Wavefield Separation for Frequency-domain Elastic Reverse-time Migration Using Finite-element Method

To obtain P- or S-wave reflection images via reverse-time migration (RTM) for elastic media, a wavefield-separation method is required. One of the methods for wavefield separation is using the Helmholtz decomposition. The application of the Helmholtz decomposition can be different according to numerical algorithm used for RTM. In this study, we show how to separate wavefields based on the Helmholtz decomposition when we use the finite-element method (FEM) and the frequency-domain full waveform inversion (FWI) algorithm for RTM. As RTM image corresponds to the first gradient image of FWI, we can generate RTM images by back-propagating wavefields recorded at the surface rather than residual in the frequency-domain FWI algorithm. In the RTM algorithm based on the FWI and FEM, the Helmholtz decomposition cannot be applied in each element. Instead, we first compose a global matrix of virtual source for all the nodal points by assembling virtual sources for each element, and then apply the wavefield separation technique. We apply our RTM algorithm to the Hess model. While we obtain clear PP reflection image, SS reflection image shows some artifacts caused by unwanted interferences between wave modes. Our RTM algorithm can be used to compare reflection images according to parameterizations.