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

For isotropic media, the Helmholtz equations for the P-wave are transformed into the wavenumber-domain as,

From these equations, the vector decomposition equation of the separated P-wave is given by:

where represents the normalized wave vector.

In a TI medium, equation 8 is extended to separate and decompose qP-wave by substituting for ,

Similar equations

and

are proposed to decompose qSV and SH waves using their respective polarization vectors. Note that vector decomposition satisfies the linear superposition relation , and the separated wavefields are orthogonal to one another and have the same amplitude, phase, and physical units as the input wavefields.

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

2014-06-24