Fast algorithms for elastic-wave-mode separation and vector decomposition using low-rank approximation for anisotropic media |

For comparison, we only change the second layer to a TTI medium with a tilt angle and azimuth (other paramters continue to use). Figure 6 displays the corresponding elastic wavefields and their mode separation results. It took 4087.8, 4280.8 and 206.2 seconds to construct the separated forms of the mode separation matrixes for qP-, qSV- and SH-waves, respectively. For one time step, it took 101.0 seconds to extrapolate the elastic wavefield, and 15.2 and 15.8 seconds to separate qP- and qSV-wave modes with the rank . It took 14.1 seconds to separate SH-wave with the rank . As we observed, the most time-consuming task here is to construct the separated forms of the mode separation matrixes. More CPU time is required to separate SH-wave in 3D TTI media as well.

Polxp1,Polzp1,Polxp2,Polzp2,Errpolxp1,Errpolzp1,Errpolxp2,Errpolzp2
Low-rank approximate mode separators of qP-wave in a 2D two-layer TI model:
(a)
and (b)
constructed by using low-rank decomposition in the VTI layer;
(c)
and (d)
constructed by using low-rank decomposition in the TTI layer;
(e), (f), (g) and (h) represent the low-rank approximation errors of these operators.
According to the qP-qSV mode polarization orthogonality, we have the following relations:
and
. Therefore, the above pictures also
demonstrate the low-rank approximate separators and their errors for qSV-wave.
Figure 1. |
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ElasticxInterf,ElasticzInterf,ElasticSepPInterf,ElasticSepSVInterf
Elastic wave mode separation in the two-layer TI model:
(a) x- and (b) z-components of the synthetic elastic displacement wavefields synthesized at 0.3s;
(c) and (d) are the separated scalar qP- and qSV-wave fields using low-rank approximation.
Figure 2. |
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Decompxp1,Decompzp1,Decompxzp1,Errdecxp1,Errdeczp1,Errdecxzp1,Decompxp2,Decompzp2,Decompxzp2,Errdecxp2,Errdeczp2,Errdecxzp2
Low-rank approximate vector decomposition operators of qP-wave in the 2D two-layer TI model:
(a)
,
(b)
,
and (c)
,
and (e), (f) and (g) represent their low-rank approximation errors in the VTI layer.
(h), (i), (j), (k), (l) and (m) are these operators and their low-rank approximation errors in the TTI layer.
Figure 3. |
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ElasticPxInterf,ElasticPzInterf,ElasticSVxInterf,ElasticSVzInterf
Elastic wave vector decomposition in the two-layer VTI/VTI model:
(a) x- and (b) z-components of vector qP-wave fields;
(c) x- and (d) z-components of vector qSV-wave fields.
Figure 4. |
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ElasticxInterf,ElasticyInterf,ElasticzInterf,ElasticPInterf,ElasticSVInterf,ElasticSHInterf
Elastic wave mode separation in the 3D two-layer VTI model:
(a) x-, (b) y- and (c) z-components of the synthetic elastic displacement wavefields synthesized at 0.17s;
(d) qP-, (e) qSV- and (e) SH-wave fields separated from the elastic wavefields.
Figure 5. |
---|

ElasticxInterf,ElasticyInterf,ElasticzInterf,ElasticPInterf,ElasticSVInterf,ElasticSHInterf
Elastic wave mode separation in the 3D two-layer VTI/TTI model:
(a) x-, (b) y- and (c) z-components of the synthetic elastic displacement wavefields synthesized at 0.17s;
(d) qP-, (e) qSV- and (e) SH-wave fields separated from the elastic wavefields.
Figure 6. |
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Fast algorithms for elastic-wave-mode separation and vector decomposition using low-rank approximation for anisotropic media |

2014-06-24