0.6, 0.9 km. Since the
operators correspond to different combination of the parameters
and
, they have different forms. The isotropic
operator at coordinates
km and
km, shown
in Figure 12(a), is purely vertical and horizontal, while
the anisotropic operators (Figure 12(b)
to fig:separate3-aop22) have ``tails'' radiating from the
center. The operators become larger at locations where the medium is
more anisotropic, for example, at coordinates
km and
km.
Figure 13(a) shows the vertical and horizontal components of
one snapshot of the simulated elastic anisotropic
wavefield, Figure 13(b) shows the separation to qP and
qS modes using conventional isotropic
and
operators,
and Figure 13(c) shows the mode separation obtained using the
pseudo operators constructed using the local medium parameters.
A comparison of Figure 13(b) and 13(c) indicates
that the spatially-varying derivative operators successfully separate
the elastic wavefields into qP and qS modes, while the
and
operators only work in the isotropic region of
the model.
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aoppos,vs,ro,epsilon,delta
Figure 10. A ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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uI-f06,qI-f06,pI-f06
Figure 11. (a) One snapshot of the isotropic wavefield modeled with a vertical point force source at ![]() ![]() ![]() ![]() |
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aop00,aop10,aop20,aop01,aop12,aop21,aop02,aop12,aop22
Figure 12. The ![]() ![]() ![]() ![]() ![]() |
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uA-f06,qA-f06,pA-f06
Figure 13. (a) One snapshot of the anisotropic wavefield modeled with a vertical point force source at ![]() ![]() ![]() ![]() ![]() ![]() |
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![]() | Elastic wave-mode separation for VTI media | ![]() |
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