We have developed the theory and synthetic tests of elastic least-squares reverse time migration (ELSRTM). In this method, a least-squares reverse time migration algorithm is used to image multicomponent seismic data based on the first-order elastic velocity-stress wave equation, in which the linearized elastic modeling equations are used for forward modeling and its adjoint equations are derived based on the adjoint-state method for back propagating the data residuals. Also, we have developed another ELSRTM scheme based on the wavefield separation technique, in which the P-wave image is obtained using P-wave forward and adjoint wavefields and the S-wave image is obtained using P-wave forward and S-wave adjoint wavefields. In this way, the crosstalk artifacts can be minimized to a significant extent. In general, seismic data inevitably contain noise. We apply the hybrid [ ] misfit function to the ELSRTM algorithm to improve the robustness of our ELSRTM to noise. Numerical tests on synthetic data reveal that our ELSRTM, when compared with elastic reverse time migration, can produce images with higher spatial resolution, more-balanced amplitudes, and fewer artifacts. Moreover, the hybrid [ ] misfit function makes the ELSRTM more robust than the [ ] misfit function in the presence of noise.

In this paper, we present a frequency-wavenumber domain scheme to separate P- and S-waves from multi-component seismic data at the free surface. Based on the relationship between the P- and S-wave separated elastic equation, and the divergence and curl operators, we modify the equation to make it applicable to surface seismic data. In the modified equation, the P-wavenumber is chosen to reject the P-waves, and the S-wavenumber is chosen to eliminate the S-waves. The changes in the P-S amplitude ratio caused by the wavenumber choice are corrected. For the free surface condition, an up-going wavefield separation filter is introduced into the modified equation, which can remove the free surface effects from the surface seismic data. In the case of a free surface exhibiting lateral heterogeneity, the seismic data are first transformed into the frequency domain using the fast Fourier transform (FFT), and then are transformed into the wavenumber domain using the discrete Fourier transform (DFT). In the second transform using the DFT, the modified equation is used to separate the P- and S-waves. Numerical tests on synthetic data for three models demonstrate the good performance and accuracy of the scheme.

Full-waveform inversion (FWI) has the potential to obtain an accurate velocity model. Nevertheless, it depends strongly on the low-frequency data and the initial model. When the starting model is far from the real model, FWI tends to converge to a local minimum. Based on a scale separation of the model (into the background model and reflectivity model), reflection waveform inversion (RWI) can separate out the tomography term in the conventional FWI kernel and invert for the long-wavelength components of the velocity model by smearing the reflected wave residuals along the transmission (or “rabbit-ear”) paths. We have developed a new elastic RWI method to build the P- and S-wave velocity macromodels. Our method exploits a traveltime-based misfit function to highlight the contribution of tomography terms in the sensitivity kernels and a sensitivity kernel decomposition scheme based on the P- and S-wave separation to suppress the high-wavenumber artifacts caused by the crosstalk of different wave modes. Numerical examples reveal that the gradients of the background models become sufficiently smooth owing to the decomposition of sensitivity kernels and the traveltime-based misfit function. We implement our elastic RWI in an alternating way. At each loop, the reflectivity model is generated by elastic least-squares reverse time migration, and then the background model is updated using the separated traveltime kernels. Our RWI method has been successfully applied in synthetic and real reflection seismic data. Inversion results demonstrate that the proposed method can retrieve preferable low-wavenumber components of the P- and S-wave velocity models, which are reliable to serve as a starting model for conventional elastic FWI. Also, our method with a two-stage inversion workflow, first updating the P-wave velocity using the PP kernels and then updating the S-wave velocity using the PS kernels, is feasible and robust even when P- and S-wave velocities have different structures.

Elastic least-squares reverse time migration (ELSRTM) has the potential to provide improved subsurface reflectivity estimation. Compared with the elastic reverse time migration (ERTM), ELSRTM can produce images with higher spatial resolution, more balanced amplitudes and fewer artifacts. However, the crosstalk between compressional (P-) and shear (S-) waves can significantly degrade the imaging quality of ELSRTM. We developed an ELSRTM method to suppress the crosstalk artifacts. This method includes three crucial points. The first is that both the forward and backward wavefield are extrapolated based on the separated elastic velocity-stress equation of P- and S-waves. The second is that the separated vector P- and S-wave residuals are migrated to form reflectivity images of Lamé constants λ and μ independently. The third is that the reflectivity images of λ and μ are obtained by the vector P-wave wavefields achieved in the backward extrapolation of the separated vector P-wave residuals and the vector S-wave wavefields achieved in the backward extrapolation of the separated vector S-wave residuals respectively. Numerical tests with synthetic data demonstrate that our ELSRTM method can produce images free of the crosstalk artifacts. Compared with ELSRTM based on the coupled wavefields, our ELSRTM method has better convergence and higher accuracy.

Exploration Geophysics is published by CSIRO PUBLISHING on behalf of the Australian Society of Exploration Geophysicists. Papers published report the results of significant case histories and relevant original research in geophysics, with emphasis on the Australian and similar environments.