


 Fast algorithms for elasticwavemode separation and vector decomposition using lowrank approximation for anisotropic media  

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We have developed two fast algorithms for wave mode separation and vector decomposition for heterogeneous TI media.
They are based on the lowrank approximation of the spacewavenumberdomain operators, and reduces the
cost to that of a small number of FFT operations per time step, corresponding to the approximation rank times
the number of components. Synthetic examples show that our approach have high accuracy and efficiency.
In general TI media, the rank increases when the models become complex but is always far smallar than the model size.
For the 3D elastic wave mode separation and decomposition in heterogeneous TI media, however,
constructing the separated representations of the
mixeddomain operator matrixes is still time consuming due to the substantial increase of the model size.
Parallelizing the algorithm for this procedure may provide a practical solution.
The key concepts of mode separation and vector decomposition are based on polarizations. Unlike the wellbehaved
Pwave mode, the Swave modes do not consistently polarize as a function of the propagation direction,
and thus can not be designated as SV and SH waves, except in isotropic and TI media. For a 3D TI medium,
the effects of kiss singularity are mitigated by using the mutual orthogonality among the qP, qSV and SH modes.
This procedure only ensures that the two Smodes are accurately separated in kinematics.
It is a challenge to find the right solution of the singularity problem and obtain completely separated
two Smodes with correct amplitudes.



 Fast algorithms for elasticwavemode separation and vector decomposition using lowrank approximation for anisotropic media  

Next: Acknowledgments
Up: Cheng & Fomel: Anisotropic
Previous: BP 2007 TTI model
20140624