Simulating propagation of decoupled elastic waves using low-rank approximate mixed-domain integral operators for anisotropic media |

ElasticxKSSInterf,ElasticzKSSInterf
Horizontal and vertical components of the elastic wavefields at the time of 0.3 s synthesized by solving the
2nd-order elastic wave equation with
m and
ms.
Figure 1. |
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ElasticzFDwave,ElasticzPSLRwave,ElasticzKSwave
Vertical slices through the vertical components of the synthetic elastic wavefields at
km: (a) 10th-order FD, (b) low-rank pseudo-spectral and (c) low-rank pseudo-spectral using the
-space adjustment.
Figure 2. |
---|

ElasticzFDInterfC,ElasticzPSLRInterfC,ElasticzKSSInterfC
Vertical components of the elastic wavefields at the time of 0.6 s synthesized using three schemes with the same spatial sampling
m: (a) 10th-order FD and (b) low-rank pseudo-spectral with
ms,
and (c) low-rank pseudo-spectral solution using the
-space adjustment with
ms.
Figure 3. |
---|

ElasticzFDwave,ElasticzPSLRwave,ElasticzKSSwave
Vertical slices through the vertical components at
km in Figure 3: (a) 10th-order FD,
(b) low-rank pseudo-spectral and (c) low-rank pseudo-spectral using the
-space adjustment.
Figure 4. |
---|

Secondly, we compare two approaches to get the decoupled elastic wavefields during time extrapolation. The first approach uses the low-rank pseudo-spectral algorithm to synthesize the elastic wavefields and then apply the low-rank vector decomposition algorithm (Cheng and Fomel, 2014) to get the vector qP- and qSV-wave fields (Figure 5). The second extrapolates the decoupled qP- and qSV-wave fields using the proposed low-rank mixed-domain integral operations (Figure 6). Extrapolation steps of m and ms are used in this example. The ranks are still for the involved low-rank decomposition of the propagation matrices defined in equation 20. The Two approaches produce comparable elastic wavefields, in which we can observe all transmitted and reflected waves including mode conversions. For one step of time extrapolation, it takes the CPU time of 0.6 ms for the first approach and 0.5 ms for the second. This means that merging time extrapolation and vector decomposition into a unified Fourier integral framework provides more efficient solution than operating them in sequence for anisotropic media thanks to the reduced number of forward and inverse FFTs.

ElasticxPSLR1Interf,ElasticzPSLR1Interf,ElasticPxPSLR1Interf,ElasticPzPSLR1Interf,ElasticSxPSLR1Interf,ElasticSzPSLR1Interf
Elastic wavefields at the time of 0.6 s synthesized by using low-rank pseudo-spectral solution of the displacement
wave equation followed with low-rank vector decomposition:
(a) x- and (b) z-components of the displacement wavefields;
(c) x- and (d) z-components of the qP-wave fields;
(e) x- and (f) z-components of the qSV-wave fields.
Figure 5. |
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ElasticPxPSLRInterf,ElasticPzPSLRInterf,ElasticSxPSLRInterf,ElasticSzPSLRInterf,ElasticxPSLRInterf,ElasticzPSLRInterf
Elastic wavefields at the time of 0.6 s synthesized by using low-rank pseudo-spectral operators
for extrapolating and decomposing the elastic waves simultaneously:
(a) x- and (b) z-components of the qP-wave displacement wavefields;
(c) x- and (d) z-components of the qSV-wave displacement wavefields;
(e) x- and (f) z-components of the total elastic wavefields.
Figure 6. |
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Simulating propagation of decoupled elastic waves using low-rank approximate mixed-domain integral operators for anisotropic media |

2016-11-21