Yunyue Elita Li has joined the Department of Civil and Environmental Engineering at the National University of Singapore as an Assistant Professor in 2016. She did her Postdoctoral Research at Massachusetts Institute of Technology, holding a joint position in the Earth Resources Laboratory and the Department of Mathematics. She has received her PhD and MS degrees in Geophysics from Stanford University in 2014 and 2010, respectively. She has obtained her BS degree (Highest Honors) in Information and Computational Science from China University of Petroleum, Beijing in 2008.
Elastic wave imaging has been a significant challenge in the exploration industry due to the complexities in wave physics and in numerical implementation. In this paper, we derive the elastic wave equations without the assumptions of homogeneous Lame parameters to capture the mode conversion between the P- and S-waves in an isotropic, constant-density medium. The resulting set of two coupled second-order equations for P- and S-potentials clearly demonstrates that mode conversion only occurs at the discontinuities of the shear modulus. Applying Born approximation to the new equations, we derive PP and PS imaging conditions as the first gradients of waveform matching objective functions. The resulting images are consistent with the perturbations of the elastic parameters and hence are automatically free of the polarity reversal artifacts in the converted images. When implementing reverse time migration (RTM), we show that scalar wave equations can be to back propagate the recorded P-potential, as well as individual components in the vector field of the S-potential. Compared with conventional elastic RTM, the proposed elastic RTM implementation using acoustic propagators not only simplifies the imaging condition, but also reduces the computational cost. We demonstrate the accuracy of the proposed method using both 2D and 3D numerical examples.