Elastic wave-vector decomposition in heterogeneous anisotropic media |

Alternatively to solving the Christoffel equation numerically for exact values of polarizations, one may choose to use an analytical approximation in weakly anisotropic media derived from perturbation theory (Farra and Pšencík, 2003). This choice may lead to increased computational efficiency in complex models.

Generally, the knowledge of polarization vectors and their applicability are based on the underlying assumption in which the medium is assumed to be locally homogeneous relative to the propagating frequency of the waves. In the case of a larger degree of heterogeneity such as strong contrasts and considerable velocity gradients, this assumption is approximate and may need special care.

To implement wave-vector decomposition, the proposed method uses the low-rank approximations for the decomposition operator (equation 12). This allows us to avoid explicitly computing and storing the polarizations of the mode of interest at every grid point, which would be prohibitively expensive. The proposed method is appropriate for decomposing the elastic wavefields during the backward propagation step in elastic reverse-time migration (RTM) (Wang et al., 2016) and full-waveform inversion (FWI) (Wang et al., 2015). We did not consider the problem of separating wave modes in recorded surface seismic data.

Elastic wave-vector decomposition in heterogeneous anisotropic media |

2017-04-18