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3D two-layer VTI model

Figure 4 shows an example of simulating the propagation of pseudo-pure-mode qSV-wave fields in a 3D two-layer VTI model (see Figure 4a), with $ v_{p0}=2500 m/s$ , $ v_{s0}=1200 m/s$ , $ \epsilon =0.25$ , $ \delta=-0.25$ and $ \gamma=0.3$ in the first layer, and $ v_{p0}=3600 m/s$ , $ v_{s0}=1800 m/s$ , $ \epsilon=0.2$ , $ \delta=0.1$ and $ \gamma=0.05$ in the second layer. We propagate the 3D pseudo-pure-mode qSV-wave fields using equation 28. Figure 4d displays the pseudo-pure-mode scalar qSV-wave fields resulting from the summation of the horizontal (Figure 4b) and vertical (Figure 4c) components, namely $ \overline {u}_{xy}$ and $ \overline {u}_z$ . We see that the qS-waves dominate the scalar wavefields in energy. As shown in Figure 5, we also obtain pure-mode scalar SH-wave fields either using the summation of the horizontal components synthesized by using the pseudo-pure-mode wave equation 17 or directly using the scalar wave equation, i.e., equation 18.

vp0Interf PseudoPureSVxyInterf PseudoPureSVzInterf PseudoPureSVInterf
vp0Interf,PseudoPureSVxyInterf,PseudoPureSVzInterf,PseudoPureSVInterf
Figure 4.
Synthesized wavefield snapshots in a 3D two-layer VTI model using equation 28 : (a) vertical velocity of qSV-wave, (b) horizontal component $ \overline {u}_{xy}$ and (c) vertical component $ \overline {u}_z$ of the pseudo-pure-mode qSV-wave fields, (d) pseudo-pure-mode scalar qSV-wave fields. The dash line indicates the interface.
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SHxInterf SHyInterf SHInterf
SHxInterf,SHyInterf,SHInterf
Figure 5.
Synthesized wavefield snapshots in a 3D two-layer VTI model using equation 17: (a) x- and (b) y-components of the pseudo-pure-mode wavefields, (c) pure-mode scalar SH-wave fields calculated as the summation of the two horizontal components of the pseudo-pure-mode wavefields. Note that the same scalar wavefields are obtained if we directly use the scalar wave equation for SH-waves, namely equation 18.
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Next: BP 2007 TTI model Up: EXAMPLES Previous: 2D homogeneous VTI models

2016-10-14